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100 results found for "2y square" in Class 10.

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 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 Medium Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 1

किस कारण से वर्ग को ज्यामितीय आकार कहा जाता है?

Why is a square called a geometric shape?

Explanation opens after your attempt
Correct Answer

C. क्योंकि उसकी भुजाएं और कोण नियमित होते हैंBecause its sides and angles are regular

Step 1

Concept

A square is a regular rule-based shape. Exam tip: treat measured and regular shapes as geometric.

Step 2

Why this answer is correct

The correct answer is C. क्योंकि उसकी भुजाएं और कोण नियमित होते हैं / Because its sides and angles are regular. A square is a regular rule-based shape. Exam tip: treat measured and regular shapes as geometric.

Step 3

Exam Tip

वर्ग नियमित नियमों वाला आकार है। परीक्षा में measured and regular shapes को geometric मानें।

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Question Easy Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 1

वर्ग और आयत किस प्रकार के आकार हैं?

Square and rectangle are which type of shapes?

Explanation opens after your attempt
Correct Answer

C. ज्यामितीय आकारGeometric shapes

Step 1

Concept

Square and rectangle are geometric shapes with clear rules. Exam tip: understand regular shapes as geometric.

Step 2

Why this answer is correct

The correct answer is C. ज्यामितीय आकार / Geometric shapes. Square and rectangle are geometric shapes with clear rules. Exam tip: understand regular shapes as geometric.

Step 3

Exam Tip

वर्ग और आयत स्पष्ट नियमों वाले ज्यामितीय आकार हैं। परीक्षा में नियमित आकार को ज्यामितीय समझें।

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Question Easy Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 1

वृत्त वर्ग और त्रिभुज किसके उदाहरण हैं?

Circle square and triangle are examples of what?

Explanation opens after your attempt
Correct Answer

B. आकारShape

Step 1

Concept

Circle square and triangle are geometric shapes. Exam tip: call closed flat figures shapes.

Step 2

Why this answer is correct

The correct answer is B. आकार / Shape. Circle square and triangle are geometric shapes. Exam tip: call closed flat figures shapes.

Step 3

Exam Tip

वृत्त वर्ग और त्रिभुज ज्यामितीय आकार हैं। परीक्षा में बंद समतल आकृतियों को आकार कहें।

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Question Medium General Knowledge World History World Heritage Sites Class 10 Level 82

क्रेमलिन और रेड स्क्वायर किस रूसी पहचान का प्रतीक हैं?

The Kremlin and Red Square are symbols of which Russian identity?

Explanation opens after your attempt
Correct Answer

B. राजनीतिक सत्ता और ऐतिहासिक केंद्रPolitical power and historic center

Step 1

Concept

The Kremlin and Red Square show Moscow's political and historical importance. For exams remember Russia and Moscow.

Step 2

Why this answer is correct

The correct answer is B. राजनीतिक सत्ता और ऐतिहासिक केंद्र / Political power and historic center. The Kremlin and Red Square show Moscow's political and historical importance. For exams remember Russia and Moscow.

Step 3

Exam Tip

क्रेमलिन और रेड स्क्वायर मॉस्को के राजनीतिक और ऐतिहासिक महत्व को दिखाते हैं। परीक्षा में रूस और मॉस्को याद रखें।

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Question Easy General Knowledge World History World Heritage Sites Class 10 Level 82

क्रेमलिन और रेड स्क्वायर किस शहर में स्थित हैं?

The Kremlin and Red Square are located in which city?

Explanation opens after your attempt
Correct Answer

D. मॉस्कोMoscow

Step 1

Concept

The Kremlin and Red Square are located in Moscow. For exams remember Russia's political and historical heritage.

Step 2

Why this answer is correct

The correct answer is D. मॉस्को / Moscow. The Kremlin and Red Square are located in Moscow. For exams remember Russia's political and historical heritage.

Step 3

Exam Tip

क्रेमलिन और रेड स्क्वायर मॉस्को में स्थित हैं। परीक्षा में रूस की राजनीतिक और ऐतिहासिक धरोहर याद रखें।

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Question Expert General Knowledge World History Important Historical Events Class 10 Level 74

तियानआनमेन स्क्वायर घटना आर्थिक सुधार और राजनीतिक नियंत्रण के संबंध में कौन सा प्रश्न उठाती है?

What question does the Tiananmen Square incident raise about economic reform and political control?

Explanation opens after your attempt
Correct Answer

A. क्या आर्थिक खुलापन अपने आप राजनीतिक खुलापन लाता हैWhether economic openness automatically brings political openness

Step 1

Concept

The Tiananmen incident shows that economic change and political control can coexist. For exams understand modern Chinese context.

