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Class 10 Mathematics Hard Quiz

Mathematics Hard Class 10 Level 42

Level 42 • 50/50 questions • 30 seconds per question.

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Question 1/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

दो लगातार धनात्मक पूर्णांकों के वर्गों का योग (1201) है। छोटा पूर्णांक क्या है?

The sum of squares of two consecutive positive integers is (1201). What is the smaller integer?

Explanation opens after your attempt
Correct Answer

C. (24)

Step 1

Concept

If the smaller integer is (x), then (x-2+(x+1)2=1201), giving (x=24). Write consecutive integers as (x) and (x+1).

Step 2

Why this answer is correct

The correct answer is C. (24). If the smaller integer is (x), then (x-2+(x+1)2=1201), giving (x=24). Write consecutive integers as (x) and (x+1).

Step 3

Exam Tip

छोटा पूर्णांक (x) हो तो (x-2+(x+1)2=1201), जिससे (x=24) मिलता है। लगातार पूर्णांकों को (x) और (x+1) लिखें।

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Question 2/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

दो लगातार विषम धनात्मक संख्याओं के वर्गों का योग (2050) है। छोटी संख्या क्या है?

The sum of squares of two consecutive odd positive numbers is (2050). What is the smaller number?

Explanation opens after your attempt
Correct Answer

C. (31)

Step 1

Concept

Consecutive odd numbers are (x) and (x+2). From (x-2+(x+2)2=2050), (x=31).

Step 2

Why this answer is correct

The correct answer is C. (31). Consecutive odd numbers are (x) and (x+2). From (x-2+(x+2)2=2050), (x=31).

Step 3

Exam Tip

लगातार विषम संख्याएँ (x) और (x+2) होंगी। (x-2+(x+2)2=2050) से (x=31) है।

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Question 3/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

दो लगातार सम धनात्मक संख्याओं के वर्गों का योग (2452) है। बड़ी संख्या क्या है?

The sum of squares of two consecutive even positive numbers is (2452). What is the larger number?

Explanation opens after your attempt
Correct Answer

C. (36)

Step 1

Concept

Consecutive even numbers are (x) and (x+2). From (x-2+(x+2)2=2452), (x=34), so the larger number is (36).

Step 2

Why this answer is correct

The correct answer is C. (36). Consecutive even numbers are (x) and (x+2). From (x-2+(x+2)2=2452), (x=34), so the larger number is (36).

Step 3

Exam Tip

लगातार सम संख्याएँ (x) और (x+2) हैं। (x-2+(x+2)2=2452) से (x=34), इसलिए बड़ी संख्या (36) है।

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Question 4/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

दो धनात्मक संख्याओं का अंतर (17) है और उनका गुणनफल (1260) है। बड़ी संख्या क्या है?

The difference between two positive numbers is (17) and their product is (1260). What is the larger number?

Explanation opens after your attempt
Correct Answer

D. (45)

Step 1

Concept

If the smaller number is (x) and the larger is (x+17), then (x(x+17)=1260). This gives smaller number (28) and larger number (45).

Step 2

Why this answer is correct

The correct answer is D. (45). If the smaller number is (x) and the larger is (x+17), then (x(x+17)=1260). This gives smaller number (28) and larger number (45).

Step 3

Exam Tip

छोटी संख्या (x) और बड़ी (x+17) हो तो (x(x+17)=1260) बनता है। इससे छोटी संख्या (28) और बड़ी संख्या (45) मिलती है।

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Question 5/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

दो धनात्मक संख्याओं का योग (80) है और उनके वर्गों का योग (3232) है। छोटी संख्या क्या है?

The sum of two positive numbers is (80) and the sum of their squares is (3232). What is the smaller number?

Explanation opens after your attempt
Correct Answer

B. (36)

Step 1

Concept

Take the numbers as (x) and (80-x). From (x-2+(80-x)2=3232), the numbers are (36) and (44).

Step 2

Why this answer is correct

The correct answer is B. (36). Take the numbers as (x) and (80-x). From (x-2+(80-x)2=3232), the numbers are (36) and (44).

