Search: square of difference

Question Medium Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 62

अनुक्रम \(5,12,19,26,\ldots\) में पहले दो पदों का अंतर और तीसरे-चौथे पदों का अंतर क्या है?

In \(5,12,19,26,\ldots\), what are the difference of the first two terms and the difference of the third and fourth terms?

Explanation opens after your attempt

Correct Answer

A. (7) और (7)(7) and (7)

Step 1

Concept

The first difference is (12-5=7), and the second is (26-19=7). Equal differences confirm an arithmetic progression.

Step 2

Why this answer is correct

The correct answer is A. (7) और (7) / (7) and (7). The first difference is (12-5=7), and the second is (26-19=7). Equal differences confirm an arithmetic progression.

Step 3

Exam Tip

पहला अंतर (12-5=7) और दूसरा (26-19=7) है। समान अंतर समांतर श्रेढ़ी की पुष्टि करता है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक वर्गाकार मैदान की भुजा (4) मीटर बढ़ाने पर क्षेत्रफल (96) वर्ग मीटर बढ़ जाता है। मूल भुजा कितनी थी?

When the side of a square field is increased by (4) m, its area increases by (96) square m. What was the original side?

Explanation opens after your attempt

Correct Answer

B. (10) मीटर(10) m

Step 1

Concept

If the original side is (x), then ((x+4)²-x^-2=96). Thus (8x+16=96), giving (x=10).

Step 2

Why this answer is correct

The correct answer is B. (10) मीटर / (10) m. If the original side is (x), then ((x+4)²-x^-2=96). Thus (8x+16=96), giving (x=10).

Step 3

Exam Tip

मूल भुजा (x) हो तो ((x+4)²-x^-2=96)। इससे (8x+16=96) और (x=10) मिलता है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक वर्गाकार मैदान के अंदर समान चौड़ाई (x) मीटर की सीमा छोड़ने के बाद अंदर का वर्ग (60) मीटर भुजा का बचता है। बाहरी भुजा (92) मीटर है। (x) क्या है?

Inside a square field, after leaving a uniform border of width (x) m, the inner square has side (60) m. The outer side is (92) m. What is (x)?

Explanation opens after your attempt

Correct Answer

C. (16) मीटर(16) m

Step 1

Concept

The inner side is (92-2x) and (92-2x=60), so (x=16). The border is subtracted from both sides.

Step 2

Why this answer is correct

The correct answer is C. (16) मीटर / (16) m. The inner side is (92-2x) and (92-2x=60), so (x=16). The border is subtracted from both sides.

Step 3

Exam Tip

अंदर की भुजा (92-2x) है और (92-2x=60), इसलिए (x=16) है। सीमा दोनों तरफ से घटती है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक तार को वर्ग के रूप में मोड़ने पर क्षेत्रफल (3025) वर्ग सेमी है। तार की लंबाई क्या है?

A wire is bent into a square and the area is (3025) square cm. What is the length of the wire?

Explanation opens after your attempt

Correct Answer

C. (220) सेमी(220) cm

Step 1

Concept

If the side of the square is (x), then \(x^2=3025\), so (x=55). The wire length is the perimeter (4x=220) cm.

Step 2

Why this answer is correct

The correct answer is C. (220) सेमी / (220) cm. If the side of the square is (x), then \(x^2=3025\), so (x=55). The wire length is the perimeter (4x=220) cm.

Step 3

Exam Tip

वर्ग की भुजा (x) हो तो \(x^2=3025\), इसलिए (x=55) है। तार की लंबाई परिमाप (4x=220) सेमी होगी।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक वर्ग की भुजा (x) सेमी है। भुजा (9) सेमी घटाने पर क्षेत्रफल (1681) वर्ग सेमी हो जाता है। मूल भुजा क्या है?

The side of a square is (x) cm. When the side is reduced by (9) cm, the area becomes (1681) square cm. What is the original side?

Explanation opens after your attempt

Correct Answer

C. (50) सेमी(50) cm

Step 1

Concept

((x-9)²=1681) gives (x-9=41), so (x=50). Write the reduced side as (x-9).

Step 2

Why this answer is correct

The correct answer is C. (50) सेमी / (50) cm. ((x-9)²=1681) gives (x-9=41), so (x=50). Write the reduced side as (x-9).

Step 3

Exam Tip

((x-9)²=1681) से (x-9=41), इसलिए (x=50) है। घटाई गई भुजा को (x-9) लिखें।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक वर्गाकार टाइल की भुजा (x-12) सेमी है और क्षेत्रफल (1849) वर्ग सेमी है। (x) क्या है?

The side of a square tile is (x-12) cm and its area is (1849) square cm. What is (x)?

Explanation opens after your attempt

Correct Answer

C. (55)

Step 1

Concept

((x-12)²=1849) and (x-12=43), so (x=55). Remember that the side must be positive.

Step 2

Why this answer is correct

The correct answer is C. (55). ((x-12)²=1849) and (x-12=43), so (x=55). Remember that the side must be positive.

Step 3

Exam Tip

((x-12)²=1849) और (x-12=43), इसलिए (x=55) है। भुजा धनात्मक होने की शर्त याद रखें।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक वर्ग की भुजा (x+17) सेमी है। उसका क्षेत्रफल (3249) वर्ग सेमी है। (x) का मान क्या है?

The side of a square is (x+17) cm. Its area is (3249) square cm. What is the value of (x)?

Explanation opens after your attempt

Correct Answer

C. (40)

Step 1

Concept

((x+17)²=3249) gives (x+17=57), so (x=40). Take the positive square root for length.

Step 2

Why this answer is correct

The correct answer is C. (40). ((x+17)²=3249) gives (x+17=57), so (x=40). Take the positive square root for length.

Step 3

Exam Tip

((x+17)²=3249) से (x+17=57), इसलिए (x=40) है। लंबाई के लिए धनात्मक वर्गमूल लें।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक वर्गाकार मैदान के अंदर समान चौड़ाई (x) मीटर की सीमा छोड़ने के बाद अंदर का वर्ग (44) मीटर भुजा का बचता है। बाहरी भुजा (68) मीटर है। (x) क्या है?

Inside a square field, after leaving a uniform border of width (x) m, the inner square has side (44) m. The outer side is (68) m. What is (x)?

Explanation opens after your attempt

Correct Answer

C. (12) मीटर(12) m

Step 1

Concept

The inner side is (68-2x) and (68-2x=44), so (x=12). The border is subtracted from both sides.

Step 2

Why this answer is correct

The correct answer is C. (12) मीटर / (12) m. The inner side is (68-2x) and (68-2x=44), so (x=12). The border is subtracted from both sides.

Step 3

Exam Tip

अंदर की भुजा (68-2x) है और (68-2x=44), इसलिए (x=12) है। सीमा दोनों तरफ से घटती है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक तार को वर्ग के रूप में मोड़ने पर क्षेत्रफल (2025) वर्ग सेमी है। तार की लंबाई क्या है?

A wire is bent into a square and the area is (2025) square cm. What is the length of the wire?

Explanation opens after your attempt

Correct Answer

B. (180) सेमी(180) cm

Step 1

Concept

If the side of the square is (x), then \(x^2=2025\), so (x=45). The wire length is the perimeter (4x=180) cm.

Step 2

Why this answer is correct

The correct answer is B. (180) सेमी / (180) cm. If the side of the square is (x), then \(x^2=2025\), so (x=45). The wire length is the perimeter (4x=180) cm.

Step 3

Exam Tip

वर्ग की भुजा (x) हो तो \(x^2=2025\), इसलिए (x=45) है। तार की लंबाई परिमाप (4x=180) सेमी होगी।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक वर्ग की भुजा (x) सेमी है। भुजा (7) सेमी घटाने पर क्षेत्रफल (1296) वर्ग सेमी हो जाता है। मूल भुजा क्या है?

The side of a square is (x) cm. When the side is reduced by (7) cm, the area becomes (1296) square cm. What is the original side?

Explanation opens after your attempt

Correct Answer

C. (43) सेमी(43) cm

Step 1

Concept

((x-7)²=1296) gives (x-7=36), so (x=43). Write the reduced side as (x-7).

Step 2

Why this answer is correct

The correct answer is C. (43) सेमी / (43) cm. ((x-7)²=1296) gives (x-7=36), so (x=43). Write the reduced side as (x-7).

Step 3

Exam Tip

((x-7)²=1296) से (x-7=36), इसलिए (x=43) है। घटाई गई भुजा को (x-7) लिखें।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक वर्गाकार टाइल की भुजा (x-13) सेमी है और क्षेत्रफल (1600) वर्ग सेमी है। (x) क्या है?

The side of a square tile is (x-13) cm and its area is (1600) square cm. What is (x)?

Explanation opens after your attempt

Correct Answer

C. (53)

Step 1

Concept

((x-13)²=1600) and (x-13=40), so (x=53). Remember that the side must be positive.

Step 2

Why this answer is correct

The correct answer is C. (53). ((x-13)²=1600) and (x-13=40), so (x=53). Remember that the side must be positive.

Step 3

Exam Tip

((x-13)²=1600) और (x-13=40), इसलिए (x=53) है। भुजा धनात्मक होने की शर्त याद रखें।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक वर्ग की भुजा (x+12) सेमी है। उसका क्षेत्रफल (1764) वर्ग सेमी है। (x) का मान क्या है?

The side of a square is (x+12) cm. Its area is (1764) square cm. What is the value of (x)?

Explanation opens after your attempt

Correct Answer

C. (30)

Step 1

Concept

((x+12)²=1764) gives (x+12=42), so (x=30). Take the positive square root for length.

Step 2

Why this answer is correct

The correct answer is C. (30). ((x+12)²=1764) gives (x+12=42), so (x=30). Take the positive square root for length.

Step 3

Exam Tip

((x+12)²=1764) से (x+12=42), इसलिए (x=30) है। लंबाई के लिए धनात्मक वर्गमूल लें।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक वर्गाकार मैदान के अंदर समान चौड़ाई (x) मीटर की सीमा छोड़ने के बाद अंदर का वर्ग (36) मीटर भुजा का बचता है। बाहरी भुजा (52) मीटर है। (x) क्या है?

Inside a square field, after leaving a uniform border of width (x) m, the inner square has side (36) m. The outer side is (52) m. What is (x)?

Explanation opens after your attempt

Correct Answer

B. (8) मीटर(8) m

Step 1

Concept

The inner side is (52-2x) and (52-2x=36), so (x=8). The border is subtracted from both sides.