Step 2

Why this answer is correct

The correct answer is A. क्या आर्थिक खुलापन अपने आप राजनीतिक खुलापन लाता है / Whether economic openness automatically brings political openness. The Tiananmen incident shows that economic change and political control can coexist. For exams understand modern Chinese context.

Step 3

Exam Tip

तियानआनमेन घटना दिखाती है कि आर्थिक बदलाव और राजनीतिक नियंत्रण साथ चल सकते हैं। परीक्षा में चीन का आधुनिक संदर्भ समझें।

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Question Expert General Knowledge World History Important Historical Events Class 10 Level 72

तियानआनमेन स्क्वायर घटना आर्थिक सुधार और राजनीतिक सुधार के संबंध में कौन सा सवाल उठाती है?

What question does the Tiananmen Square incident raise about economic reform and political reform?

Explanation opens after your attempt
Correct Answer

A. क्या आर्थिक खुलापन अपने आप राजनीतिक खुलापन लाता हैWhether economic openness automatically brings political openness

Step 1

Concept

The Tiananmen incident shows economic change and political control can coexist. For exams understand modern Chinese context.

Step 2

Why this answer is correct

The correct answer is A. क्या आर्थिक खुलापन अपने आप राजनीतिक खुलापन लाता है / Whether economic openness automatically brings political openness. The Tiananmen incident shows economic change and political control can coexist. For exams understand modern Chinese context.

Step 3

Exam Tip

तियानआनमेन घटना दिखाती है कि आर्थिक बदलाव और राजनीतिक नियंत्रण साथ चल सकते हैं। परीक्षा में चीन के आधुनिक संदर्भ को समझें।

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Question Hard General Knowledge World History Important Historical Events Class 10 Level 72

तियानआनमेन स्क्वायर घटना आधुनिक चीन में किस तनाव को दिखाती है?

The Tiananmen Square incident shows which tension in modern China?

Explanation opens after your attempt
Correct Answer

A. राजनीतिक उदारीकरण की मांग और राज्य नियंत्रण के बीच तनावTension between demand for political liberalization and state control

Step 1

Concept

The Tiananmen incident shows complexity of modern Chinese politics. For exams connect it with civic demands and state response.

Step 2

Why this answer is correct

The correct answer is A. राजनीतिक उदारीकरण की मांग और राज्य नियंत्रण के बीच तनाव / Tension between demand for political liberalization and state control. The Tiananmen incident shows complexity of modern Chinese politics. For exams connect it with civic demands and state response.

Step 3

Exam Tip

तियानआनमेन घटना आधुनिक चीनी राजनीति की जटिलता दिखाती है। परीक्षा में इसे नागरिक मांग और राज्य प्रतिक्रिया से जोड़ें।

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Question Medium General Knowledge World History Important Historical Events Class 10 Level 72

तियानआनमेन स्क्वायर घटना आधुनिक चीन के अध्ययन में क्यों महत्वपूर्ण है?

Why is the Tiananmen Square incident important in studying modern China?

Explanation opens after your attempt
Correct Answer

A. यह राजनीतिक सुधार मांगों और राज्य नियंत्रण के तनाव को दिखाती हैIt shows tension between demands for political reform and state control

Step 1

Concept

The Tiananmen incident is linked with modern Chinese politics and civic demands. For exams remember it with balanced context.

Step 2

Why this answer is correct

The correct answer is A. यह राजनीतिक सुधार मांगों और राज्य नियंत्रण के तनाव को दिखाती है / It shows tension between demands for political reform and state control. The Tiananmen incident is linked with modern Chinese politics and civic demands. For exams remember it with balanced context.

Step 3

Exam Tip

तियानआनमेन घटना आधुनिक चीन की राजनीति और नागरिक मांगों से जुड़ी है। परीक्षा में इसे संतुलित संदर्भ से याद रखें।

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Question Easy General Knowledge World History Important Historical Events Class 10 Level 73

तियानआनमेन स्क्वायर घटना किस देश से जुड़ी है?

The Tiananmen Square incident is related to which country?

Explanation opens after your attempt
Correct Answer

A. चीनChina

Step 1

Concept

The Tiananmen Square incident is related to China. For exams remember it as an important event in modern Chinese history.

Step 2

Why this answer is correct

The correct answer is A. चीन / China. The Tiananmen Square incident is related to China. For exams remember it as an important event in modern Chinese history.