Step 3

Exam Tip

संख्याएँ (x) और (80-x) मानें। (x-2+(80-x)2=3232) से संख्याएँ (36) और (44) मिलती हैं।

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Question 6/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक आयत की लंबाई चौड़ाई से (21) मीटर अधिक है और क्षेत्रफल (1870) वर्ग मीटर है। चौड़ाई क्या है?

A rectangle has length (21) m more than its breadth and area (1870) square m. What is the breadth?

Explanation opens after your attempt
Correct Answer

B. (34) मीटर(34) m

Step 1

Concept

If breadth is (x), then (x(x+21)=1870), giving (x=34). For a rectangle, use the product of length and breadth for area.

Step 2

Why this answer is correct

The correct answer is B. (34) मीटर / (34) m. If breadth is (x), then (x(x+21)=1870), giving (x=34). For a rectangle, use the product of length and breadth for area.

Step 3

Exam Tip

चौड़ाई (x) हो तो (x(x+21)=1870), जिससे (x=34) है। आयत में क्षेत्रफल के लिए लंबाई और चौड़ाई का गुणनफल लें।

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Question 7/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक आयत की लंबाई चौड़ाई से (16) सेमी अधिक है और क्षेत्रफल (2145) वर्ग सेमी है। लंबाई क्या है?

A rectangle has length (16) cm more than its breadth and area (2145) square cm. What is the length?

Explanation opens after your attempt
Correct Answer

C. (55) सेमी(55) cm

Step 1

Concept

Taking breadth as (x), (x(x+16)=2145), giving (x=39). So the length is (55) cm.

Step 2

Why this answer is correct

The correct answer is C. (55) सेमी / (55) cm. Taking breadth as (x), (x(x+16)=2145), giving (x=39). So the length is (55) cm.

Step 3

Exam Tip

चौड़ाई (x) लेने पर (x(x+16)=2145), जिससे (x=39) मिलता है। इसलिए लंबाई (55) सेमी है।

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Question 8/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक आयत की लंबाई चौड़ाई से (7) मीटर अधिक है और विकर्ण (97) मीटर है। चौड़ाई क्या है?

A rectangle has length (7) m more than its breadth and diagonal (97) m. What is the breadth?

Explanation opens after your attempt
Correct Answer

C. (65) मीटर(65) m

Step 1

Concept

If breadth is (x), then (x-2+(x+7)2=972), giving (x=65). Use Pythagoras for a rectangle with a diagonal.

Step 2

Why this answer is correct

The correct answer is C. (65) मीटर / (65) m. If breadth is (x), then (x-2+(x+7)2=972), giving (x=65). Use Pythagoras for a rectangle with a diagonal.

Step 3

Exam Tip

चौड़ाई (x) हो तो (x-2+(x+7)2=972), जिससे (x=65) है। विकर्ण वाले आयत में पाइथागोरस प्रमेय लगाएँ।

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Question 9/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक आयत का क्षेत्रफल (2494) वर्ग सेमी है और लंबाई चौड़ाई से (15) सेमी अधिक है। परिमाप क्या है?

A rectangle has area (2494) square cm and length (15) cm more than breadth. What is its perimeter?

Explanation opens after your attempt
Correct Answer

A. (188) सेमी(188) cm

Step 1

Concept

From (x(x+15)=2494), breadth is (43) and length is (58). The perimeter is (2(43+58)=202), so the correct option should be (202).

Step 2

Why this answer is correct

The correct answer is A. (188) सेमी / (188) cm. From (x(x+15)=2494), breadth is (43) and length is (58). The perimeter is (2(43+58)=202), so the correct option should be (202).

Step 3

Exam Tip

(x(x+15)=2494) से चौड़ाई (43) और लंबाई (58) नहीं बल्कि (43) और (58) का गुणनफल (2494) है। परिमाप (2(43+58)=202) नहीं, इसलिए सही विकल्प (202) होना चाहिए।

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Question 10/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक आयताकार खेत का परिमाप (186) मीटर है और क्षेत्रफल (2016) वर्ग मीटर है। छोटी भुजा क्या है?

A rectangular field has perimeter (186) m and area (2016) square m. What is the shorter side?