Step 2

Why this answer is correct

The correct answer is B. (8) मीटर / (8) m. The inner side is (52-2x) and (52-2x=36), so (x=8). The border is subtracted from both sides.

Step 3

Exam Tip

अंदर की भुजा (52-2x) है और (52-2x=36), इसलिए (x=8) है। सीमा दोनों तरफ से घटती है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक तार को वर्ग के रूप में मोड़ने पर क्षेत्रफल (1296) वर्ग सेमी है। तार की लंबाई क्या है?

A wire is bent into a square and the area is (1296) square cm. What is the length of the wire?

Explanation opens after your attempt

Correct Answer

C. (144) सेमी(144) cm

Step 1

Concept

If the side of the square is (x), then \(x^2=1296\), so (x=36). The wire length is the perimeter (4x=144) cm.

Step 2

Why this answer is correct

The correct answer is C. (144) सेमी / (144) cm. If the side of the square is (x), then \(x^2=1296\), so (x=36). The wire length is the perimeter (4x=144) cm.

Step 3

Exam Tip

वर्ग की भुजा (x) हो तो \(x^2=1296\), इसलिए (x=36) है। तार की लंबाई परिमाप (4x=144) सेमी होगी।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक वर्ग की भुजा (x) सेमी है। भुजा (5) सेमी घटाने पर क्षेत्रफल (784) वर्ग सेमी हो जाता है। मूल भुजा क्या है?

The side of a square is (x) cm. When the side is reduced by (5) cm, the area becomes (784) square cm. What is the original side?

Explanation opens after your attempt

Correct Answer

C. (33) सेमी(33) cm

Step 1

Concept

((x-5)²=784) gives (x-5=28), so (x=33). Write the reduced side as (x-5).

Step 2

Why this answer is correct

The correct answer is C. (33) सेमी / (33) cm. ((x-5)²=784) gives (x-5=28), so (x=33). Write the reduced side as (x-5).

Step 3

Exam Tip

((x-5)²=784) से (x-5=28), इसलिए (x=33) है। घटाई गई भुजा को (x-5) लिखें।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक वर्गाकार टाइल की भुजा (x-8) सेमी है और क्षेत्रफल (900) वर्ग सेमी है। (x) क्या है?

The side of a square tile is (x-8) cm and its area is (900) square cm. What is (x)?

Explanation opens after your attempt

Correct Answer

C. (38)

Step 1

Concept

((x-8)²=900) and (x-8=30), so (x=38). Remember that the side must be positive.

Step 2

Why this answer is correct

The correct answer is C. (38). ((x-8)²=900) and (x-8=30), so (x=38). Remember that the side must be positive.

Step 3

Exam Tip

((x-8)²=900) और (x-8=30), इसलिए (x=38) है। भुजा धनात्मक होने की शर्त याद रखें।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक वर्ग की भुजा (x+6) सेमी है। उसका क्षेत्रफल (1225) वर्ग सेमी है। (x) का मान क्या है?

The side of a square is (x+6) cm. Its area is (1225) square cm. What is the value of (x)?

Explanation opens after your attempt

Correct Answer

C. (29)

Step 1

Concept

((x+6)²=1225) gives (x+6=35), so (x=29). Take the positive square root for length.

Step 2

Why this answer is correct

The correct answer is C. (29). ((x+6)²=1225) gives (x+6=35), so (x=29). Take the positive square root for length.

Step 3

Exam Tip

((x+6)²=1225) से (x+6=35), इसलिए (x=29) है। लंबाई के लिए धनात्मक वर्गमूल लें।

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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक वर्ग का क्षेत्रफल उसके परिमाप से (96) अधिक है। वर्ग की भुजा क्या है?

The area of a square is (96) more than its perimeter. What is the side of the square?

Explanation opens after your attempt

Correct Answer

A. (12)

Step 1

Concept

If the side is (x), then \(x^2=4x+96\). This gives \(x^2-4x-96=0\), so the positive side is (12).

Step 2

Why this answer is correct

The correct answer is A. (12). If the side is (x), then \(x^2=4x+96\). This gives \(x^2-4x-96=0\), so the positive side is (12).

Step 3

Exam Tip

यदि भुजा (x) है, तो \(x^2=4x+96\)। इससे \(x^2-4x-96=0\), इसलिए धनात्मक भुजा (12) है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक वर्गाकार मैदान के अंदर समान चौड़ाई (x) मीटर की सीमा छोड़ने के बाद अंदर का वर्ग (20) मीटर भुजा का बचता है। बाहरी भुजा (28) मीटर है। (x) क्या है?

Inside a square field, after leaving a uniform border of width (x) m, the inner square has side (20) m. The outer side is (28) m. What is (x)?

Explanation opens after your attempt

Correct Answer

B. (4) मीटर(4) m

Step 1

Concept

The inner side is (28-2x) and (28-2x=20), so (x=4). The border is subtracted from both sides.

Step 2

Why this answer is correct

The correct answer is B. (4) मीटर / (4) m. The inner side is (28-2x) and (28-2x=20), so (x=4). The border is subtracted from both sides.

Step 3

Exam Tip

अंदर की भुजा (28-2x) है और (28-2x=20), इसलिए (x=4) है। सीमा दोनों तरफ से घटती है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक तार को वर्ग के रूप में मोड़ने पर क्षेत्रफल (625) वर्ग सेमी है। तार की लंबाई क्या है?

A wire is bent into a square and the area is (625) square cm. What is the length of the wire?

Explanation opens after your attempt

Correct Answer

C. (100) सेमी(100) cm

Step 1

Concept

If the side of the square is (x), then \(x^2=625\), so (x=25). The wire length is the perimeter (4x=100) cm.

Step 2

Why this answer is correct

The correct answer is C. (100) सेमी / (100) cm. If the side of the square is (x), then \(x^2=625\), so (x=25). The wire length is the perimeter (4x=100) cm.

Step 3

Exam Tip

वर्ग की भुजा (x) हो तो \(x^2=625\), इसलिए (x=25) है। तार की लंबाई परिमाप (4x=100) सेमी होगी।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक वर्ग की भुजा (x) सेमी है। भुजा (3) सेमी घटाने पर क्षेत्रफल (225) वर्ग सेमी हो जाता है। मूल भुजा क्या है?

The side of a square is (x) cm. When the side is reduced by (3) cm, the area becomes (225) square cm. What is the original side?

Explanation opens after your attempt

Correct Answer

B. (18) सेमी(18) cm

Step 1

Concept

((x-3)²=225) gives (x-3=15), so (x=18). Write the reduced side as (x-3).

Step 2

Why this answer is correct

The correct answer is B. (18) सेमी / (18) cm. ((x-3)²=225) gives (x-3=15), so (x=18). Write the reduced side as (x-3).

Step 3

Exam Tip

((x-3)²=225) से (x-3=15), इसलिए (x=18) है। घटाई गई भुजा को (x-3) लिखें।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक वर्गाकार मैदान की भुजा (x) मीटर है। यदि भुजा (5) मीटर बढ़ाने पर क्षेत्रफल (425) वर्ग मीटर बढ़ता है, तो (x) क्या है?

A square field has side (x) m. If increasing the side by (5) m increases the area by (425) square m, what is (x)?

Explanation opens after your attempt

Correct Answer

C. (40)

Step 1

Concept

The area increase is ((x+5)²-x^-2=425). This gives (10x+25=425), so (x=40).

Step 2

Why this answer is correct

The correct answer is C. (40). The area increase is ((x+5)²-x^-2=425). This gives (10x+25=425), so (x=40).

Step 3

Exam Tip

क्षेत्रफल वृद्धि ((x+5)²-x^-2=425) है। इससे (10x+25=425), इसलिए (x=40) है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक वर्गाकार टाइल की भुजा (x-3) सेमी है और क्षेत्रफल (441) वर्ग सेमी है। (x) क्या है?

The side of a square tile is (x-3) cm and its area is (441) square cm. What is (x)?

Explanation opens after your attempt

Correct Answer

C. (24)

Step 1

Concept

((x-3)²=441) and (x-3=21), so (x=24). Remember that the side must be positive.

Step 2

Why this answer is correct

The correct answer is C. (24). ((x-3)²=441) and (x-3=21), so (x=24). Remember that the side must be positive.

Step 3

Exam Tip

((x-3)²=441) और (x-3=21), इसलिए (x=24) है। भुजा धनात्मक होने की शर्त याद रखें।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक वर्ग की भुजा (x+4) सेमी है। उसका क्षेत्रफल (576) वर्ग सेमी है। (x) का मान क्या है?

The side of a square is (x+4) cm. Its area is (576) square cm. What is the value of (x)?

Explanation opens after your attempt

Correct Answer

C. (20)

Step 1

Concept

((x+4)²=576) gives (x+4=24), so (x=20). Take the positive square root for length.

Step 2

Why this answer is correct

The correct answer is C. (20). ((x+4)²=576) gives (x+4=24), so (x=20). Take the positive square root for length.

Step 3

Exam Tip

((x+4)²=576) से (x+4=24), इसलिए (x=20) है। लंबाई के लिए धनात्मक वर्गमूल लें।

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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक वर्ग का क्षेत्रफल उसके परिमाप से (45) अधिक है। वर्ग की भुजा क्या है?

The area of a square is (45) more than its perimeter. What is the side of the square?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

If the side is (x), then \(x^2=4x+45\). This gives \(x^2-4x-45=0\), so the positive side is (9).

Step 2

Why this answer is correct

The correct answer is A. (9). If the side is (x), then \(x^2=4x+45\). This gives \(x^2-4x-45=0\), so the positive side is (9).

Step 3

Exam Tip

यदि भुजा (x) है, तो \(x^2=4x+45\)। इससे \(x^2-4x-45=0\), इसलिए धनात्मक भुजा (9) है।

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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक वर्गाकार खेत की भुजा (x) मीटर है। यदि क्षेत्रफल (729) वर्ग मीटर है, तो (x) क्या है?

A square field has side (x) m. If its area is (729) square m, what is (x)?

Explanation opens after your attempt

Correct Answer

C. (27)

Step 1

Concept

\(x^2=729\) gives (x=27). In a square region, the side is the positive square root of area.

Step 2

Why this answer is correct

The correct answer is C. (27). \(x^2=729\) gives (x=27). In a square region, the side is the positive square root of area.

Step 3

Exam Tip

\(x^2=729\) से (x=27) है। वर्गाकार क्षेत्र में भुजा क्षेत्रफल का धनात्मक वर्गमूल होती है।

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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक वर्गाकार फर्श का क्षेत्रफल (625) वर्ग मीटर है। उसका परिमाप क्या है?

