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Q.1. If a + b + c = 0, then the value of (a + b – c)2
+ (b + c – a)2 + (c + a – b)2 is -
यदि a + b + c = 0 हो तो (a + b – c)2
+ (b + c – a)2 + (c + a – b)2 का मान है -
A. 0
B. 8abc
C. 4(a2 + b2 + c2)
D. 4(ab + bc + ca)
Q.2. A hemispherical bowl of internal radius 15 cm. contains a liquid. The liquid is to be filled in to a cylindrical-shaped bottles of diameter 5 cm. and height 6 cm. The number of bottles required to empty the bowl is -
एक अर्द्धवृत्त कटोरा है जिसमें तरल पदार्थ भरा है और उसकी आन्तरिक त्रिज्या 15 सेमी. है। उस तरल पदार्थ को 5 सेमी. व्यास और 6 सेमी. ऊँचाई वाली बेलनाकार बोतलों में भरा जाता है। उस कटोरे को खाली करने के लिए कितनी बोतलों की आवश्यकता होगी?
A. 30
B. 40
C. 50
D. 60
Q.3. Let A, B, C, D be the angles of a quadrilateral. If they are concyclic, then the value of cos A + cos B + cos C + cos D is -
A, B, C, D चतुर्भुज के कोण है। यदि वे एक वृत्तीय हो तो cos A + cos B + cos C + cos D का मान है -
A. 0
B. 1
C. - 1
D. 2
Q.4. If
, 
, then sin2
is equal to - यदि
, 
, तो sin2
बराबर है – A.
B.
C.
D.
Q.5. A double bed is sold at Rs.6423.90. The shopkeeper allows successive discounts of 8%, 5% and 2% on it. What is the marked price?
एक डबलबेड को 6423.90 रू. में बेचा गया । दुकानदार उस पर 8%, 5% और 2% की क्रमिक छूट देता है। अंकित मूल्य क्या है ?
A. Rs./रु.8500
B. Rs./रु.8000
C. Rs./रु.7500
D. Rs./रु.7500.50
Q.6. A got twice as many marks in English as in Science. His total marks in English, Science and Mathematics is 180. If the ratio of his marks in English and Mathematics is 2: 3, what is his marks in Science?
A को अंग्रेजी विषय में विज्ञान विषय की अपेक्षा दुगुने अंक मिले। अंग्रेजी, विज्ञान और गणित विषयों में उसे कुल मिला कर 180 अंक प्राप्त हुए। यदि उसे अंग्रेजी और गणित विषयों में प्राप्त अंकों का अनुपात 2: 3 है तो उसे विज्ञान विषय में कितने अंक प्राप्त हुए?
A. 20
B. 60
C. 30
D. 40
Q.7. Find the difference between the compound interest and the simple interest on Rs.32000 at 10% p.a. for 4 years.
32000 की धनराशि पर 4 वर्ष के लिए 10% वार्षिक की दर से चक्रवृद्धि ब्याज और साधारण ब्याज का अन्तर बताइए।
A. 2051.20
B. 2052.50
C. 2025.20
D. 2501.20
Q.8. Two trains start from stations A and B and travel towards each other at speeds of 50 km./hr. and 60 km./hr. respectively. At the time of their meeting, the second train has travelled 120 km. more than the first. The distance between A and B is -
दो रेलगाड़ियां A और B स्टेशनों से रवाना होती है और क्रमशः 50 किमी./घं. व 60 किमी./घं. की चाल से एक-दूसरे की ओर चलती है। जब वे एक-दूसरे से मिलती है उस स्थान तक दूसरी रेलगाड़ी पहली वाली की अपेक्षा 120 किमी. अधिक यात्रा करती है। A और B के बीच की दूरी बताइए।
A. 1200 km.
B. 1440 km.
C. 1320 km.
D. 990 km.
Q.9. If P3 + 3P2 + 3P = 7, then the value of P2 + 2P is
यदि P3 + 3P2 + 3P = 7, हो तो P2
+ 2P का मान क्या होगा?
A. 4 B. 3
C. 5
D. 6
Q.10. If 3a2 = b2 ≠ 0, then the value of
is –यदि 3a2 = b2 ≠ 0, हो तो
का मान है - A.
B. b
C.
D.
ANSWER KEY:
Q1. (C) a + b + c = 0
a + b = - c, b + c = - a, c + a = - b
(a + b – c)2 + (b + c – a)2 + (c + a – b)2
= 4c2 + 4a2 + 4b2
= 4 (a2 + b2 + c2)
Q2. (D)
Q3. (A)
Q4. (C)
Q5. (C)
The marked price/अंकित मूल्य
= 6423.90 ×
= Rs.7500
Q6. (C)
Let his marks in science is x/ माना विज्ञान में प्राप्त अंक x हैं ।
Marks in English/अंग्रेजी में अंक = 2x
Marks in Mathematics/गणित में अंक = 180 - x - 2x = 180-3x
According to question/प्रश्नानुसार,
3x = 180 – 3x
6x = 180
x = 30
Q7. (A)
Compound interest/चक्रवृद्धि ब्याज
= 3200
=
= 3.2 (4641)
= 14851.2
Simple interest/साधारण ब्याज =
= 12800
Req. difference/अभीष्ट अन्तर = 14851.2 - 12800
= Rs. 2051.20
Q8. (C)
Let train A covers x km/माना ट्रेन A, x किमी. की दूरी तय करती है ।
Þ 60x = 50x + 6000
Þ 10x = 6000
Þ x = 600 km/किमी.
Total distance/कुल दूरी = 600 + 600 + 120
= 1320 km/किमी.
Q9. (B)
(P + 1)3 = P3 + 1 + 3P2 +
3P
P3 + 1 + 3P2 + 3P = 8
Þ (P + 1)3
= 23
Þ P + 1 = 2
Þ P = 1
Þ P2 + 2P
= 1 + 2 = 3
Q10. (A)
3a2 = b2