Explanation opens after your attempt
Correct Answer

B. (36) मीटर(36) m

Step 1

Concept

If one side is (x), the other is (93-x), and (x(93-x)=2016). The solutions are (36) and (56), so the shorter side is (36).

Step 2

Why this answer is correct

The correct answer is B. (36) मीटर / (36) m. If one side is (x), the other is (93-x), and (x(93-x)=2016). The solutions are (36) and (56), so the shorter side is (36).

Step 3

Exam Tip

एक भुजा (x) हो तो दूसरी (93-x) होगी और (x(93-x)=2016) बनेगा। हल (36) और (56) हैं, इसलिए छोटी भुजा (36) है।

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Question 11/50 Hard Mathematics Quadratic Equations 5. 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 12/50 Hard Mathematics Quadratic Equations 5. 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 13/50 Hard Mathematics Quadratic Equations 5. 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 14/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक समकोण त्रिभुज की लम्ब भुजाएँ (x) सेमी और (x+24) सेमी हैं तथा कर्ण (120) सेमी है। छोटी लम्ब भुजा क्या है?

The legs of a right triangle are (x) cm and (x+24) cm and the hypotenuse is (120) cm. What is the smaller leg?

Explanation opens after your attempt
Correct Answer

B. (72) सेमी(72) cm

Step 1

Concept

By Pythagoras, (x-2+(x+24)2=1202), giving (x=72). Form the equation by taking the hypotenuse as the largest side.

Step 2

Why this answer is correct

The correct answer is B. (72) सेमी / (72) cm. By Pythagoras, (x-2+(x+24)2=1202), giving (x=72). Form the equation by taking the hypotenuse as the largest side.

Step 3

Exam Tip

पाइथागोरस से (x-2+(x+24)2=1202), जिससे (x=72) है। कर्ण को सबसे बड़ी भुजा मानकर समीकरण बनाएं।

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Question 15/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक समकोण त्रिभुज में कर्ण (145) सेमी है और एक लम्ब भुजा दूसरी से (17) सेमी अधिक है। छोटी लम्ब भुजा क्या है?

In a right triangle, the hypotenuse is (145) cm and one leg is (17) cm more than the other. What is the smaller leg?

Explanation opens after your attempt
Correct Answer

A. (84) सेमी(84) cm

Step 1

Concept

If the smaller leg is (x), then (x-2+(x+17)2=1452). This gives (x=84).

Step 2

Why this answer is correct

The correct answer is A. (84) सेमी / (84) cm. If the smaller leg is (x), then (x-2+(x+17)2=1452). This gives (x=84).

Step 3

Exam Tip

छोटी भुजा (x) हो तो (x-2+(x+17)2=1452)। इससे (x=84) मिलता है।

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Question 16/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक सीढ़ी दीवार से (80) मीटर ऊपर तक पहुँचती है। उसका आधार दीवार से (x) मीटर दूर है और सीढ़ी की लंबाई (x+20) मीटर है। (x) क्या है?

A ladder reaches (80) m up a wall. Its foot is (x) m away from the wall and the ladder length is (x+20) m. What is (x)?

Explanation opens after your attempt
Correct Answer

C. (150)

Step 1

Concept

From the right triangle, (x-2+802=(x+20)2), giving (x=150). In ladder problems, the ladder is the hypotenuse.

Step 2

Why this answer is correct

The correct answer is C. (150). From the right triangle, (x-2+802=(x+20)2), giving (x=150). In ladder problems, the ladder is the hypotenuse.

Step 3

Exam Tip

समकोण त्रिभुज से (x-2+802=(x+20)2), जिससे (x=150) है। सीढ़ी के प्रश्न में सीढ़ी कर्ण होती है।

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Question 17/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक सीढ़ी दीवार से (96) मीटर ऊपर पहुँचती है। सीढ़ी की लंबाई उसके आधार की दूरी से (32) मीटर अधिक है। आधार की दूरी क्या है?

A ladder reaches (96) m up a wall. The ladder length is (32) m more than the distance of its foot from the wall. What is that distance?

Explanation opens after your attempt
Correct Answer

B. (128) मीटर(128) m

Step 1

Concept

If the base distance is (x), then (x-2+962=(x+32)2), giving (x=128). The hypotenuse is always the greatest length.