A square floor has area (625) square m. What is its perimeter?

Explanation opens after your attempt

Correct Answer

C. (100) मीटर(100) m

Step 1

Concept

From \(x^2=625\), the side is (25) m and perimeter is (4x=100) m. Keep area and perimeter formulas separate.

Step 2

Why this answer is correct

The correct answer is C. (100) मीटर / (100) m. From \(x^2=625\), the side is (25) m and perimeter is (4x=100) m. Keep area and perimeter formulas separate.

Step 3

Exam Tip

\(x^2=625\) से भुजा (25) मीटर है और परिमाप (4x=100) मीटर है। क्षेत्रफल और परिमाप के सूत्र अलग रखें।

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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक वर्गाकार हॉल का क्षेत्रफल (529) वर्ग मीटर है। उसकी भुजा क्या है?

A square hall has area (529) square m. What is its side?

Explanation opens after your attempt

Correct Answer

C. (23) मीटर(23) m

Step 1

Concept

If the side is (x), then \(x^2=529\), so (x=23). For length, take only the positive square root.

Step 2

Why this answer is correct

The correct answer is C. (23) मीटर / (23) m. If the side is (x), then \(x^2=529\), so (x=23). For length, take only the positive square root.

Step 3

Exam Tip

भुजा (x) हो तो \(x^2=529\), इसलिए (x=23) है। लंबाई के लिए केवल धनात्मक वर्गमूल लें।

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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक वर्गाकार आँगन का क्षेत्रफल (400) वर्ग मीटर है। उसका परिमाप क्या है?

A square courtyard has area (400) square m. What is its perimeter?

Explanation opens after your attempt

Correct Answer

C. (80) मीटर(80) m

Step 1

Concept

\(x^2=400\) gives side (20) m and perimeter (4x=80) m. Area and perimeter formulas are different.

Step 2

Why this answer is correct

The correct answer is C. (80) मीटर / (80) m. \(x^2=400\) gives side (20) m and perimeter (4x=80) m. Area and perimeter formulas are different.

Step 3

Exam Tip

\(x^2=400\) से भुजा (20) मीटर और परिमाप (4x=80) मीटर है। क्षेत्रफल और परिमाप के सूत्र अलग होते हैं।

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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक वर्गाकार कार्ड का क्षेत्रफल (361) वर्ग सेमी है। उसकी भुजा क्या है?

A square card has area (361) square cm. What is its side?

Explanation opens after your attempt

Correct Answer

C. (19) सेमी(19) cm

Step 1

Concept

\(x^2=361\) gives (x=19). While taking the square root, keep length positive.

Step 2

Why this answer is correct

The correct answer is C. (19) सेमी / (19) cm. \(x^2=361\) gives (x=19). While taking the square root, keep length positive.

Step 3

Exam Tip

\(x^2=361\) से (x=19) है। वर्गमूल लेते समय लंबाई को धनात्मक रखें।

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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक वर्गाकार मंच का क्षेत्रफल (289) वर्ग मीटर है। उसका परिमाप क्या है?

A square stage has area (289) square m. What is its perimeter?

Explanation opens after your attempt

Correct Answer

C. (68) मीटर(68) m

Step 1

Concept

From \(x^2=289\), the side is (17) m and perimeter is (4x=68) m. First find the side and then apply perimeter.

Step 2

Why this answer is correct

The correct answer is C. (68) मीटर / (68) m. From \(x^2=289\), the side is (17) m and perimeter is (4x=68) m. First find the side and then apply perimeter.

Step 3

Exam Tip

\(x^2=289\) से भुजा (17) मीटर है और परिमाप (4x=68) मीटर है। पहले भुजा निकालें और फिर परिमाप लगाएँ।

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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक वर्गाकार पार्क का क्षेत्रफल (196) वर्ग मीटर है। उसकी भुजा क्या है?

A square park has area (196) square m. What is its side?

Explanation opens after your attempt

Correct Answer

C. (14) मीटर(14) m

Step 1

Concept

If the side is (x), then \(x^2=196\), so (x=14). The side of a square is always taken positive.

Step 2

Why this answer is correct

The correct answer is C. (14) मीटर / (14) m. If the side is (x), then \(x^2=196\), so (x=14). The side of a square is always taken positive.

Step 3

Exam Tip

भुजा (x) हो तो \(x^2=196\), इसलिए (x=14) है। वर्ग की भुजा हमेशा धनात्मक मानी जाती है।

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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक वर्गाकार शीट का क्षेत्रफल (144) वर्ग सेमी है। उसकी परिमाप क्या है?

A square sheet has area (144) square cm. What is its perimeter?

Explanation opens after your attempt

Correct Answer

D. (48) सेमी(48) cm

Step 1

Concept

\(x^2=144\) gives side (12) cm and perimeter (4x=48) cm. If perimeter is asked, do not stop after finding the side.

Step 2

Why this answer is correct

The correct answer is D. (48) सेमी / (48) cm. \(x^2=144\) gives side (12) cm and perimeter (4x=48) cm. If perimeter is asked, do not stop after finding the side.

Step 3

Exam Tip

\(x^2=144\) से भुजा (12) सेमी है और परिमाप (4x=48) सेमी है। परिमाप पूछे जाने पर केवल भुजा लिखकर न रुकें।

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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक वर्गाकार टाइल का क्षेत्रफल (64) वर्ग सेमी है। उसकी भुजा क्या है?

A square tile has area (64) square cm. What is its side?

Explanation opens after your attempt

Correct Answer

C. (8) सेमी(8) cm

Step 1

Concept

If the side is (x), then \(x^2=64\), so (x=8). In a square, area equals the square of the side.

Step 2

Why this answer is correct

The correct answer is C. (8) सेमी / (8) cm. If the side is (x), then \(x^2=64\), so (x=8). In a square, area equals the square of the side.

Step 3

Exam Tip

भुजा (x) हो तो \(x^2=64\), इसलिए (x=8) है। वर्ग में क्षेत्रफल भुजा के वर्ग के बराबर होता है।

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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक वर्गाकार मैदान का क्षेत्रफल (225) वर्ग मीटर है। उसकी परिमाप क्या है?

A square field has area (225) square m. What is its perimeter?

Explanation opens after your attempt

Correct Answer

C. (60) मीटर(60) m

Step 1

Concept

From \(x^2=225\), the side is (15) m and perimeter is (4x=60) m. First find the side, then apply perimeter.

Step 2

Why this answer is correct

The correct answer is C. (60) मीटर / (60) m. From \(x^2=225\), the side is (15) m and perimeter is (4x=60) m. First find the side, then apply perimeter.

Step 3

Exam Tip

\(x^2=225\) से भुजा (15) मीटर है और परिमाप (4x=60) मीटर है। पहले भुजा निकालें, फिर परिमाप लगाएँ।

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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक वर्गाकार बगीचे का क्षेत्रफल (169) वर्ग मीटर है। उसकी भुजा क्या है?

A square garden has area (169) square m. What is its side?

Explanation opens after your attempt

Correct Answer

C. (13) मीटर(13) m

Step 1

Concept

If the side of the square is (x), then \(x^2=169\), so (x=13). A side length is always taken positive.

Step 2

Why this answer is correct

The correct answer is C. (13) मीटर / (13) m. If the side of the square is (x), then \(x^2=169\), so (x=13). A side length is always taken positive.

Step 3

Exam Tip

वर्ग की भुजा (x) हो तो \(x^2=169\), इसलिए (x=13) है। भुजा हमेशा धनात्मक ली जाती है।

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Question Easy Mathematics Real Numbers Proof of irrationality of √2, √3, √5 Class 10 Level 16

निम्न में से कौन सी संख्या पूर्ण वर्ग नहीं है और उसका वर्गमूल अपरिमेय सिद्ध किया जाता है?

Which of the following is not a perfect square and its square root is proved irrational?

Explanation opens after your attempt

Correct Answer

A. (2)

Step 1

Concept

(4), (9), and (25) are perfect squares.

Step 2

Why this answer is correct

(2) is not a perfect square, so \(\sqrt{2}\) is proved irrational.

Step 3

Exam Tip

First identify perfect and non-perfect squares. चरण 1: (4), (9) और (25) पूर्ण वर्ग हैं। चरण 2: (2) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{2}\) अपरिमेय सिद्ध किया जाता है। चरण 3: पूर्ण वर्ग और अपूर्ण वर्ग की पहचान पहले करें।

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Question Expert Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

एक समांतर श्रेणी का सामान्य अंतर (d) है। \(a_1,a_3,a_5,\ldots\) से बने अनुक्रम का सामान्य अंतर क्या होगा?

An AP has common difference (d). What is the common difference of the sequence \(a_1,a_3,a_5,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (2d)

Step 1

Concept

The new sequence jumps two original terms each time, so the difference is (2d). In exams, multiply (d) by the term-number jump.

Step 2

Why this answer is correct

The correct answer is B. (2d). The new sequence jumps two original terms each time, so the difference is (2d). In exams, multiply (d) by the term-number jump.

Step 3

Exam Tip

नए अनुक्रम में दो-दो मूल पदों की छलांग है, इसलिए अंतर (2d) है। परीक्षा में पद-संख्या की छलांग को (d) से गुणा करें।

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Question Expert Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

एक सीमित समांतर श्रेणी का सामान्य अंतर (-6) है। उसे उलटे क्रम में लिखने पर नया सामान्य अंतर क्या होगा?

A finite AP has common difference (-6). What will be the new common difference after writing it in reverse order?

Explanation opens after your attempt

Correct Answer

D. (6)

Step 1

Concept

Reversing changes each step to the opposite sign. In exams, reverse order changes (d) to (-d).

Step 2

Why this answer is correct

The correct answer is D. (6). Reversing changes each step to the opposite sign. In exams, reverse order changes (d) to (-d).

Step 3

Exam Tip

उलटने पर हर कदम का अंतर विपरीत चिन्ह वाला हो जाता है। परीक्षा में उलटा क्रम (d) को (-d) कर देता है।

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Question Expert Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

एक समांतर श्रेणी का सामान्य अंतर (4) है। पद \(a_2,a_5,a_8,\ldots\) से बने नए अनुक्रम का सामान्य अंतर क्या है?

An AP has common difference (4). What is the common difference of the new sequence \(a_2,a_5,a_8,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (12)

Step 1

Concept

The new sequence jumps three original terms each time, so its difference is (3d=12). In exams, count the gap between selected term numbers.

Step 2

Why this answer is correct

The correct answer is C. (12). The new sequence jumps three original terms each time, so its difference is (3d=12). In exams, count the gap between selected term numbers.