Step 3

Exam Tip

तियानआनमेन स्क्वायर घटना चीन से जुड़ी है। परीक्षा में इसे आधुनिक चीनी इतिहास की महत्वपूर्ण घटना के रूप में याद रखें।

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Question Medium General Knowledge World History Revolutions of the World Class 10 Level 58

अरब स्प्रिंग में मिस्र का तहरीर चौक क्यों प्रतीकात्मक बना?

Why did Egypt's Tahrir Square become symbolic in the Arab Spring?

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Correct Answer

A. वह बड़े जन विरोध और राजनीतिक मांगों का केंद्र बनाIt became a center of mass protest and political demands

Step 1

Concept

Tahrir Square gave visible and organized form to public protest. For exams remember symbolic importance of places.

Step 2

Why this answer is correct

The correct answer is A. वह बड़े जन विरोध और राजनीतिक मांगों का केंद्र बना / It became a center of mass protest and political demands. Tahrir Square gave visible and organized form to public protest. For exams remember symbolic importance of places.

Step 3

Exam Tip

तहरीर चौक ने जनता के विरोध को दृश्य और संगठित रूप दिया। परीक्षा में स्थानों का प्रतीकात्मक महत्व याद 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 Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=x-2+kx+25) पूर्ण वर्ग बहुपद है और (k<0), तो (k) क्या है?

If (p(x)=x-2+kx+25) is a perfect square polynomial and (k<0), what is (k)?

Explanation opens after your attempt
Correct Answer

A. (-10)

Step 1

Concept

For (x-2+kx+25=(x-5)2), (k=-10). In a perfect square, the middle term is (2ab).

Step 2

Why this answer is correct

The correct answer is A. (-10). For (x-2+kx+25=(x-5)2), (k=-10). In a perfect square, the middle term is (2ab).

Step 3

Exam Tip

(x-2+kx+25=(x-5)2) होने पर (k=-10)। पूर्ण वर्ग में मध्य पद (2ab) होता है।

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x-2+kx+16) पूर्ण वर्ग बहुपद है और (k<0), तो (k) क्या है?

If (p(x)=x-2+kx+16) is a perfect square polynomial and (k<0), what is (k)?

Explanation opens after your attempt
Correct Answer

A. (-8)

Step 1

Concept

For (x-2+kx+16=(x-4)2), (k=-8). In a perfect square, the middle term is (2ab).

Step 2

Why this answer is correct

The correct answer is A. (-8). For (x-2+kx+16=(x-4)2), (k=-8). In a perfect square, the middle term is (2ab).

Step 3

Exam Tip

(x-2+kx+16=(x-4)2) होने पर (k=-8)। पूर्ण वर्ग में मध्य पद (2ab) होता है।

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

कौन सा बहुपद पूर्ण वर्ग है?

Which polynomial is a perfect square?

Explanation opens after your attempt
Correct Answer

A. \(x^2+10x+25\)

Step 1

Concept

(x-2+10x+25=(x+5)2). Check the squares of first and last terms and the middle term (2ab).

Step 2

Why this answer is correct

The correct answer is A. \(x^2+10x+25\). (x-2+10x+25=(x+5)2). Check the squares of first and last terms and the middle term (2ab).

Step 3

Exam Tip

(x-2+10x+25=(x+5)2) है। पहले और अंतिम पद के वर्ग तथा मध्य पद (2ab) को जांचें।

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=x-2+kx+9) पूर्ण वर्ग बहुपद है और (k>0), तो (k) क्या है?

If (p(x)=x-2+kx+9) is a perfect square polynomial and (k>0), what is (k)?

Explanation opens after your attempt
Correct Answer

B. (6)

Step 1

Concept

For (x-2+kx+9=(x+3)2), (k=6). In a perfect square, the middle term is (2ab).

Step 2

Why this answer is correct

The correct answer is B. (6). For (x-2+kx+9=(x+3)2), (k=6). In a perfect square, the middle term is (2ab).

Step 3

Exam Tip

(x-2+kx+9=(x+3)2) होने पर (k=6)। पूर्ण वर्ग में मध्य पद (2ab) होता है।

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

एक धनात्मक संख्या का वर्ग उसके (11) गुने से (60) अधिक है। संख्या क्या है?

The square of a positive number is (60) more than (11) times the number. What is the number?

Explanation opens after your attempt
Correct Answer

B. (15)

Step 1

Concept

The equation is \(x^2=11x+60\). From \(x^2-11x-60=0\), the positive root is (x=15).

Step 2

Why this answer is correct

The correct answer is B. (15). The equation is \(x^2=11x+60\). From \(x^2-11x-60=0\), the positive root is (x=15).