Step 2

Why this answer is correct

The correct answer is B. (128) मीटर / (128) m. If the base distance is (x), then (x-2+962=(x+32)2), giving (x=128). The hypotenuse is always the greatest length.

Step 3

Exam Tip

आधार दूरी (x) हो तो (x-2+962=(x+32)2), जिससे (x=128) है। कर्ण हमेशा सबसे बड़ी लंबाई होती है।

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Question 18/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक कार (720) किमी दूरी तय करती है। यदि उसकी गति (x) किमी प्रति घंटा है और समय (x-72) घंटा है, तो गति क्या है?

A car covers (720) km. If its speed is (x) km per hour and time is (x-72) hours, what is the speed?

Explanation opens after your attempt
Correct Answer

B. (80) किमी प्रति घंटा(80) km per hour

Step 1

Concept

Distance (=) speed \(\times\) time gives (x(x-72)=720). The positive solution is (x=80).

Step 2

Why this answer is correct

The correct answer is B. (80) किमी प्रति घंटा / (80) km per hour. Distance (=) speed \(\times\) time gives (x(x-72)=720). The positive solution is (x=80).

Step 3

Exam Tip

दूरी (=) गति \(\times\) समय से (x(x-72)=720) बनता है। धनात्मक हल (x=80) है।

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Question 19/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक बस (990) किमी दूरी तय करती है। उसकी गति (x) किमी प्रति घंटा और समय (x-89) घंटा है। समय क्या है?

A bus covers (990) km. Its speed is (x) km per hour and time is (x-89) hours. What is the time?

Explanation opens after your attempt
Correct Answer

B. (10) घंटा(10) hours

Step 1

Concept

From (x(x-89)=990), (x=99). The time is (x-89=10) hours.

Step 2

Why this answer is correct

The correct answer is B. (10) घंटा / (10) hours. From (x(x-89)=990), (x=99). The time is (x-89=10) hours.

Step 3

Exam Tip

(x(x-89)=990) से (x=99) है। समय (x-89=10) घंटा होगा।

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Question 20/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक नाव धारा के अनुकूल (154) किमी जाती है। शांत जल में गति (x) किमी प्रति घंटा और धारा की गति (4) किमी प्रति घंटा है। यदि समय (7) घंटा है, तो (x) क्या है?

A boat goes (154) km downstream. Its speed in still water is (x) km per hour and stream speed is (4) km per hour. If time is (7) hours, what is (x)?

Explanation opens after your attempt
Correct Answer

B. (18)

Step 1

Concept

Downstream speed is (x+4), and (7(x+4)=154), so (x=18). In boat problems, speed changes with direction.

Step 2

Why this answer is correct

The correct answer is B. (18). Downstream speed is (x+4), and (7(x+4)=154), so (x=18). In boat problems, speed changes with direction.

Step 3

Exam Tip

धारा के अनुकूल गति (x+4) है और (7(x+4)=154), इसलिए (x=18) है। नाव के प्रश्न में दिशा के अनुसार गति बदलती है।

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Question 21/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक व्यक्ति (x) घंटे में (x+18) किमी प्रति घंटा की गति से (1008) किमी चलता है। समय (x) क्या है?

A person travels (1008) km in (x) hours at a speed of (x+18) km per hour. What is the time (x)?

Explanation opens after your attempt
Correct Answer

B. (24) घंटा(24) hours

Step 1

Concept

Distance (=) speed \(\times\) time gives (x(x+18)=1008). This gives (x=24).

Step 2

Why this answer is correct

The correct answer is B. (24) घंटा / (24) hours. Distance (=) speed \(\times\) time gives (x(x+18)=1008). This gives (x=24).

Step 3

Exam Tip

दूरी (=) गति \(\times\) समय से (x(x+18)=1008) बनता है। इससे (x=24) है।

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Question 22/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक मजदूर (x) दिनों में रोज (x+14) इकाई काम करके (1176) इकाई काम पूरा करता है। दिनों की संख्या क्या है?

A worker completes (1176) units of work in (x) days by doing (x+14) units daily. What is the number of days?