Step 3

Exam Tip

नए अनुक्रम में हर बार तीन पदों की छलांग है, इसलिए अंतर (3d=12) है। परीक्षा में चुने गए पदों के बीच की दूरी गिनें।

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Question Expert Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि \(a_n\) का सामान्य अंतर (-9) है और \(b_n=\frac{a_n}{3}+5\), तो \(b_n\) का सामान्य अंतर क्या होगा?

If \(a_n\) has common difference (-9) and \(b_n=\frac{a_n}{3}+5\), what is the common difference of \(b_n\)?

Explanation opens after your attempt

Correct Answer

C. (-3)

Step 1

Concept

Multiplying by \(\frac{1}{3}\) changes the difference from (-9) to (-3), and adding (5) does not change it. In exams, separate the effects of addition and multiplication.

Step 2

Why this answer is correct

The correct answer is C. (-3). Multiplying by \(\frac{1}{3}\) changes the difference from (-9) to (-3), and adding (5) does not change it. In exams, separate the effects of addition and multiplication.

Step 3

Exam Tip

\(\frac{1}{3}\) से गुणा करने पर अंतर (-9) से (-3) हो जाता है, और (5) जोड़ने से अंतर नहीं बदलता। परीक्षा में जोड़ और गुणन के प्रभाव अलग करें।

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Question Expert Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 62

यदि \(a_n\) एक समांतर श्रेणी है जिसका सामान्य अंतर (4) है और \(b_n=2a_n-3\), तो \(b_n\) का सामान्य अंतर क्या है?

If \(a_n\) is an AP with common difference (4) and \(b_n=2a_n-3\), what is the common difference of \(b_n\)?

Explanation opens after your attempt

Correct Answer

D. (8)

Step 1

Concept

Multiplying terms by (2) multiplies the difference by (2), so it becomes (8). In exams, adding or subtracting a constant does not change the difference, but multiplication does.

Step 2

Why this answer is correct

The correct answer is D. (8). Multiplying terms by (2) multiplies the difference by (2), so it becomes (8). In exams, adding or subtracting a constant does not change the difference, but multiplication does.

Step 3

Exam Tip

पदों को (2) से गुणा करने पर अंतर भी (2) गुना हो जाता है, इसलिए (8)। परीक्षा में जोड़ना-घटाना अंतर नहीं बदलता, गुणा बदलता है।

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Question Expert Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

यदि \(1, 5, 9,\ldots\) और \(2, 8, 14,\ldots\) के पद-दर-पद अंतर से नया अनुक्रम बने, तो उसका (d) क्या होगा?

If a new sequence is formed by termwise difference of \(1, 5, 9,\ldots\) and \(2, 8, 14,\ldots\), what will be its (d)?

Explanation opens after your attempt

Correct Answer

A. (-2)

Step 1

Concept

The first sequence has (d=4) and the second has (d=6), so the difference sequence has (d=4-6=-2). In termwise difference, take the difference of common differences.

Step 2

Why this answer is correct

The correct answer is A. (-2). The first sequence has (d=4) and the second has (d=6), so the difference sequence has (d=4-6=-2). In termwise difference, take the difference of common differences.

Step 3

Exam Tip

पहले अनुक्रम का (d=4) और दूसरे का (d=6) है, इसलिए अंतर अनुक्रम का (d=4-6=-2)। पद-दर-पद अंतर में सार्व अंतरों का अंतर लें।

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Question Medium Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

अनुक्रम \(75,69,63,57,\ldots\) में तीसरे और चौथे पद का अंतर क्या है?

What is the difference between the third and fourth terms of \(75,69,63,57,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (-6)

Step 1

Concept

The third term is (63) and the fourth is (57), so the difference is (57-63=-6). While finding difference subtract the previous term from the next term.

Step 2

Why this answer is correct

The correct answer is B. (-6). The third term is (63) and the fourth is (57), so the difference is (57-63=-6). While finding difference subtract the previous term from the next term.

Step 3

Exam Tip

तीसरा पद (63) और चौथा (57) है इसलिए अंतर (57-63=-6) है। अंतर निकालते समय अगला पद घटा पिछला पद करें।

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Question Medium Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

अनुक्रम \(42,39,36,33,\ldots\) में तीसरा और चौथा पद का अंतर क्या है?

What is the difference between the third and fourth terms of \(42,39,36,33,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (-3)

Step 1

Concept

The third term is (36) and the fourth is (33), so (33-36=-3). While finding the difference subtract the previous term from the next term.

Step 2

Why this answer is correct

The correct answer is B. (-3). The third term is (36) and the fourth is (33), so (33-36=-3). While finding the difference subtract the previous term from the next term.

Step 3

Exam Tip

तीसरा पद (36) और चौथा (33) है इसलिए (33-36=-3)। अंतर निकालते समय बाद वाला पद घटा पहले वाला पद करें।

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Question Easy Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 62

अनुक्रम \(6,10,14,18,\ldots\) में दूसरा और तीसरा पद का अंतर क्या है?

What is the difference between the second and third terms in \(6,10,14,18,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

The second term is (10) and the third term is (14), so the difference is (14-10=4). It equals (d).

Step 2

Why this answer is correct

The correct answer is A. (4). The second term is (10) and the third term is (14), so the difference is (14-10=4). It equals (d).

Step 3

Exam Tip

दूसरा पद (10) और तीसरा पद (14) है इसलिए अंतर (14-10=4) है। यह (d) के बराबर है।

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Question Easy Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 62

अनुक्रम \(100,90,80,70,\ldots\) में सार्व अंतर कितना है?

What is the common difference in the sequence \(100,90,80,70,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (-10)

Step 1

Concept

The common difference is (90-100=-10). In a decreasing sequence carefully check the sign.

Step 2

Why this answer is correct

The correct answer is C. (-10). The common difference is (90-100=-10). In a decreasing sequence carefully check the sign.

Step 3

Exam Tip

सार्व अंतर (90-100=-10) है। घटते अनुक्रम में उत्तर का चिह्न जरूर देखें।

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Question Easy Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 62

अनुक्रम \(20,15,10,5,\ldots\) में पहला पद और सार्व अंतर क्रमशः क्या हैं?

In the sequence \(20,15,10,5,\ldots\), what are the first term and common difference respectively?

Explanation opens after your attempt

Correct Answer

A. (20) और (-5)(20) and (-5)

Step 1

Concept

The first term is (20) and (15-20=-5). When asked respectively keep the order in mind.

Step 2

Why this answer is correct

The correct answer is A. (20) और (-5) / (20) and (-5). The first term is (20) and (15-20=-5). When asked respectively keep the order in mind.

Step 3

Exam Tip

पहला पद (20) है और (15-20=-5) है। क्रमशः पूछे जाने पर क्रम का ध्यान रखें।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

यदि \(1,4,7,\ldots\) के प्रत्येक पद में पद संख्या का वर्ग जोड़ा जाए तो नया अनुक्रम कैसा होगा?

If the square of the term number is added to each term of \(1,4,7,\ldots\), what type will the new sequence be?

Explanation opens after your attempt

Correct Answer

C. अंकगणितीय श्रेणी नहीं क्योंकि नए अंतर समान नहीं होंगेNot an arithmetic progression because new differences will not be equal

Step 1

Concept

The new terms are \(2,8,16,\ldots\), and the differences are \(6,8,\ldots\), which are not equal. Adding squares of term numbers does not preserve equal difference.

Step 2

Why this answer is correct

The correct answer is C. अंकगणितीय श्रेणी नहीं क्योंकि नए अंतर समान नहीं होंगे / Not an arithmetic progression because new differences will not be equal. The new terms are \(2,8,16,\ldots\), and the differences are \(6,8,\ldots\), which are not equal. Adding squares of term numbers does not preserve equal difference.

Step 3

Exam Tip

नए पद \(2,8,16,\ldots\) मिलते हैं और अंतर \(6,8,\ldots\) हैं, जो समान नहीं हैं। पद संख्या के वर्ग जोड़ने से समान अंतर नहीं बचता।

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Question Expert Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

यदि \(7, 11, 15,\ldots\) में हर पद में उसकी पद संख्या का वर्ग जोड़ा जाए, तो क्या नया अनुक्रम अंकगणितीय श्रेणी होगा?

If the square of its term number is added to each term of \(7, 11, 15,\ldots\), will the new sequence be an arithmetic progression?

Explanation opens after your attempt

Correct Answer

C. नहीं, क्योंकि नए अंतर समान नहीं होंगेNo, because new differences will not be equal

Step 1

Concept

The added squares \(1,4,9,\ldots\) have differences \(3,5,\ldots\), which are not equal, so the new sequence will not remain arithmetic. Squares of term numbers do not create equal differences.

Step 2

Why this answer is correct

The correct answer is C. नहीं, क्योंकि नए अंतर समान नहीं होंगे / No, because new differences will not be equal. The added squares \(1,4,9,\ldots\) have differences \(3,5,\ldots\), which are not equal, so the new sequence will not remain arithmetic. Squares of term numbers do not create equal differences.

Step 3

Exam Tip

नए जोड़े गए वर्ग \(1,4,9,\ldots\) के अंतर \(3,5,\ldots\) समान नहीं हैं, इसलिए नया अनुक्रम अंकगणितीय नहीं रहेगा। पद संख्या के वर्ग से समान अंतर नहीं बनता।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक धनात्मक संख्या के वर्ग और संख्या के (40) गुने का अंतर (3825) है। संख्या क्या है?

The difference between the square of a positive number and (40) times the number is (3825). What is the number?

Explanation opens after your attempt

Correct Answer

C. (85)

Step 1

Concept

\(x^2-40x=3825\) gives \(x^2-40x-3825=0\). The positive solution is (x=85).

Step 2

Why this answer is correct

The correct answer is C. (85). \(x^2-40x=3825\) gives \(x^2-40x-3825=0\). The positive solution is (x=85).

Step 3

Exam Tip

\(x^2-40x=3825\) से \(x^2-40x-3825=0\) बनता है। धनात्मक हल (x=85) है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक धनात्मक संख्या के वर्ग और संख्या के (27) गुने का अंतर (1000) है। संख्या क्या है?

The difference between the square of a positive number and (27) times the number is (1000). What is the number?

Explanation opens after your attempt

Correct Answer

C. (50)

Step 1

Concept

\(x^2-27x=1000\) gives \(x^2-27x-1000=0\). The positive solution is (x=50).

Step 2

Why this answer is correct

The correct answer is C. (50). \(x^2-27x=1000\) gives \(x^2-27x-1000=0\). The positive solution is (x=50).