Step 3

Exam Tip

समीकरण \(x^2=11x+60\) है। \(x^2-11x-60=0\) से धनात्मक हल (x=15) है।

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

एक संख्या के वर्ग में उस संख्या का (9) गुना जोड़ने पर (400) मिलता है। धनात्मक संख्या क्या है?

When (9) times a number is added to its square, the result is (400). What is the positive number?

Explanation opens after your attempt
Correct Answer

A. (16)

Step 1

Concept

The equation is \(x^2+9x=400\). From \(x^2+9x-400=0\), the positive root is (x=16).

Step 2

Why this answer is correct

The correct answer is A. (16). The equation is \(x^2+9x=400\). From \(x^2+9x-400=0\), the positive root is (x=16).

Step 3

Exam Tip

समीकरण \(x^2+9x=400\) है। \(x^2+9x-400=0\) से धनात्मक हल (x=16) है।

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

एक धनात्मक संख्या और उसके वर्ग का योग (156) है। संख्या क्या है?

The sum of a positive number and its square is (156). What is the number?

Explanation opens after your attempt
Correct Answer

C. (12)

Step 1

Concept

Let the number be (x), then \(x^2+x=156\). This gives \(x^2+x-156=0\), so the positive root is (12).

Step 2

Why this answer is correct

The correct answer is C. (12). Let the number be (x), then \(x^2+x=156\). This gives \(x^2+x-156=0\), so the positive root is (12).

Step 3

Exam Tip

संख्या (x) हो, तो \(x^2+x=156\)। इससे \(x^2+x-156=0\), इसलिए धनात्मक मूल (12) है।

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

एक वर्ग का क्षेत्रफल \(225 cm^2\) है। यदि उसकी भुजा (x cm) बढ़ाकर नया क्षेत्रफल (400 cm\(^2) कर दिया जाए, तो (x) क्या है\)?

The area of a square is (225 cm\(^2). If its side is increased by (x\) cm) and the new area becomes (400 cm\(^2), what is (x)\)?

Explanation opens after your attempt
Correct Answer

C. (5 cm)

Step 1

Concept

The original side is \(\sqrt{225}=15\), and the new side is \(\sqrt{400}=20\). Hence (x=20-15=5).

Step 2

Why this answer is correct

The correct answer is C. (5 cm\(). The original side is (\sqrt{225}=15), and the new side is (\sqrt{400}=20). Hence (x=20-15=5).\)

Step 3

Exam Tip

मूल भुजा \(\sqrt{225}=15\) है और नई भुजा \(\sqrt{400}=20\) है। अतः (x=20-15=5)।

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

एक वर्गाकार मैदान के चारों ओर (2 m) चौड़ा रास्ता है। रास्ते सहित कुल क्षेत्रफल \(196 m^2\) है। मैदान की भुजा क्या है?

A square field has a (2 m) wide path around it. The total area including the path is (196 m\(^2). What is the side of the field\)?

Explanation opens after your attempt
Correct Answer

B. (10 m)

Step 1

Concept

Let the side of the field be (x m\(), so the outer side is (x+4) and ((x+4)^2=196). Hence (x=10).\)

Step 2

Why this answer is correct

The correct answer is B. (10 m). Let the side of the field be (x m\(), so the outer side is (x+4) and ((x+4)^2=196). Hence (x=10).\)

Step 3

Exam Tip

मैदान की भुजा (x m) हो, तो बाहरी भुजा (x+4) होगी और ((x+4)2=196)। \(इसलिए (x=10)\)।

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

एक संख्या के (22) कम मान का वर्ग (2500) है। धनात्मक स्थिति में संख्या क्या है?

The square of (22) less than a number is (2500). In the positive case, what is the number?

Explanation opens after your attempt
Correct Answer

C. (72)

Step 1

Concept

((x-22)2=2500) and (x-22=50), so (x=72). After taking square root, choose the sign according to the condition.

Step 2

Why this answer is correct

The correct answer is C. (72). ((x-22)2=2500) and (x-22=50), so (x=72). After taking square root, choose the sign according to the condition.

Step 3

Exam Tip

((x-22)2=2500) और (x-22=50), इसलिए (x=72) है। वर्गमूल के बाद शर्त के अनुसार चिन्ह चुनें।

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

एक संख्या के (18) अधिक मान का वर्ग (4096) है। धनात्मक स्थिति में संख्या क्या है?

The square of (18) more than a number is (4096). In the positive case, what is the number?

Explanation opens after your attempt
Correct Answer

B. (46)

Step 1

Concept

((x+18)2=4096) and (x+18=64), so (x=46). If the positive case is clear, take the positive square root.