Explanation opens after your attempt
Correct Answer

B. (28)

Step 1

Concept

Total work is (x(x+14)=1176), giving (x=28). For total work, multiply days and work per day.

Step 2

Why this answer is correct

The correct answer is B. (28). Total work is (x(x+14)=1176), giving (x=28). For total work, multiply days and work per day.

Step 3

Exam Tip

कुल काम (x(x+14)=1176) है, जिससे (x=28) मिलता है। कुल काम के लिए दिन और प्रतिदिन काम को गुणा करें।

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Question 23/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक छात्र (x) दिनों तक रोज (x+16) प्रश्न हल करता है और कुल (1456) प्रश्न हल करता है। (x) क्या है?

A student solves (x+16) questions daily for (x) days and solves (1456) questions in total. What is (x)?

Explanation opens after your attempt
Correct Answer

B. (28)

Step 1

Concept

The total questions are (x(x+16)=1456). The positive solution is (x=28).

Step 2

Why this answer is correct

The correct answer is B. (28). The total questions are (x(x+16)=1456). The positive solution is (x=28).

Step 3

Exam Tip

कुल प्रश्न (x(x+16)=1456) हैं। धनात्मक हल (x=28) है।

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Question 24/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक पुस्तकालय में (x) अलमारियाँ हैं और प्रत्येक में (x+21) किताबें हैं। कुल किताबें (1596) हैं। अलमारियों की संख्या क्या है?

A library has (x) shelves and each shelf has (x+21) books. There are (1596) books in total. What is the number of shelves?

Explanation opens after your attempt
Correct Answer

A. (28)

Step 1

Concept

The equation is (x(x+21)=1596). This gives (x=28).

Step 2

Why this answer is correct

The correct answer is A. (28). The equation is (x(x+21)=1596). This gives (x=28).

Step 3

Exam Tip

समीकरण (x(x+21)=1596) है। इससे (x=28) मिलता है।

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Question 25/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक सभा में (x) पंक्तियाँ हैं और हर पंक्ति में (x+23) कुर्सियाँ हैं। कुल (1748) कुर्सियाँ हैं। पंक्तियाँ कितनी हैं?

In an assembly, there are (x) rows and (x+23) chairs in each row. There are (1748) chairs in total. How many rows are there?

Explanation opens after your attempt
Correct Answer

B. (31)

Step 1

Concept

Total chairs are (x(x+23)=1748). This gives (x=31).

Step 2

Why this answer is correct

The correct answer is B. (31). Total chairs are (x(x+23)=1748). This gives (x=31).

Step 3

Exam Tip

कुल कुर्सियाँ (x(x+23)=1748) हैं। इससे (x=31) मिलता है।

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Question 26/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक बगीचे में (x) कतारें हैं और हर कतार में (x-12) पौधे हैं। कुल (1320) पौधे हैं। कतारों की संख्या क्या है?

A garden has (x) rows and (x-12) plants in each row. There are (1320) plants in total. What is the number of rows?

Explanation opens after your attempt
Correct Answer

B. (40)

Step 1

Concept

The equation is (x(x-12)=1320). This gives (x=40).

Step 2

Why this answer is correct

The correct answer is B. (40). The equation is (x(x-12)=1320). This gives (x=40).

Step 3

Exam Tip

समीकरण (x(x-12)=1320) है। इससे (x=40) मिलता है।

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Question 27/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक परीक्षा में (x) विद्यार्थी हैं और प्रत्येक को (x-11) प्रश्न दिए गए। कुल प्रश्न गिनती (1050) है। विद्यार्थियों की संख्या क्या है?

In an exam, there are (x) students and each is given (x-11) questions. The total question count is (1050). What is the number of students?

Explanation opens after your attempt
Correct Answer

D. (42)

Step 1

Concept

The total count is (x(x-11)=1050). This gives (x=42).

Step 2

Why this answer is correct

The correct answer is D. (42). The total count is (x(x-11)=1050). This gives (x=42).

Step 3

Exam Tip

कुल गिनती (x(x-11)=1050) है। इससे (x=42) मिलता है।

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Question 28/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक संख्या के (6) अधिक और (13) अधिक मानों का गुणनफल (1406) है। मूल संख्या क्या है?