Step 3

Exam Tip

\(x^2-27x=1000\) से \(x^2-27x-1000=0\) बनता है। धनात्मक हल (x=50) है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक धनात्मक संख्या के वर्ग और संख्या के (20) गुने का अंतर (621) है। संख्या क्या है?

The difference between the square of a positive number and (20) times the number is (621). What is the number?

Explanation opens after your attempt

Correct Answer

C. (39)

Step 1

Concept

\(x^2-20x=621\) gives \(x^2-20x-621=0\). The positive solution is (x=39).

Step 2

Why this answer is correct

The correct answer is C. (39). \(x^2-20x=621\) gives \(x^2-20x-621=0\). The positive solution is (x=39).

Step 3

Exam Tip

\(x^2-20x=621\) से \(x^2-20x-621=0\) बनता है। धनात्मक हल (x=39) है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक धनात्मक संख्या के वर्ग और संख्या के (16) गुने का अंतर (425) है। संख्या क्या है?

The difference between the square of a positive number and (16) times the number is (425). What is the number?

Explanation opens after your attempt

Correct Answer

B. (29)

Step 1

Concept

\(x^2-16x=425\) gives \(x^2-16x-425=0\). The positive solution is (x=29).

Step 2

Why this answer is correct

The correct answer is B. (29). \(x^2-16x=425\) gives \(x^2-16x-425=0\). The positive solution is (x=29).

Step 3

Exam Tip

\(x^2-16x=425\) से \(x^2-16x-425=0\) बनता है। धनात्मक हल (x=29) है।

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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक संख्या के वर्ग और संख्या के (12) गुने का अंतर (589) है। धनात्मक संख्या क्या है?

The difference between the square of a number and (12) times the number is (589). What is the positive number?

Explanation opens after your attempt

Correct Answer

C. (31)

Step 1

Concept

The equation is \(x^2-12x=589\), or \(x^2-12x-589=0\), giving (x=31). In a difference statement, keep the subtraction order correct.

Step 2

Why this answer is correct

The correct answer is C. (31). The equation is \(x^2-12x=589\), or \(x^2-12x-589=0\), giving (x=31). In a difference statement, keep the subtraction order correct.

Step 3

Exam Tip

समीकरण \(x^2-12x=589\) है, यानी \(x^2-12x-589=0\), जिससे (x=31) मिलता है। अंतर में घटाव का क्रम ध्यान रखें।

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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक संख्या के वर्ग और संख्या के (9) गुने का अंतर (90) है। धनात्मक संख्या क्या है?

The difference between the square of a number and (9) times the number is (90). What is the positive number?

Explanation opens after your attempt

Correct Answer

C. (15)

Step 1

Concept

The equation is \(x^2-9x=90\), or \(x^2-9x-90=0\), which gives (x=15). Keep the subtraction order correct in difference statements.

Step 2

Why this answer is correct

The correct answer is C. (15). The equation is \(x^2-9x=90\), or \(x^2-9x-90=0\), which gives (x=15). Keep the subtraction order correct in difference statements.

Step 3

Exam Tip

समीकरण \(x^2-9x=90\) है, यानी \(x^2-9x-90=0\), जिससे (x=15) मिलता है। अंतर वाले वाक्य में घटाव का क्रम सही रखें।

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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक संख्या के वर्ग और संख्या के (6) गुने का अंतर (16) है। धनात्मक संख्या क्या है?

The difference between the square of a number and (6) times the number is (16). What is the positive number?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

The equation is \(x^2-6x=16\), or \(x^2-6x-16=0\), giving (x=8). In difference questions, read the order carefully.

Step 2

Why this answer is correct

The correct answer is C. (8). The equation is \(x^2-6x=16\), or \(x^2-6x-16=0\), giving (x=8). In difference questions, read the order carefully.

Step 3

Exam Tip

समीकरण \(x^2-6x=16\) है, यानी \(x^2-6x-16=0\), जिससे (x=8) है। अंतर वाले प्रश्न में क्रम ध्यान से पढ़ें।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक वर्गाकार टाइल की भुजा (x) सेमी है। यदि (5) सेमी चौड़ा बॉर्डर लगाने पर कुल क्षेत्रफल (900) वर्ग सेमी हो जाता है तो मूल भुजा क्या है?

A square tile has side (x) cm. If a (5) cm wide border is added all around and the total area becomes (900) square cm, what is the original side?

Explanation opens after your attempt

Correct Answer

C. (20) सेमी(20) cm

Step 1

Concept

After the border, the side becomes (x+10). From ((x+10)²=900), (x+10=30), so (x=20).

Step 2

Why this answer is correct

The correct answer is C. (20) सेमी / (20) cm. After the border, the side becomes (x+10). From ((x+10)²=900), (x+10=30), so (x=20).

Step 3

Exam Tip

बॉर्डर के बाद भुजा (x+10) होगी। ((x+10)²=900) से (x+10=30) और (x=20) मिलता है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक वर्गाकार कागज से (3 cm) चौड़ी पट्टी एक ओर से काट दी जाती है। शेष आयत का क्षेत्रफल \(70 cm^2\) है। मूल वर्ग की भुजा क्या थी?

A (3 cm) wide strip is cut from one side of a square sheet. The remaining rectangle has area (70 cm\(^2). What was the side of the original square\)?

Explanation opens after your attempt

Correct Answer

B. (10 cm)

Step 1

Concept

Let the square side be (x), then the remaining area is (x(x-3)=70). This gives \(x^2-3x-70=0\), so (x=10).

Step 2

Why this answer is correct

The correct answer is B. (10 cm\(). Let the square side be (x), then the remaining area is (x(x-3)=70). This gives (x^2-3x-70=0), so (x=10).\)

Step 3

Exam Tip

वर्ग की भुजा (x) हो, तो शेष क्षेत्रफल (x(x-3)=70)। इससे \(x^2-3x-70=0\), इसलिए (x=10)।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक वर्गाकार मैदान की भुजा (x) मीटर है। यदि भुजा (12) मीटर बढ़ाने पर क्षेत्रफल (2448) वर्ग मीटर बढ़ता है, तो (x) क्या है?

A square field has side (x) m. If increasing the side by (12) m increases the area by (2448) square m, what is (x)?

Explanation opens after your attempt

Correct Answer

C. (96)

Step 1

Concept

The area increase is ((x+12)²-x^-2=2448). This gives (24x+144=2448), so (x=96).

Step 2

Why this answer is correct

The correct answer is C. (96). The area increase is ((x+12)²-x^-2=2448). This gives (24x+144=2448), so (x=96).

Step 3

Exam Tip

क्षेत्रफल वृद्धि ((x+12)²-x^-2=2448) है। इससे (24x+144=2448), इसलिए (x=96) है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक वर्गाकार पार्क का क्षेत्रफल एक आयत के क्षेत्रफल के बराबर है। वर्ग की भुजा (56) मीटर है और आयत की चौड़ाई (x) तथा लंबाई (x+66) है। (x) क्या है?

A square park has the same area as a rectangle. The square side is (56) m and the rectangle has breadth (x) and length (x+66). What is (x)?

Explanation opens after your attempt

Correct Answer

B. (32)

Step 1

Concept

Equal areas give (x(x+66)=56²). This gives (x=32).

Step 2

Why this answer is correct

The correct answer is B. (32). Equal areas give (x(x+66)=56²). This gives (x=32).

Step 3

Exam Tip

बराबर क्षेत्रफल से (x(x+66)=56²) बनता है। इससे (x=32) मिलता है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक वर्गाकार मैदान की भुजा (x) मीटर है। यदि भुजा (10) मीटर बढ़ाने पर क्षेत्रफल (1700) वर्ग मीटर बढ़ता है, तो (x) क्या है?

A square field has side (x) m. If increasing the side by (10) m increases the area by (1700) square m, what is (x)?

Explanation opens after your attempt

Correct Answer

B. (80)

Step 1

Concept

The area increase is ((x+10)²-x^-2=1700). This gives (20x+100=1700), so (x=80).

Step 2

Why this answer is correct

The correct answer is B. (80). The area increase is ((x+10)²-x^-2=1700). This gives (20x+100=1700), so (x=80).

Step 3

Exam Tip

क्षेत्रफल वृद्धि ((x+10)²-x^-2=1700) है। इससे (20x+100=1700), इसलिए (x=80) है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक वर्गाकार पार्क का क्षेत्रफल एक आयत के क्षेत्रफल के बराबर है। वर्ग की भुजा (48) मीटर है और आयत की चौड़ाई (x) तथा लंबाई (x+28) है। (x) क्या है?

A square park has the same area as a rectangle. The square side is (48) m and the rectangle has breadth (x) and length (x+28). What is (x)?

Explanation opens after your attempt

Correct Answer

D. (36)

Step 1

Concept

Equal areas give (x(x+28)=48²). This gives (x=36).

Step 2

Why this answer is correct

The correct answer is D. (36). Equal areas give (x(x+28)=48²). This gives (x=36).

Step 3

Exam Tip

बराबर क्षेत्रफल से (x(x+28)=48²) बनता है। इससे (x=36) मिलता है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक वर्गाकार मैदान की भुजा (x) मीटर है। यदि भुजा (8) मीटर बढ़ाने पर क्षेत्रफल (1216) वर्ग मीटर बढ़ता है, तो (x) क्या है?

A square field has side (x) m. If increasing the side by (8) m increases the area by (1216) square m, what is (x)?

Explanation opens after your attempt

Correct Answer

B. (72)

Step 1

Concept

The area increase is ((x+8)²-x^-2=1216). This gives (16x+64=1216), so (x=72).

Step 2

Why this answer is correct

The correct answer is B. (72). The area increase is ((x+8)²-x^-2=1216). This gives (16x+64=1216), so (x=72).

Step 3

Exam Tip

क्षेत्रफल वृद्धि ((x+8)²-x^-2=1216) है। इससे (16x+64=1216), इसलिए (x=72) है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक वर्गाकार पार्क का क्षेत्रफल एक आयत के क्षेत्रफल के बराबर है। वर्ग की भुजा (42) मीटर है और आयत की चौड़ाई (x) तथा लंबाई (x+20) है। (x) क्या है?

A square park has the same area as a rectangle. The square side is (42) m and the rectangle has breadth (x) and length (x+20). What is (x)?

Explanation opens after your attempt

Correct Answer

D. (34)

Step 1

Concept

Equal areas give (x(x+20)=42²). This gives (x=34).

Step 2

Why this answer is correct

The correct answer is D. (34). Equal areas give (x(x+20)=42²). This gives (x=34).

