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Q.1 – ABCD is a cyclic quadrilateral. A tangent PQ is drawn on the point B of the circle. If ∠DBP = 650 then find ∠BCD-
ABCD एक चक्रीय चतुर्भुज है। एक स्पर्श रेखा PQ वृत्त के बिंदु B पर खींची गई है। यदि ∠ DBP = 650 तो ∠ BCD ज्ञात कीजिये-
(A) 105o
(B) 115o
(C) 125o
(D) 95o
Q.2 – Two chords AB and CD of a circle intersect at E such that AE = 2.4 cm, BE = 3.2 cm, and CE = 1.6 cm. The length of DE is-
एक वृत्त की दो जीवा AB और CD, E पर इस प्रकार प्रतिच्छेदित करती है कि AE = 2.4 सेमी, BE = 3.2 सेमी और CE = 1.6 सेमी. DE की लम्बाई क्या है?
(A) 1.6 cm/सेमी.
(B) 3.2 cm/सेमी
(C) 4.8 cm/सेमी
(D) 6.4 cm/सेमी
Q.3 – The areas of two similar triangle are 12 cm2 and 48 cm2 . If the height of the smaller one is 2.1 cm, then the corresponding height of the bigger one is-
दो समरूप त्रिभुजों के क्षेत्रफल 12 सेमी2 और 48 सेमी2 है यदि छोटे त्रिभुज की ऊँचाई 2.1 सेमी है तो बड़े त्रिभुज की संगत ऊँचाई क्या है?
(A) 4.8 cm/सेमी
(B) 8.4 cm/सेमी
(C) 4.2 cm/सेमी
(D) 0.525 cm/सेमी
Q.4 – 10 years ago Ram was 5 times as old as Shyam but 20 year later from now he will be only twice as old as Shyam. How many years old is Shyam?
10 वर्ष पहले राम, श्याम से आयु में 5 गुना था, लेकिन अब से 20 वर्ष बाद वह, श्याम की आयु का केवल दोगुना होगा। श्याम की आयु क्या है?
(A) 20 years/वर्ष
(B) 30 years/वर्ष
(C) 40 years/वर्ष
(D) 50 years/वर्ष
Q.5 – When x40 + 2 is divided by x4 +1, what is the remainder?
जब x40 + 2 को x4 +1 से भग दिया जाता है तो शेषफल क्या है?
(A) 1
(B) 2
(C) 3
(D) 4
Q-6 If x = 2015, y = 2014 and z = 2013, then value of x2+y2 +z2 – xy – yz – zx is
यदि x = 2015, y = 2014 और z = 2013 हो तो x2+y2 +z2 – xy – yz – zx का मान है-
(A) 7.5
(B) 5
(C) 4.5
(D) 3
Q-7 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) (a2 + b2 + c2 )
(B) 2 (a2 + b2 + c2 ).
(C) 8 (a2 + b2 + c2 )
(D) 4 (a2 + b2 + c2 )
Q-8 DE is a tangent to the circum-circle of ΔABC at the vertex A such that DE||BC. If AB = 17 cm., then the length of AC is equal to -
ΔABC के परिवृत्त में DE रेखा A शीर्ष बिन्दु पर इस प्रकार स्पर्श करती है कि DE||BC यदि AB = 17 सेमी. है तो AC की लम्बाई बराबर है-
(A) 20
(B) 18
(C) 15
(D) 17
Q-9 The distance between the centres of two circles with radii 9 cm. and 16 cm. is 25 cm. Then find the length of the common transverse tangent.
दो 9 सेमी. और 16 सेमी. त्रिज्या वाले वृत्तों के केन्द्रों के बीच की दूरी 25 सेमी. है तो उनके उभयनिष्ठ अनुस्पर्श रेखा खण्ड की लम्बाई ज्ञात कीजिए।
(A) 27
(B) 24
(C) 25
(D) 29
Q-10 The sum of two numbers is 232 and their HCF is 29. What is the numbers of such pairs of numbers satisfied the above condition.
दो संख्याओं का योग 232 और उनका म.स.प. 29 है। ऐसी संख्याओं के कितने जोड़े संभव है जो उपरोक्त शर्त को संतुष्ट करेंगे।
(A) 0
(B) 1
(C) 2
(D) 3
Answers:
Q.1) Sol. – (B)
∠DBQ = 180o – ∠DBP = 180o – 65o = 115o
∠DBP = ∠DCB = 115o (alternate angle/एकान्तर कोण)
∠BCD = 115o
Q.2) Sol. – (C)
AE × BE = CE × DE
2.4 × 3.2 = 1.6 × x
x = 
= 4.8 cm. /सेमी
= 4.8 cm. /सेमी
Q.3) Sol. – (C)
Q.4) Sol. – (A)
Let the present age of Ram and Shyam be x and y years./माना राम और श्याम की वर्तमान आयु x और y वर्ष हैं |
(x – 10) = 5 (y – 10)
x – 5y = – 40 ________(I)
and/और (x+20) = 2(y+20)
x – 2y = 20 _________(II)
On solving/हल करने पर,
y = 20 years/वर्ष
Q.5) Sol. – (C)
Let/माना f(x) = x40 + 2
Put/रखिये x4 = –1,
f(x) = (–1)10 + 2 = 3
Q.6) Sol-(D)
Q.7) Sol-(D)
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 )
Q.8) Sol-(D)
OA = OB = OC
AB = BC = AC
AC = 17 cm
Q.9) Sol-(A)
Length of tangent /स्पर्श रेखा की लम्बाई
Q.10) Sol-(C)
Let two number is 29a and 29b
माना दो संख्याएं 29a तथा 29b हैं
29a + 29b = 232
a + b = 232/29 = 8
(a,b)= (1,7) (3,5)
The pair is / युग्म हैं (87, 145) (29,203)
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