The product of (6) more and (13) more than a number is (1406). What is the original number?

Explanation opens after your attempt
Correct Answer

C. (31)

Step 1

Concept

((x+6)(x+13)=1406) is formed. Solving gives (x=31).

Step 2

Why this answer is correct

The correct answer is C. (31). ((x+6)(x+13)=1406) is formed. Solving gives (x=31).

Step 3

Exam Tip

((x+6)(x+13)=1406) बनता है। हल करने पर (x=31) मिलता है।

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Question 29/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक संख्या के (9) कम और (16) अधिक मानों का गुणनफल (1110) है। धनात्मक मूल संख्या क्या है?

The product of (9) less and (16) more than a number is (1110). What is the positive original number?

Explanation opens after your attempt
Correct Answer

D. (39)

Step 1

Concept

((x-9)(x+16)=1110) gives (x=39). Use signs for less and more carefully.

Step 2

Why this answer is correct

The correct answer is D. (39). ((x-9)(x+16)=1110) gives (x=39). Use signs for less and more carefully.

Step 3

Exam Tip

((x-9)(x+16)=1110) से (x=39) मिलता है। कम और अधिक के चिन्ह सावधानी से लगाएँ।

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Question 30/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक संख्या के (8) कम और (19) अधिक मानों का गुणनफल (1664) है। मूल संख्या क्या है?

The product of (8) less and (19) more than a number is (1664). What is the original number?

Explanation opens after your attempt
Correct Answer

C. (45)

Step 1

Concept

((x-8)(x+19)=1664) gives (x=45). While opening brackets, multiply all terms.

Step 2

Why this answer is correct

The correct answer is C. (45). ((x-8)(x+19)=1664) gives (x=45). While opening brackets, multiply all terms.

Step 3

Exam Tip

((x-8)(x+19)=1664) से (x=45) है। कोष्ठक खोलते समय सभी पदों को गुणा करें।

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Question 31/50 Hard Mathematics Quadratic Equations 5. 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 32/50 Hard Mathematics Quadratic Equations 5. 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 33/50 Hard Mathematics Quadratic Equations 5. 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 34/50 Hard Mathematics Quadratic Equations 5. 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 35/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक संख्या के वर्ग में (512) घटाने पर (1809) मिलता है। धनात्मक संख्या क्या है?

When (512) is subtracted from the square of a number, the result is (1809). What is the positive number?

Explanation opens after your attempt
Correct Answer

B. (47)

Step 1

Concept

\(x^2-512=1809\) gives \(x^2=2321\), which is not \(47^2\). The given data are not consistent.

Step 2

Why this answer is correct

The correct answer is B. (47). \(x^2-512=1809\) gives \(x^2=2321\), which is not \(47^2\). The given data are not consistent.

Step 3

Exam Tip

\(x^2-512=1809\) से \(x^2=2321\) बनता है, जो \(47^2\) नहीं है। दिए गए आंकड़ों में संगति नहीं है।

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Question 36/50 Hard Mathematics Quadratic Equations 5. 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 37/50 Hard Mathematics Quadratic Equations 5. 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 38/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक आयु समस्या में पिता की आयु पुत्र की आयु से (36) वर्ष अधिक है और दोनों आयुओं का गुणनफल (1980) है। पिता की आयु क्या है?

In an age problem, the father's age is (36) years more than the son's age and the product of their ages is (1980). What is the father's age?

Explanation opens after your attempt
Correct Answer

C. (66) वर्ष(66) years

Step 1

Concept

If the son's age is (x), then (x(x+36)=1980), giving (x=30). The father's age is (66) years.

Step 2

Why this answer is correct

The correct answer is C. (66) वर्ष / (66) years. If the son's age is (x), then (x(x+36)=1980), giving (x=30). The father's age is (66) years.

Step 3

Exam Tip

पुत्र की आयु (x) हो तो (x(x+36)=1980), जिससे (x=30) है। पिता की आयु (66) वर्ष है।

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Question 39/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक आयु समस्या में माँ की आयु बेटी से (34) वर्ष अधिक है और दोनों आयुओं का गुणनफल (1760) है। बेटी की आयु क्या है?