Step 3

Exam Tip

बराबर क्षेत्रफल से (x(x+20)=42²) बनता है। इससे (x=34) मिलता है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक वर्गाकार पार्क का क्षेत्रफल एक आयत के क्षेत्रफल के बराबर है। वर्ग की भुजा (30) मीटर है और आयत की चौड़ाई (x) तथा लंबाई (x+15) है। (x) क्या है?

A square park has the same area as a rectangle. The square side is (30) m and the rectangle has breadth (x) and length (x+15). What is (x)?

Explanation opens after your attempt

Correct Answer

B. (20)

Step 1

Concept

Equal areas give (x(x+15)=30²). This gives (x=20).

Step 2

Why this answer is correct

The correct answer is B. (20). Equal areas give (x(x+15)=30²). This gives (x=20).

Step 3

Exam Tip

बराबर क्षेत्रफल से (x(x+15)=30²) बनता है। इससे (x=20) मिलता है।

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Question Easy Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक वर्गाकार कार्ड और एक आयताकार कार्ड का क्षेत्रफल समान है। वर्ग की भुजा (18) सेमी है और आयत की चौड़ाई (12) सेमी है। आयत की लंबाई क्या है?

A square card and a rectangular card have equal area. The side of the square is (18) cm and the breadth of the rectangle is (12) cm. What is the length of the rectangle?

Explanation opens after your attempt

Correct Answer

C. (27) सेमी(27) cm

Step 1

Concept

The square area is \(18^2=324\), and (12x=324) gives (x=27). For equal areas, equate both areas.

Step 2

Why this answer is correct

The correct answer is C. (27) सेमी / (27) cm. The square area is \(18^2=324\), and (12x=324) gives (x=27). For equal areas, equate both areas.

Step 3

Exam Tip

वर्ग का क्षेत्रफल \(18^2=324\) है और (12x=324) से (x=27) है। समान क्षेत्रफल में दोनों क्षेत्रों को बराबर रखें।

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Question Easy Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

पूर्ण वर्ग बनाकर \(x^2+8x=0\) में \(x^2+8x+16\) किसके बराबर होगा?

By completing the square in \(x^2+8x=0\), what is \(x^2+8x+16\) equal to?

Explanation opens after your attempt

Correct Answer

A. ((x+4)²)

Step 1

Concept

(x^-2+8x+16=(x+4)²). In exams, take half of (8), which is (4), and add its square.

Step 2

Why this answer is correct

The correct answer is A. ((x+4)²). (x^-2+8x+16=(x+4)²). In exams, take half of (8), which is (4), and add its square.

Step 3

Exam Tip

(x^-2+8x+16=(x+4)²) होता है। परीक्षा में (8) का आधा (4) लेकर उसका वर्ग जोड़ें।

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Question Hard Mathematics Real Numbers Proof of irrationality of √2, √3, √5 Class 10 Level 18

कौन-सा विकल्प पूर्ण वर्ग न होने के कारण अपरिमेय वर्गमूल का सही उदाहरण है?

Which option is a correct example of an irrational square root because it is not a perfect square?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{5}\)

Step 1

Concept

(4,9,25) are perfect squares, so their square roots are integers.

Step 2

Why this answer is correct

(5) is not a perfect square, and \(\sqrt{5}\) is irrational.

Step 3

Exam Tip

In options, identify perfect squares first. चरण 1: (4,9,25) पूर्ण वर्ग हैं, इसलिए उनके वर्गमूल पूर्णांक हैं। चरण 2: (5) पूर्ण वर्ग नहीं है और \(\sqrt{5}\) अपरिमेय है। चरण 3: विकल्पों में पहले पूर्ण वर्ग पहचानें।

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Question Easy Mathematics Real Numbers Proof of irrationality of √2, √3, √5 Class 10 Level 18

कौन सा वर्गमूल परिमेय है, इसलिए उस पर \(\sqrt{2}\) जैसी अपरिमेयता सिद्धि लागू नहीं होती?

Which square root is rational, so an irrationality proof like \(\sqrt{2}\) does not apply to it?

Explanation opens after your attempt

Correct Answer

C. \(\sqrt{4}\)

Step 1

Concept

(4) is a perfect square.

Step 2

Why this answer is correct

\(\sqrt{4}=2\), which is rational.

Step 3

Exam Tip

Square roots of perfect squares are rational. चरण 1: (4) पूर्ण वर्ग है। चरण 2: \(\sqrt{4}=2\), जो परिमेय संख्या है। चरण 3: पूर्ण वर्गों के वर्गमूल परिमेय होते हैं।

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Question Easy Mathematics Real Numbers Proof of irrationality of √2, √3, √5 Class 10 Level 17

कौन सा वर्गमूल इस अध्याय की अपरिमेयता सिद्धि का उदाहरण नहीं है क्योंकि वह परिमेय है?

Which square root is not an example of irrationality proof in this chapter because it is rational?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{9}\)

Step 1

Concept

(9) is a perfect square.

Step 2

Why this answer is correct

\(\sqrt{9}=3\), which is rational.

Step 3

Exam Tip

A square root of a perfect square does not need an irrationality proof. चरण 1: (9) पूर्ण वर्ग है। चरण 2: \(\sqrt{9}=3\), जो परिमेय है। चरण 3: पूर्ण वर्ग के वर्गमूल को अपरिमेय सिद्ध करने की जरूरत नहीं होती।

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Question Easy Mathematics Real Numbers Proof of irrationality of √2, √3, √5 Class 10 Level 16

कौन सा वर्गमूल परिमेय है, इसलिए \(\sqrt{2}\), \(\sqrt{3}\), \(\sqrt{5}\) जैसी सिद्धि की जरूरत नहीं है?

Which square root is rational, so it does not need a proof like \(\sqrt{2}\), \(\sqrt{3}\), or \(\sqrt{5}\)?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{4}\)

Step 1

Concept

(4) is a perfect square.

Step 2

Why this answer is correct

\(\sqrt{4}=2\), which is rational.

Step 3

Exam Tip

The square root of a perfect square is not proved irrational. चरण 1: (4) पूर्ण वर्ग है। चरण 2: \(\sqrt{4}=2\), जो परिमेय संख्या है। चरण 3: पूर्ण वर्ग के वर्गमूल को अपरिमेय सिद्ध नहीं करते।

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Question Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{13}\) का वर्ग किसके बराबर है?

The square of \(\sqrt{13}\) is equal to what?

Explanation opens after your attempt

Correct Answer

C. (13)

Step 1

Concept

Squaring a square root gives the number inside it.

Step 2

Why this answer is correct

(\(\sqrt{13}\)²=13).

Step 3

Exam Tip

Apply (\(\sqrt{a}\)²=a) directly. चरण 1: वर्गमूल का वर्ग करने पर अंदर की संख्या मिलती है। चरण 2: (\(\sqrt{13}\)²=13)। चरण 3: (\(\sqrt{a}\)²=a) को सीधे लागू करें।

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Question Expert Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 62

यदि किसी समांतर श्रेणी का सामान्य अंतर (7) है और प्रत्येक पद से (12) घटाया जाए, तो नया सामान्य अंतर क्या होगा?

If an AP has common difference (7) and (12) is subtracted from every term, what is the new common difference?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

Subtracting the same number from every term does not change the difference. In exams, treat uniform subtraction as changing only the first term.

Step 2

Why this answer is correct

The correct answer is B. (7). Subtracting the same number from every term does not change the difference. In exams, treat uniform subtraction as changing only the first term.

Step 3

Exam Tip

हर पद से समान संख्या घटाने पर अंतर नहीं बदलता। परीक्षा में समान घटाव को केवल पहला पद बदलने वाला समझें।

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Question Expert Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 62

एक समांतर श्रेणी का सामान्य अंतर (d) है। हर पद को (-3) से गुणा करने पर नया सामान्य अंतर क्या होगा?

An AP has common difference (d). If every term is multiplied by (-3), what is the new common difference?

Explanation opens after your attempt

Correct Answer

B. (-3d)

Step 1

Concept

Multiplication scales all differences by the same factor, so the new difference is (-3d). In exams, apply the transformation to the difference.

Step 2

Why this answer is correct

The correct answer is B. (-3d). Multiplication scales all differences by the same factor, so the new difference is (-3d). In exams, apply the transformation to the difference.

Step 3

Exam Tip

गुणन से सभी अंतर उसी गुणक से गुणा होते हैं, इसलिए नया अंतर (-3d) है। परीक्षा में रूपांतरण का असर अंतर पर लगाएं।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

यदि \(5,12,19,26,\ldots\) में हर दूसरा पद चुना जाए तो बने अनुक्रम का सार्व अंतर क्या होगा?

If every second term is selected from \(5,12,19,26,\ldots\), what will be the common difference of the formed sequence?

Explanation opens after your attempt

Correct Answer

C. (14)

Step 1

Concept

The selected sequence is \(5,19,33,\ldots\), and its difference is (14). Selecting every second term makes the new (d) twice the original (d).

Step 2

Why this answer is correct

The correct answer is C. (14). The selected sequence is \(5,19,33,\ldots\), and its difference is (14). Selecting every second term makes the new (d) twice the original (d).

Step 3

Exam Tip

चुना गया अनुक्रम \(5,19,33,\ldots\) होगा और इसका अंतर (14) है। हर दूसरा पद लेने पर नया (d) मूल (d) का (2) गुना होता है।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

यदि \(3,8,13,\ldots\) में प्रत्येक पद से (4n) घटाया जाए तो नया सार्व अंतर क्या होगा?

If (4n) is subtracted from each term of \(3,8,13,\ldots\), what will be the new common difference?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

The original (d=5), and (4n) has (d=4), so the new (d=1). In term-number changes, subtract its difference.

Step 2

Why this answer is correct

The correct answer is A. (1). The original (d=5), and (4n) has (d=4), so the new (d=1). In term-number changes, subtract its difference.

Step 3

Exam Tip

मूल (d=5) है और (4n) का (d=4) है, इसलिए नया (d=1)। पद संख्या से जुड़े परिवर्तन में उसके अंतर को घटाएं।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

यदि \(8,13,18,\ldots\) और \(4,10,16,\ldots\) के पद-दर-पद अंतर से अनुक्रम बने तो उसका (d) क्या होगा?

If a sequence is formed by termwise difference of \(8,13,18,\ldots\) and \(4,10,16,\ldots\), what will be its (d)?

Explanation opens after your attempt

Correct Answer

A. (-1)

Step 1

Concept

The first sequence has (d=5) and the second has (d=6), so the difference sequence has (d=5-6=-1). In termwise difference, take the difference of common differences.

