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Q.1) A solid sphere of diameter 7 cm is cut into two equal halves. What will be the increase (in cm.2) in the total surface area?
7 से.मी. व्यास वाले एक ठोस गोले को दो बराबर भागों में काटा जाता है। कुल पृष्ठीय क्षेत्रफल में कितनी वृद्धि (से.मी.2 में) होगी?
A. 56 cm.2 B. 66 cm.2 C. 88cm.2 D. 77 cm.2
Q.2) The radius of circle is increased by 1%. How much does the area of the circle increased?
किसी वृत्त की त्रिज्या को 1% से बढ़ाया गया वृत्त के क्षेत्रफल में % वृद्धि ज्ञात कीजिए?
A. 0.331% B. 2.02% C. 2.01% D. 3.302%
Q.3) In the given figure, PQ = 30, RS = 24 and OM = 12, then what is the value of ON?
दी गयी आकृति में, PQ = 30, RS = 24 तथा OM = 12 है, तो ON का मान क्या है?
A. 18 B. 15 C. 21 D. 24
Q.4) What is the simplified value of (1– sin A cos A)(sin A + cos A)?
(1– sin A cos A)(sin A + cos A) का सरलीकृत मान क्या है?
A. sin3A + cos3A B. sin2A – cos2A C. cos2A – sin2A D. 0
Q.5) If sec x + cos x = 2, then the value of sec16 x + cos16 x will be-
यदि sec x + cos x = 2, तो sec16 x + cos16 x का मान होगा-
A.1 B. √3 C. 2 D. 0
Q.6) The simple and compound interest that can be earned in two years at the same rate is Rs 1500 and Rs 1575 respectively. What is the rate (% per annum) of interest?
दो वर्षों में समान दर पर अर्जित हो सकने वाले साधारण और चक्रवृद्धि ब्याज क्रमशः 1500 रु और 1575 रु है। ब्याज दर (% प्रति वर्ष) कितनी है?
A. 10% B. 5% C. 12.5% D. 20%
Q.7) A person lent certain sum of money at 5% per annum simple interest and in 15 years the interest amounted to Rs 250 less than the sum lent. What was the sum lent (in Rs)?
एक व्यक्ति किसी निश्चित राशि को 5% की वार्षिक दर से साधारण ब्याज पर उधार देता है तथा 15 वर्षों में संयोजित ब्याज की राशि उधार दी गई राशि से 250 रु. कम है । उधार दी गई राशि (रु. में) कितनी थी ?
A. 3000 B. 2000 C. 1500 D. 1000
Q.8) In the given figure, ∠QRN = 40o, ∠PQR = 46o and MN is a taangent at R. What is the value of x, y and z respectively?
दी गयी आकृति में, ∠QRN = 40o, ∠PQR = 46o और MN बिन्दु R पर एक स्पर्श रेखा है | x, y और z का क्रमशः मान क्या है ?
A. 45, 32, 90 B. 32, 45,94 C. 45, 40, 90 D. 40, 46, 94
Q.9) D and E are midpoints of side AB and AC respectively of the ΔABC. A line drawn from A meets BC at H and DE at K. AK : KH = ?
D और E, ΔABC की भुजा AB और AC के क्रमशः मध्यबिन्दु है। A से खींची गयी रेखा H पर BC से और K पर DE से मिलती हैं। AK : KH = ?
A. 2 : 1 B. 3 : 2 C. 1 : 1 D. 1: 2
Q.10) When a positive integer n is divided by 5 the remainder is 2. What is the remainder when the number 3n is is divided by 5 ?
जब एक घन पूर्णांक को 5 से विभाजित किया जाता है तो शेषफल 2 आता है। जब संख्या 3n को 5 से विभाजित करते है। तो शेषफल क्या है?
A. 4 B. 3 C. 2 D. 1
ANSWER-KEY
Q.1- D
If a solid sphere is cut into two equal parts./जब एक ठोस गोले को दो बराबर भागों में काटा जाता है |
Then total surface area of the two parts/तो दोनों भागों का कुल पृष्ठीय क्षेत्रफल = 6πr2
Original surface area/मूल पृष्ठीय क्षेत्रफल = 4πr2
Difference/अन्तर = 2πr2
= 
Q.2- C
= 2 + .01
= 2.01%
Q.3- B
PM = MQ = 15
RN = NS = 12
In ΔOPM/ΔOPM में,
OP2 = PM2 + OM2
OP2 = 152 + 122
OP2 = 225 + 144
OP2 = 369
Now in ΔORN/अब ΔORN में,
OR2 = ON2 + RN2
OP2 - RN2 = ON2
ON2 = 369 - 144 = 225
ON = 15
Q.4- A
Q.5- C
Q.6- A
Simple interest for two years/दो वर्षों के लिए साधारण ब्याज = Rs./रु . 1500
Simple interest for first year/पहले वर्ष के लिए साधारण ब्याज = Rs./रु . 750
Compound interest for second year/दूसरे वर्ष के लिए चक्रवृद्धि ब्याज = Rs./रु . 1575 - Rs./रु . 750 = Rs./रु . 825
Rate of interest/ब्याज की दर = 
Q.7-D
Let the sum lent be Rs.P/माना उधार ली गयी धनराशि P रु. है |
According to the question/प्रश्नानुसार,
(P - 250) × 100 = P × 5 × 15
100 P - 25000 = 75 P
25 P = 25000
P = 1000
Q.8- D
x = 40o (Angles in alternate segment/एकान्तर वृत्त - खंड में स्थित कोण)
y = 46o (Angles in alternate segment/एकान्तर वृत्त - खंड में स्थित कोण)
We know that/हम जानते हैं,
y + z + 40 = 180
46 + 40 + z = 180
z = 180 - 86
z = 94
Q.9- C
According to thales theorem-
AK : KH = 1 : 1
Q.10- D
Suppose /माना
n = 5q + 2
3n = 3(5q + 2)
3n = 15q + 6
= 5(3q + 1) + 1
remainder /शेष
= 1