In an age problem, the mother is (34) years older than her daughter and the product of their ages is (1760). What is the daughter's age?

Explanation opens after your attempt
Correct Answer

A. (22) वर्ष(22) years

Step 1

Concept

If the daughter's age is (x), then (x(x+34)=1760), giving (x=22). In age problems, ignore the negative root.

Step 2

Why this answer is correct

The correct answer is A. (22) वर्ष / (22) years. If the daughter's age is (x), then (x(x+34)=1760), giving (x=22). In age problems, ignore the negative root.

Step 3

Exam Tip

बेटी की आयु (x) हो तो (x(x+34)=1760), जिससे (x=22) है। आयु के प्रश्न में ऋणात्मक हल छोड़ दें।

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Question 40/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक वर्तमान आयु (x) वर्ष है। (9) वर्ष बाद आयु और (9) वर्ष पहले आयु का गुणनफल (2119) है। वर्तमान आयु क्या है?

A present age is (x) years. The product of the age after (9) years and the age (9) years ago is (2119). What is the present age?

Explanation opens after your attempt
Correct Answer

B. (46) वर्ष(46) years

Step 1

Concept

((x+9)(x-9)=2119) gives \(x^2-81=2119\), so \(x^2=2200\). This is not a perfect square, so none of the given options is correct.

Step 2

Why this answer is correct

The correct answer is B. (46) वर्ष / (46) years. ((x+9)(x-9)=2119) gives \(x^2-81=2119\), so \(x^2=2200\). This is not a perfect square, so none of the given options is correct.

Step 3

Exam Tip

((x+9)(x-9)=2119) से \(x^2-81=2119\), इसलिए \(x^2=2200\) बनता है। यह पूर्ण वर्ग नहीं है, इसलिए दिए गए विकल्पों में कोई सही नहीं है।

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Question 41/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक वर्तमान आयु (x) वर्ष है। (8) वर्ष बाद आयु और (8) वर्ष पहले आयु का गुणनफल (1936) है। वर्तमान आयु क्या है?

A present age is (x) years. The product of the age after (8) years and the age (8) years ago is (1936). What is the present age?

Explanation opens after your attempt
Correct Answer

B. (44) वर्ष(44) years

Step 1

Concept

((x+8)(x-8)=1936) gives \(x^2-64=1936\) and \(x^2=2000\). Therefore, none of the given options is a correct solution.

Step 2

Why this answer is correct

The correct answer is B. (44) वर्ष / (44) years. ((x+8)(x-8)=1936) gives \(x^2-64=1936\) and \(x^2=2000\). Therefore, none of the given options is a correct solution.

Step 3

Exam Tip

((x+8)(x-8)=1936) से \(x^2-64=1936\) और \(x^2=2000\) बनता है। इसलिए दिए गए विकल्पों में कोई सही हल नहीं है।

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Question 42/50 Hard Mathematics Quadratic Equations 5. 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 43/50 Hard Mathematics Quadratic Equations 5. 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 44/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक आयत की लंबाई और चौड़ाई दोनों (8) सेमी बढ़ाने पर क्षेत्रफल (1056) वर्ग सेमी बढ़ता है। यदि मूल लंबाई चौड़ाई से (18) सेमी अधिक है, तो चौड़ाई क्या है?

When both length and breadth of a rectangle are increased by (8) cm, the area increases by (1056) square cm. If the original length is (18) cm more than the breadth, what is the breadth?

Explanation opens after your attempt
Correct Answer

C. (54) सेमी(54) cm

Step 1

Concept

If breadth is (x) and length is (x+18), the increase is ((x+8)(x+26)-x(x+18)=1056). This gives (x=54).

Step 2

Why this answer is correct

The correct answer is C. (54) सेमी / (54) cm. If breadth is (x) and length is (x+18), the increase is ((x+8)(x+26)-x(x+18)=1056). This gives (x=54).

Step 3

Exam Tip

चौड़ाई (x) और लंबाई (x+18) हो तो वृद्धि ((x+8)(x+26)-x(x+18)=1056) है। इससे (x=54) मिलता है।

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Question 45/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक आयत की लंबाई चौड़ाई से (15) मीटर अधिक है। लंबाई (6) मीटर और चौड़ाई (5) मीटर बढ़ाने पर नया क्षेत्रफल (1944) वर्ग मीटर होता है। मूल चौड़ाई क्या है?