Step 2

Why this answer is correct

The correct answer is A. (-1). The first sequence has (d=5) and the second has (d=6), so the difference sequence has (d=5-6=-1). In termwise difference, take the difference of common differences.

Step 3

Exam Tip

पहले अनुक्रम का (d=5) और दूसरे का (d=6) है, इसलिए अंतर अनुक्रम का (d=5-6=-1)। पद-दर-पद अंतर में सार्व अंतरों का अंतर लें।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

यदि (a,a+d,a+2d) के तीनों पदों में क्रमशः (3,6,9) जोड़े जाएं तो नया सार्व अंतर क्या होगा?

If (3,6,9) are added respectively to (a,a+d,a+2d), what will be the new common difference?

Explanation opens after your attempt

Correct Answer

C. (d+3)

Step 1

Concept

The new terms are (a+3,a+d+6,a+2d+9), and both differences are (d+3). The difference of the added numbers is added to (d).

Step 2

Why this answer is correct

The correct answer is C. (d+3). The new terms are (a+3,a+d+6,a+2d+9), and both differences are (d+3). The difference of the added numbers is added to (d).

Step 3

Exam Tip

नए पद (a+3,a+d+6,a+2d+9) हैं और दोनों अंतर (d+3) हैं। क्रमशः बढ़ते जोड़ का अंतर (d) में जुड़ता है।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

एक अंकगणितीय श्रेणी में पांचवें और पहले पद का अंतर (-20) है। सार्व अंतर क्या है?

In an arithmetic progression, the difference between the fifth and first terms is (-20). What is the common difference?

Explanation opens after your attempt

Correct Answer

B. (-5)

Step 1

Concept

From the first to the fifth term there are (4) gaps, so (4d=-20) and (d=-5). In a decreasing progression, (d) is negative.

Step 2

Why this answer is correct

The correct answer is B. (-5). From the first to the fifth term there are (4) gaps, so (4d=-20) and (d=-5). In a decreasing progression, (d) is negative.

Step 3

Exam Tip

पहले से पांचवें पद तक (4) अंतर हैं, इसलिए (4d=-20) और (d=-5)। घटती श्रेणी में (d) ऋणात्मक होता है।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

अनुक्रम \(0.6,1.05,1.50,1.95,\ldots\) का सार्व अंतर क्या है?

What is the common difference of the sequence \(0.6,1.05,1.50,1.95,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (0.45)

Step 1

Concept

(1.05-0.60=0.45) and (1.50-1.05=0.45). Adding zeros makes decimal subtraction safer.

Step 2

Why this answer is correct

The correct answer is C. (0.45). (1.05-0.60=0.45) and (1.50-1.05=0.45). Adding zeros makes decimal subtraction safer.

Step 3

Exam Tip

(1.05-0.60=0.45) और (1.50-1.05=0.45) है। दशमलव में शून्य लगाकर घटाना सुरक्षित है।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

यदि \(24,20,16,12,\ldots\) के प्रत्येक पद में (7) जोड़ा जाए तो नए अनुक्रम का सार्व अंतर क्या होगा?

If (7) is added to each term of \(24,20,16,12,\ldots\), what will be the common difference of the new sequence?

Explanation opens after your attempt

Correct Answer

B. (-4)

Step 1

Concept

Adding the same number to all terms does not change the common difference. The original (d=20-24=-4), so the new (d) remains (-4).

Step 2

Why this answer is correct

The correct answer is B. (-4). Adding the same number to all terms does not change the common difference. The original (d=20-24=-4), so the new (d) remains (-4).

Step 3

Exam Tip

सभी पदों में समान संख्या जोड़ने से सार्व अंतर नहीं बदलता। मूल (d=20-24=-4) है, इसलिए नया (d=-4) ही रहेगा।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

अनुक्रम \(\frac{3}{8},\frac{5}{8},\frac{7}{8},\frac{9}{8},\ldots\) का सार्व अंतर क्या है?

What is the common difference of the sequence \(\frac{3}{8},\frac{5}{8},\frac{7}{8},\frac{9}{8},\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(\frac{1}{4}\)

Step 1

Concept

\(\frac{5}{8}-\frac{3}{8}=\frac{2}{8}=\frac{1}{4}\). When denominators are equal, subtract the numerators.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{1}{4}\). \(\frac{5}{8}-\frac{3}{8}=\frac{2}{8}=\frac{1}{4}\). When denominators are equal, subtract the numerators.

Step 3

Exam Tip

\(\frac{5}{8}-\frac{3}{8}=\frac{2}{8}=\frac{1}{4}\) है। भिन्नों में समान हर होने पर अंशों का अंतर लें।

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Question Expert Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

यदि (a,a+d,a+2d) के तीनों पदों में क्रमशः (2,4,6) जोड़े जाएं, तो नया सार्व अंतर क्या होगा?

If (2,4,6) are added respectively to (a,a+d,a+2d), what will be the new common difference?

Explanation opens after your attempt

Correct Answer

C. (d+2)

Step 1

Concept

The new terms are (a+2, a+d+4, a+2d+6), and both differences are (d+2). The difference (2) of the added numbers is also added to (d).

Step 2

Why this answer is correct

The correct answer is C. (d+2). The new terms are (a+2, a+d+4, a+2d+6), and both differences are (d+2). The difference (2) of the added numbers is also added to (d).

Step 3

Exam Tip

नए पद (a+2, a+d+4, a+2d+6) हैं और दोनों अंतर (d+2) हैं। क्रमशः बढ़ते जोड़ का अंतर (2) भी (d) में जुड़ता है।

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Question Expert Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

एक अंकगणितीय श्रेणी में पांचवें और दूसरे पद का अंतर (-18) है। (d) क्या होगा?

In an arithmetic progression, the difference between the fifth and second terms is (-18). What will (d) be?

Explanation opens after your attempt

Correct Answer

B. (-6)

Step 1

Concept

From the second to the fifth term there are (3) gaps, so (3d=-18) and (d=-6). In a decreasing progression, (d) remains negative.

Step 2

Why this answer is correct

The correct answer is B. (-6). From the second to the fifth term there are (3) gaps, so (3d=-18) and (d=-6). In a decreasing progression, (d) remains negative.

Step 3

Exam Tip

दूसरे से पांचवें पद तक (3) अंतर हैं, इसलिए (3d=-18) और (d=-6)। घटती श्रेणी में (d) ऋणात्मक रहता है।

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Question Expert Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

एक अंकगणितीय श्रेणी में तीसरे और सातवें पद का अंतर (28) है। सार्व अंतर क्या है?

In an arithmetic progression, the difference between the third and seventh terms is (28). What is the common difference?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

From the third to the seventh term there are (4) gaps, so (4d=28) and (d=7). Convert term distance into number of gaps.

Step 2

Why this answer is correct

The correct answer is C. (7). From the third to the seventh term there are (4) gaps, so (4d=28) and (d=7). Convert term distance into number of gaps.

Step 3

Exam Tip

तीसरे से सातवें पद तक (4) अंतर होते हैं, इसलिए (4d=28) और (d=7)। पदों की दूरी को अंतरालों की संख्या में बदलें।

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Question Expert Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

अनुक्रम \(-\frac{7}{4}, -1, -\frac{1}{4}, \frac{1}{2},\ldots\) में सार्व अंतर क्या है?

What is the common difference in the sequence \(-\frac{7}{4}, -1, -\frac{1}{4}, \frac{1}{2},\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(\frac{3}{4}\)

Step 1

Concept

(-1-\left\(-\frac{7}{4}\right\)=\frac{3}{4}), and the next difference is also \(\frac{3}{4}\). Be careful while subtracting negative fractions.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{3}{4}\). (-1-\left\(-\frac{7}{4}\right\)=\frac{3}{4}), and the next difference is also \(\frac{3}{4}\). Be careful while subtracting negative fractions.

Step 3

Exam Tip

(-1-\left\(-\frac{7}{4}\right\)=\frac{3}{4}) और अगला अंतर भी \(\frac{3}{4}\) है। ऋणात्मक भिन्नों में घटाव सावधानी से करें।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (4p+1, 6p-3, 9p-10) समांतर श्रेणी में हैं, तो (p) और सामान्य अंतर का सही युग्म कौन-सा है?

If (4p+1, 6p-3, 9p-10) are in an arithmetic progression, which pair of (p) and common difference is correct?

Explanation opens after your attempt

Correct Answer

B. (p=3, d=2)

Step 1

Concept

The differences are (2p-4) and (3p-7). Equating them gives (p=3), so (d=2).

Step 2

Why this answer is correct

The correct answer is B. (p=3, d=2). The differences are (2p-4) and (3p-7). Equating them gives (p=3), so (d=2).

Step 3

Exam Tip

अंतर (2p-4) और (3p-7) हैं। बराबर करने पर (p=3), इसलिए (d=2).

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (13, 2x+1, 4x-5) समांतर श्रेणी में हैं, तो सामान्य अंतर क्या है?

If (13, 2x+1, 4x-5) are in an arithmetic progression, what is the common difference?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

From (2(2x+1)=13+(4x-5)), we get (2=8), which is impossible. Therefore no such common difference exists.

Step 2

Why this answer is correct

The correct answer is C. (7). From (2(2x+1)=13+(4x-5)), we get (2=8), which is impossible. Therefore no such common difference exists.

Step 3

Exam Tip

(2(2x+1)=13+(4x-5)) से (2=8) असंभव है। इसलिए ऐसा सामान्य अंतर नहीं होगा।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (3, 3+2m, 3+4m, 3+6m) समांतर श्रेणी है, तो सामान्य अंतर क्या है?

If (3, 3+2m, 3+4m, 3+6m) is an arithmetic progression, what is the common difference?

Explanation opens after your attempt

Correct Answer

B. (2m)

Step 1

Concept

Each time (2m) is added. Therefore the common difference is (2m).

Step 2

Why this answer is correct

The correct answer is B. (2m). Each time (2m) is added. Therefore the common difference is (2m).

Step 3

Exam Tip

हर बार (2m) जुड़ रहा है। इसलिए सामान्य अंतर (2m) है।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

किस विकल्प में दिए गए पद समांतर श्रेणी हैं लेकिन सामान्य अंतर (0) है?

In which option do the terms form an arithmetic progression with common difference (0)?

Explanation opens after your attempt

Correct Answer

A. (6, 6, 6, 6)

Step 1

Concept

When all terms are equal, every difference is (0). A constant sequence is also an arithmetic progression.

Step 2

Why this answer is correct

The correct answer is A. (6, 6, 6, 6). When all terms are equal, every difference is (0). A constant sequence is also an arithmetic progression.