Step 2

Why this answer is correct

The correct answer is B. (46). ((x+18)2=4096) and (x+18=64), so (x=46). If the positive case is clear, take the positive square root.

Step 3

Exam Tip

((x+18)2=4096) और (x+18=64), इसलिए (x=46) है। धनात्मक स्थिति स्पष्ट हो तो धनात्मक वर्गमूल लें।

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

एक संख्या के वर्ग में (975) घटाने पर (2625) मिलता है। धनात्मक संख्या क्या है?

When (975) is subtracted from the square of a number, the result is (2625). What is the positive number?

Explanation opens after your attempt
Correct Answer

C. (60)

Step 1

Concept

\(x^2-975=2625\) gives \(x^2=3600\), so (x=60). Write the subtraction sign carefully.

Step 2

Why this answer is correct

The correct answer is C. (60). \(x^2-975=2625\) gives \(x^2=3600\), so (x=60). Write the subtraction sign carefully.

Step 3

Exam Tip

\(x^2-975=2625\) से \(x^2=3600\), इसलिए (x=60) है। घटाव के चिन्ह को ध्यान से लिखें।

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

एक संख्या के वर्ग में (399) जोड़ने पर (3208) मिलता है। धनात्मक संख्या क्या है?

When (399) is added to the square of a number, the result is (3208). What is the positive number?

Explanation opens after your attempt
Correct Answer

C. (53)

Step 1

Concept

\(x^2+399=3208\) gives \(x^2=2809\), so (x=53). First move the constant to the other side.

Step 2

Why this answer is correct

The correct answer is C. (53). \(x^2+399=3208\) gives \(x^2=2809\), so (x=53). First move the constant to the other side.

Step 3

Exam Tip

\(x^2+399=3208\) से \(x^2=2809\), इसलिए (x=53) है। पहले स्थिर संख्या को दूसरी तरफ ले जाएँ।

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

एक संख्या और उसके वर्ग का योग (2352) है। धनात्मक संख्या क्या है?

The sum of a number and its square is (2352). What is the positive number?

Explanation opens after your attempt
Correct Answer

C. (48)

Step 1

Concept

\(x^2+x=2352\) gives \(x^2+x-2352=0\). The positive solution is (48).

Step 2

Why this answer is correct

The correct answer is C. (48). \(x^2+x=2352\) gives \(x^2+x-2352=0\). The positive solution is (48).

Step 3

Exam Tip

\(x^2+x=2352\) से \(x^2+x-2352=0\) मिलता है। धनात्मक हल (48) है।

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

एक संख्या का वर्ग उसी संख्या के (30) गुने से (2800) अधिक है। धनात्मक संख्या क्या है?

The square of a number is (2800) more than (30) times the number. What is the positive number?

Explanation opens after your attempt
Correct Answer

C. (70)

Step 1

Concept

The equation is \(x^2=30x+2800\). From \(x^2-30x-2800=0\), the positive solution is (70).

Step 2

Why this answer is correct

The correct answer is C. (70). The equation is \(x^2=30x+2800\). From \(x^2-30x-2800=0\), the positive solution is (70).

Step 3

Exam Tip

समीकरण \(x^2=30x+2800\) है। \(x^2-30x-2800=0\) से धनात्मक हल (70) है।

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

एक संख्या के (15) कम मान का वर्ग (2209) है। धनात्मक स्थिति में संख्या क्या है?

The square of (15) less than a number is (2209). In the positive case, what is the number?

Explanation opens after your attempt
Correct Answer

C. (62)

Step 1

Concept

((x-15)2=2209) and (x-15=47), so (x=62). After taking square root, choose the sign according to the condition.

Step 2

Why this answer is correct

The correct answer is C. (62). ((x-15)2=2209) and (x-15=47), so (x=62). After taking square root, choose the sign according to the condition.

Step 3

Exam Tip

((x-15)2=2209) और (x-15=47), इसलिए (x=62) है। वर्गमूल के बाद शर्त के अनुसार चिन्ह चुनें।

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

एक संख्या के (14) अधिक मान का वर्ग (2500) है। धनात्मक स्थिति में संख्या क्या है?

The square of (14) more than a number is (2500). In the positive case, what is the number?

Explanation opens after your attempt
Correct Answer

C. (36)

Step 1

Concept

((x+14)2=2500) and (x+14=50), so (x=36). If the positive case is clear, take the positive square root.

Step 2

Why this answer is correct

The correct answer is C. (36). ((x+14)2=2500) and (x+14=50), so (x=36). If the positive case is clear, take the positive square root.