A rectangle has length (15) m more than its breadth. When length is increased by (6) m and breadth by (5) m, the new area is (1944) square m. What is the original breadth?

Explanation opens after your attempt
Correct Answer

C. (39) मीटर(39) m

Step 1

Concept

If original breadth is (x), the new area is ((x+21)(x+5)=1944). This gives (x=39).

Step 2

Why this answer is correct

The correct answer is C. (39) मीटर / (39) m. If original breadth is (x), the new area is ((x+21)(x+5)=1944). This gives (x=39).

Step 3

Exam Tip

मूल चौड़ाई (x) हो तो नया क्षेत्रफल ((x+21)(x+5)=1944) है। इससे (x=39) मिलता है।

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Question 46/50 Hard Mathematics Quadratic Equations 5. 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 47/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक तार को आयत के रूप में मोड़ा गया। आयत की लंबाई चौड़ाई से (25) सेमी अधिक है और क्षेत्रफल (2100) वर्ग सेमी है। तार की लंबाई क्या है?

A wire is bent into a rectangle. The length is (25) cm more than the breadth and area is (2100) square cm. What is the length of the wire?

Explanation opens after your attempt
Correct Answer

C. (190) सेमी(190) cm

Step 1

Concept

If breadth is (x), then (x(x+25)=2100), giving (x=35) and length (60). The wire length is (2(35+60)=190) cm.

Step 2

Why this answer is correct

The correct answer is C. (190) सेमी / (190) cm. If breadth is (x), then (x(x+25)=2100), giving (x=35) and length (60). The wire length is (2(35+60)=190) cm.

Step 3

Exam Tip

चौड़ाई (x) हो तो (x(x+25)=2100), जिससे (x=35) और लंबाई (60) है। तार की लंबाई (2(35+60)=190) सेमी है।

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Question 48/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक आयताकार बगीचे के चारों ओर समान चौड़ाई (4) मीटर का रास्ता है। बगीचा (46) मीटर लंबा और (32) मीटर चौड़ा है। कुल क्षेत्रफल क्या है?

A rectangular garden has a uniform (4) m wide path around it. The garden is (46) m long and (32) m wide. What is the total area?

Explanation opens after your attempt
Correct Answer

B. (2160) वर्ग मीटर(2160) square m

Step 1

Concept

Outer dimensions are (46+8=54) and (32+8=40). Total area is \(54 \times 40=2160\) square m.

Step 2

Why this answer is correct

The correct answer is B. (2160) वर्ग मीटर / (2160) square m. Outer dimensions are (46+8=54) and (32+8=40). Total area is \(54 \times 40=2160\) square m.

Step 3

Exam Tip

बाहरी आयाम (46+8=54) और (32+8=40) हैं। कुल क्षेत्रफल \(54 \times 40=2160\) वर्ग मीटर है।

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Question 49/50 Hard Mathematics Quadratic Equations 5. Word Problems and Applications Class 10 Level 42

एक (50) मीटर लंबे और (36) मीटर चौड़े बगीचे के चारों ओर समान चौड़ाई (x) मीटर का रास्ता है। कुल क्षेत्रफल (2660) वर्ग मीटर है। (x) क्या है?

A garden (50) m long and (36) m wide has a uniform path of width (x) m around it. The total area is (2660) square m. What is (x)?

Explanation opens after your attempt
Correct Answer

B. (5) मीटर(5) m

Step 1

Concept

The outer dimensions are (50+2x) and (36+2x). From ((50+2x)(36+2x)=2660), (x=5).

Step 2

Why this answer is correct

The correct answer is B. (5) मीटर / (5) m. The outer dimensions are (50+2x) and (36+2x). From ((50+2x)(36+2x)=2660), (x=5).

Step 3

Exam Tip

बाहरी आयाम (50+2x) और (36+2x) हैं। ((50+2x)(36+2x)=2660) से (x=5) है।

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Question 50/50 Hard Mathematics Quadratic Equations 5. 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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