Step 3

Exam Tip

सभी पद समान हों तो हर अंतर (0) होता है। स्थिर क्रम भी समांतर श्रेणी होता है।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

क्रम \(101, 97, 93, 89, \ldots\) में सामान्य अंतर क्या है और यह कैसा है?

In the sequence \(101, 97, 93, 89, \ldots\), what is the common difference and what is its nature?

Explanation opens after your attempt

Correct Answer

B. (-4), ऋणात्मक(-4), negative

Step 1

Concept

Each next term is (4) less than the previous one, so (d=-4). A decreasing arithmetic progression has a negative common difference.

Step 2

Why this answer is correct

The correct answer is B. (-4), ऋणात्मक / (-4), negative. Each next term is (4) less than the previous one, so (d=-4). A decreasing arithmetic progression has a negative common difference.

Step 3

Exam Tip

हर अगला पद पिछले से (4) कम है, इसलिए (d=-4). घटती समांतर श्रेणी में सामान्य अंतर ऋणात्मक होता है।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

किस क्रम में सामान्य अंतर \(\frac{3}{4}\) है?

Which sequence has common difference \(\frac{3}{4}\)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{1}{4}, 1, \frac{7}{4}, \frac{5}{2}\)

Step 1

Concept

In the first option, every consecutive difference is \(\frac{3}{4}\). With fractions, using common denominators is the safer method.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{1}{4}, 1, \frac{7}{4}, \frac{5}{2}\). In the first option, every consecutive difference is \(\frac{3}{4}\). With fractions, using common denominators is the safer method.

Step 3

Exam Tip

पहले विकल्प में हर लगातार अंतर \(\frac{3}{4}\) है। भिन्नों में हर को समान बनाकर अंतर निकालना सुरक्षित तरीका है।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

क्रम (4x-3, 3x+5, x+21) समांतर श्रेणी में है। सामान्य अंतर क्या है?

The sequence (4x-3, 3x+5, x+21) is in an arithmetic progression. What is the common difference?

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

The differences are (-x+8) and (-2x+16). Equating them gives (x=8), so (d=0), not (8).

Step 2

Why this answer is correct

The correct answer is A. (8). The differences are (-x+8) and (-2x+16). Equating them gives (x=8), so (d=0), not (8).

Step 3

Exam Tip

अंतर (-x+8) और (-2x+16) हैं। बराबर करने पर (x=8), इसलिए (d=0) नहीं बल्कि (d=0) आता है।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (6, h, 30) समांतर श्रेणी में हैं, तो (h) और सामान्य अंतर का सही युग्म कौन-सा है?

If (6, h, 30) are in an arithmetic progression, which pair of (h) and common difference is correct?

Explanation opens after your attempt

Correct Answer

B. (h=18, d=12)

Step 1

Concept

The middle term is \(\frac{6+30}{2}=18\). The common difference is (18-6=12).

Step 2

Why this answer is correct

The correct answer is B. (h=18, d=12). The middle term is \(\frac{6+30}{2}=18\). The common difference is (18-6=12).

Step 3

Exam Tip

बीच का पद \(\frac{6+30}{2}=18\) है। सामान्य अंतर (18-6=12) है।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (14, 14-d, 14-2d, 14-3d) समांतर श्रेणी है, तो सामान्य अंतर क्या है?

If (14, 14-d, 14-2d, 14-3d) is an arithmetic progression, what is the common difference?

Explanation opens after your attempt

Correct Answer

B. (-d)

Step 1

Concept

Each next term is (d) less than the previous term. Therefore the common difference is (-d).

Step 2

Why this answer is correct

The correct answer is B. (-d). Each next term is (d) less than the previous term. Therefore the common difference is (-d).

Step 3

Exam Tip

हर अगला पद पिछले पद से (d) कम है। इसलिए सामान्य अंतर (-d) है।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (9, y, 2y+6) समांतर श्रेणी में हैं, तो सामान्य अंतर क्या है?

If (9, y, 2y+6) are in an arithmetic progression, what is the common difference?

Explanation opens after your attempt

Correct Answer

B. (15)

Step 1

Concept

From (2y=9+(2y+6)), we get (0=15), so it never forms an arithmetic progression. None of the listed values can be its common difference.

Step 2

Why this answer is correct

The correct answer is B. (15). From (2y=9+(2y+6)), we get (0=15), so it never forms an arithmetic progression. None of the listed values can be its common difference.

Step 3

Exam Tip

(2y=9+(2y+6)) से (0=15) नहीं, इसलिए यह कभी समांतर श्रेणी नहीं बनती। सही विकल्पों में ऐसा कोई सामान्य अंतर नहीं है।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

किस क्रम का सामान्य अंतर ऋणात्मक है और सभी लगातार अंतर बराबर हैं?

Which sequence has a negative common difference and all consecutive differences equal?

Explanation opens after your attempt

Correct Answer

B. (20, 16, 12, 8)

Step 1

Concept

In (20,16,12,8), (4) is subtracted each time, so (d=-4). Do not just see decreasing order; check equal differences too.

Step 2

Why this answer is correct

The correct answer is B. (20, 16, 12, 8). In (20,16,12,8), (4) is subtracted each time, so (d=-4). Do not just see decreasing order; check equal differences too.

Step 3

Exam Tip

(20,16,12,8) में हर बार (4) घटता है, इसलिए (d=-4). केवल घटते क्रम को देखकर नहीं, बराबर अंतर भी जांचें।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (p-4, 2p+1, 4p-2) समांतर श्रेणी में हैं, तो सामान्य अंतर क्या होगा?

If (p-4, 2p+1, 4p-2) are in an arithmetic progression, what will be the common difference?

Explanation opens after your attempt

Correct Answer

B. (13)

Step 1

Concept

First, (2(2p+1)=(p-4)+(4p-2)) gives (p=8). Then the common difference is ((2p+1)-(p-4)=13).

Step 2

Why this answer is correct

The correct answer is B. (13). First, (2(2p+1)=(p-4)+(4p-2)) gives (p=8). Then the common difference is ((2p+1)-(p-4)=13).

Step 3

Exam Tip

पहले (2(2p+1)=(p-4)+(4p-2)) से (p=8) मिलता है। तब सामान्य अंतर ((2p+1)-(p-4)=13) है।

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 62

यदि \(6, 10, 14,\ldots\) और \(3, 8, 13,\ldots\) के पद-दर-पद अंतर से अनुक्रम बने, तो वह कैसा होगा?

If a sequence is formed by termwise difference of \(6, 10, 14,\ldots\) and \(3, 8, 13,\ldots\), what type will it be?

Explanation opens after your attempt

Correct Answer

A. (d=-1) वाली अंकगणितीय श्रेणीArithmetic progression with (d=-1)

Step 1

Concept

The first has (d=4) and the second has (d=5), so the difference sequence has (d=4-5=-1). The termwise difference of two arithmetic progressions is also an arithmetic progression.

Step 2

Why this answer is correct

The correct answer is A. (d=-1) वाली अंकगणितीय श्रेणी / Arithmetic progression with (d=-1). The first has (d=4) and the second has (d=5), so the difference sequence has (d=4-5=-1). The termwise difference of two arithmetic progressions is also an arithmetic progression.

Step 3

Exam Tip

पहले (d=4) और दूसरे (d=5) हैं, इसलिए अंतर अनुक्रम का (d=4-5=-1)। दो अंकगणितीय श्रेणियों का पद-दर-पद अंतर भी अंकगणितीय श्रेणी होता है।

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अनुक्रम \(5,12,19,26,\ldots\) में पहले दो पदों का अंतर और तीसरे-चौथे पदों का अंतर क्या है?

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एक वर्गाकार मैदान की भुजा (4) मीटर बढ़ाने पर क्षेत्रफल (96) वर्ग मीटर बढ़ जाता है। मूल भुजा कितनी थी?

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Concept

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Exam Tip

एक तार को वर्ग के रूप में मोड़ने पर क्षेत्रफल (3025) वर्ग सेमी है। तार की लंबाई क्या है?

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Exam Tip

एक वर्ग की भुजा (x) सेमी है। भुजा (9) सेमी घटाने पर क्षेत्रफल (1681) वर्ग सेमी हो जाता है। मूल भुजा क्या है?

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एक वर्गाकार टाइल की भुजा (x-12) सेमी है और क्षेत्रफल (1849) वर्ग सेमी है। (x) क्या है?

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Exam Tip

एक वर्ग की भुजा (x+17) सेमी है। उसका क्षेत्रफल (3249) वर्ग सेमी है। (x) का मान क्या है?

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Exam Tip

एक तार को वर्ग के रूप में मोड़ने पर क्षेत्रफल (2025) वर्ग सेमी है। तार की लंबाई क्या है?

Concept

Why this answer is correct

Exam Tip

एक वर्ग की भुजा (x) सेमी है। भुजा (7) सेमी घटाने पर क्षेत्रफल (1296) वर्ग सेमी हो जाता है। मूल भुजा क्या है?

Concept

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Exam Tip

एक वर्गाकार टाइल की भुजा (x-13) सेमी है और क्षेत्रफल (1600) वर्ग सेमी है। (x) क्या है?

Concept

Why this answer is correct

Exam Tip

एक वर्ग की भुजा (x+12) सेमी है। उसका क्षेत्रफल (1764) वर्ग सेमी है। (x) का मान क्या है?

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Exam Tip

Concept

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Exam Tip

एक तार को वर्ग के रूप में मोड़ने पर क्षेत्रफल (1296) वर्ग सेमी है। तार की लंबाई क्या है?

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एक वर्ग की भुजा (x) सेमी है। भुजा (5) सेमी घटाने पर क्षेत्रफल (784) वर्ग सेमी हो जाता है। मूल भुजा क्या है?

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एक वर्गाकार टाइल की भुजा (x-8) सेमी है और क्षेत्रफल (900) वर्ग सेमी है। (x) क्या है?

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एक वर्ग की भुजा (x+6) सेमी है। उसका क्षेत्रफल (1225) वर्ग सेमी है। (x) का मान क्या है?

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Exam Tip

एक वर्ग का क्षेत्रफल उसके परिमाप से (96) अधिक है। वर्ग की भुजा क्या है?

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Exam Tip

एक तार को वर्ग के रूप में मोड़ने पर क्षेत्रफल (625) वर्ग सेमी है। तार की लंबाई क्या है?

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एक वर्ग की भुजा (x) सेमी है। भुजा (3) सेमी घटाने पर क्षेत्रफल (225) वर्ग सेमी हो जाता है। मूल भुजा क्या है?

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