Step 3

Exam Tip

((x+14)2=2500) और (x+14=50), इसलिए (x=36) है। धनात्मक स्थिति स्पष्ट हो तो धनात्मक वर्गमूल लें।

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

एक संख्या के वर्ग में (444) जोड़ने पर (1900) मिलता है। धनात्मक संख्या क्या है?

When (444) is added to the square of a number, the result is (1900). What is the positive number?

Explanation opens after your attempt
Correct Answer

C. (38)

Step 1

Concept

\(x^2+444=1900\) gives \(x^2=1456\), which is not a perfect square. Therefore, none of the options can be correct.

Step 2

Why this answer is correct

The correct answer is C. (38). \(x^2+444=1900\) gives \(x^2=1456\), which is not a perfect square. Therefore, none of the options can be correct.

Step 3

Exam Tip

\(x^2+444=1900\) से \(x^2=1456\) नहीं, बल्कि सही घटाव (1900-444=1456) है जो पूर्ण वर्ग नहीं है। इसलिए कोई विकल्प सही नहीं हो सकता।

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

एक संख्या और उसके वर्ग का योग (1892) है। धनात्मक संख्या क्या है?

The sum of a number and its square is (1892). What is the positive number?

Explanation opens after your attempt
Correct Answer

C. (43)

Step 1

Concept

\(x^2+x=1892\) gives \(x^2+x-1892=0\). The positive solution is (43).

Step 2

Why this answer is correct

The correct answer is C. (43). \(x^2+x=1892\) gives \(x^2+x-1892=0\). The positive solution is (43).

Step 3

Exam Tip

\(x^2+x=1892\) से \(x^2+x-1892=0\) मिलता है। धनात्मक हल (43) है।

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

एक संख्या का वर्ग उसी संख्या के (24) गुने से (640) अधिक है। धनात्मक संख्या क्या है?

The square of a number is (640) more than (24) times the number. What is the positive number?

Explanation opens after your attempt
Correct Answer

C. (40)

Step 1

Concept

The equation is \(x^2=24x+640\). From \(x^2-24x-640=0\), the positive solution is (40).

Step 2

Why this answer is correct

The correct answer is C. (40). The equation is \(x^2=24x+640\). From \(x^2-24x-640=0\), the positive solution is (40).

Step 3

Exam Tip

समीकरण \(x^2=24x+640\) है। \(x^2-24x-640=0\) से धनात्मक हल (40) है।

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

एक संख्या के (11) कम मान का वर्ग (1156) है। धनात्मक स्थिति में संख्या क्या है?

The square of (11) less than a number is (1156). In the positive case, what is the number?

Explanation opens after your attempt
Correct Answer

C. (45)

Step 1

Concept

((x-11)2=1156) and (x-11=34), so (x=45). After taking square root, choose the sign according to the condition.

Step 2

Why this answer is correct

The correct answer is C. (45). ((x-11)2=1156) and (x-11=34), so (x=45). After taking square root, choose the sign according to the condition.

Step 3

Exam Tip

((x-11)2=1156) और (x-11=34), इसलिए (x=45) है। वर्गमूल के बाद शर्त के अनुसार चिन्ह चुनें।

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

एक संख्या के (9) अधिक मान का वर्ग (1681) है। धनात्मक स्थिति में संख्या क्या है?

The square of (9) more than a number is (1681). In the positive case, what is the number?

Explanation opens after your attempt
Correct Answer

B. (32)

Step 1

Concept

((x+9)2=1681) and (x+9=41), so (x=32). If the positive case is clear, take the positive square root.

Step 2

Why this answer is correct

The correct answer is B. (32). ((x+9)2=1681) and (x+9=41), so (x=32). If the positive case is clear, take the positive square root.

Step 3

Exam Tip

((x+9)2=1681) और (x+9=41), इसलिए (x=32) है। धनात्मक स्थिति स्पष्ट हो तो धनात्मक वर्गमूल लें।

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

एक संख्या के वर्ग में (256) घटाने पर (1040) मिलता है। धनात्मक संख्या क्या है?

When (256) is subtracted from the square of a number, the result is (1040). What is the positive number?

Explanation opens after your attempt
Correct Answer

C. (36)

Step 1

Concept

\(x^2-256=1040\) gives \(x^2=1296\), so (x=36). Write the subtraction sign carefully.

Step 2

Why this answer is correct

The correct answer is C. (36). \(x^2-256=1040\) gives \(x^2=1296\), so (x=36). Write the subtraction sign carefully.

Step 3

Exam Tip

\(x^2-256=1040\) से \(x^2=1296\), इसलिए (x=36) है। घटाव के चिन्ह को ध्यान से लिखें।

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

एक संख्या के वर्ग में (175) जोड़ने पर (1076) मिलता है। धनात्मक संख्या क्या है?

When (175) is added to the square of a number, the result is (1076). What is the positive number?

Explanation opens after your attempt
Correct Answer

C. (30)

Step 1

Concept

\(x^2+175=1076\) gives \(x^2=901\), not a perfect square. If the data are inconsistent, do not choose options blindly.

Step 2

Why this answer is correct

The correct answer is C. (30). \(x^2+175=1076\) gives \(x^2=901\), not a perfect square. If the data are inconsistent, do not choose options blindly.

Step 3

Exam Tip

\(x^2+175=1076\) से \(x^2=901\) नहीं बनना चाहिए, इसलिए सही गणना देखें: \(30^2+175=1075\) होता है। दिए गए आंकड़े असंगत हों तो विकल्पों को अंधे रूप से न चुनें।

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

एक संख्या और उसके वर्ग का योग (1260) है। धनात्मक संख्या क्या है?

The sum of a number and its square is (1260). What is the positive number?

Explanation opens after your attempt
Correct Answer

C. (35)

Step 1

Concept

\(x^2+x=1260\) gives \(x^2+x-1260=0\). The positive solution is (35).

Step 2

Why this answer is correct

The correct answer is C. (35). \(x^2+x=1260\) gives \(x^2+x-1260=0\). The positive solution is (35).

Step 3

Exam Tip

\(x^2+x=1260\) से \(x^2+x-1260=0\) मिलता है। धनात्मक हल (35) है।

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

एक संख्या का वर्ग उसी संख्या के (18) गुने से (432) अधिक है। धनात्मक संख्या क्या है?

The square of a number is (432) more than (18) times the number. What is the positive number?

Explanation opens after your attempt
Correct Answer

C. (36)

Step 1

Concept

The equation is \(x^2=18x+432\). From \(x^2-18x-432=0\), the positive solution is (36).

Step 2

Why this answer is correct

The correct answer is C. (36). The equation is \(x^2=18x+432\). From \(x^2-18x-432=0\), the positive solution is (36).

Step 3

Exam Tip

समीकरण \(x^2=18x+432\) है। \(x^2-18x-432=0\) से धनात्मक हल (36) है।

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

एक संख्या का वर्ग उसके (15) गुने से (54) अधिक है। धनात्मक संख्या क्या है?

The square of a number is (54) more than (15) times the number. What is the positive number?

Explanation opens after your attempt
Correct Answer

A. (18)

Step 1

Concept

If the number is (x), then \(x^2=15x+54\). From \(x^2-15x-54=0\), the positive number is (18).

Step 2

Why this answer is correct

The correct answer is A. (18). If the number is (x), then \(x^2=15x+54\). From \(x^2-15x-54=0\), the positive number is (18).

Step 3

Exam Tip

यदि संख्या (x) है, तो \(x^2=15x+54\)। \(x^2-15x-54=0\) से धनात्मक संख्या (18) है।

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

एक वर्गाकार पार्क का क्षेत्रफल (196) है। उसकी भुजा में (4) बढ़ाने पर नया क्षेत्रफल कितना होगा?

A square park has area (196). If its side is increased by (4), what will be the new area?

Explanation opens after your attempt
Correct Answer

A. (324)

Step 1

Concept

If the original side is (x), then \(x^2=196\), so (x=14). The new side is (18), and the new area is \(18^2=324\).

Step 2

Why this answer is correct

The correct answer is A. (324). If the original side is (x), then \(x^2=196\), so (x=14). The new side is (18), and the new area is \(18^2=324\).

Step 3

Exam Tip

मूल भुजा (x) हो तो \(x^2=196\), इसलिए (x=14)। नई भुजा (18) है और नया क्षेत्रफल \(18^2=324\)।

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

एक संख्या के वर्ग में (17) घटाने पर (127) मिलता है। धनात्मक संख्या क्या है?

When (17) is subtracted from the square of a number, the result is (127). What is the positive number?

Explanation opens after your attempt
Correct Answer

A. (12)

Step 1

Concept

Let the number be (x), so \(x^2-17=127\). This gives \(x^2=144\), so the positive number is (12).

Step 2

Why this answer is correct

The correct answer is A. (12). Let the number be (x), so \(x^2-17=127\). This gives \(x^2=144\), so the positive number is (12).

Step 3

Exam Tip

मान लें संख्या (x) है, तो \(x^2-17=127\)। इससे \(x^2=144\), इसलिए धनात्मक संख्या (12) है।

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

एक संख्या का वर्ग उस संख्या के (11) गुने से (42) अधिक है। धनात्मक संख्या क्या है?

The square of a number is (42) more than (11) times the number. What is the positive number?

Explanation opens after your attempt
Correct Answer

A. (14)

Step 1

Concept

If the number is (x), then \(x^2=11x+42\). From \(x^2-11x-42=0\), the positive solution is (14).

Step 2

Why this answer is correct

The correct answer is A. (14). If the number is (x), then \(x^2=11x+42\). From \(x^2-11x-42=0\), the positive solution is (14).

Step 3

Exam Tip

यदि संख्या (x) है, तो \(x^2=11x+42\)। \(x^2-11x-42=0\) से धनात्मक हल (14) है।

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

एक संख्या के (6) कम मान का वर्ग (784) है। धनात्मक स्थिति में संख्या क्या है?

The square of (6) less than a number is (784). In the positive case, what is the number?

Explanation opens after your attempt
Correct Answer

C. (34)

Step 1

Concept

((x-6)2=784) and (x-6=28), so (x=34). After taking square root, choose the sign according to the condition.

Step 2

Why this answer is correct

The correct answer is C. (34). ((x-6)2=784) and (x-6=28), so (x=34). After taking square root, choose the sign according to the condition.

Step 3

Exam Tip

((x-6)2=784) और (x-6=28), इसलिए (x=34) है। वर्गमूल के बाद शर्त के अनुसार चिन्ह चुनें।

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

एक संख्या के (4) अधिक मान का वर्ग (900) है। धनात्मक स्थिति में संख्या क्या है?

The square of (4) more than a number is (900). In the positive case, what is the number?

Explanation opens after your attempt
Correct Answer

C. (26)

Step 1

Concept

((x+4)2=900) and (x+4=30), so (x=26). If the positive case is clear, take the positive square root.

Step 2

Why this answer is correct

The correct answer is C. (26). ((x+4)2=900) and (x+4=30), so (x=26). If the positive case is clear, take the positive square root.

Step 3

Exam Tip

((x+4)2=900) और (x+4=30), इसलिए (x=26) है। धनात्मक स्थिति स्पष्ट हो तो धनात्मक वर्गमूल लें।

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

एक संख्या के वर्ग में (156) जोड़ने पर (1057) मिलता है। धनात्मक संख्या क्या है?

When (156) is added to the square of a number, the result is (1057). What is the positive number?

Explanation opens after your attempt
Correct Answer

C. (30)

Step 1

Concept

\(x^2+156=1057\) gives \(x^2=901\), not a listed perfect square, so this is a data-error type question. In exams, check consistency before solving.

Step 2

Why this answer is correct

The correct answer is C. (30). \(x^2+156=1057\) gives \(x^2=901\), not a listed perfect square, so this is a data-error type question. In exams, check consistency before solving.

Step 3

Exam Tip

\(x^2+156=1057\) से \(x^2=901\) नहीं, इसलिए विकल्प जाँच की बजाय समीकरण सुधारें: सही वर्ग के लिए \(x^2+156=1056\) चाहिए।

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

एक संख्या और उसके वर्ग का योग (930) है। धनात्मक संख्या क्या है?

The sum of a number and its square is (930). What is the positive number?

Explanation opens after your attempt
Correct Answer

C. (30)

Step 1

Concept

\(x^2+x=930\) gives \(x^2+x-930=0\). The positive solution is (30).

Step 2

Why this answer is correct

The correct answer is C. (30). \(x^2+x=930\) gives \(x^2+x-930=0\). The positive solution is (30).

Step 3

Exam Tip

\(x^2+x=930\) से \(x^2+x-930=0\) मिलता है। धनात्मक हल (30) है।

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

एक संख्या का वर्ग उसी संख्या के (14) गुने से (240) अधिक है। धनात्मक संख्या क्या है?

The square of a number is (240) more than (14) times the number. What is the positive number?

Explanation opens after your attempt
Correct Answer

B. (24)

Step 1

Concept

The equation is \(x^2=14x+240\). From \(x^2-14x-240=0\), the positive solution is (24).

Step 2

Why this answer is correct

The correct answer is B. (24). The equation is \(x^2=14x+240\). From \(x^2-14x-240=0\), the positive solution is (24).

Step 3

Exam Tip

समीकरण \(x^2=14x+240\) है। \(x^2-14x-240=0\) से धनात्मक हल (24) है।

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