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एक संख्या को 987 से भाग देने पर शेषफल 59 आता है। जब इसी संख्या को 21 से भाग दिया जाता है, तो शेषफल क्या है?
(A) 21
(B) 19
(C) 17
(D) 15
Q.2. What is the L.C.M. of a3b – ab3, a3b2 + a2b3 and ab (a + b)?
a3b – ab3, a3b2 + a2b3 और ab (a + b) का ल.स.प. क्या है?
(A) a2b2 (a2 – b2)
(B) ab (a2 – b2)
(C) a2b2 + ab3
(D) a3b3 (a2 – b2)
दो संख्याओं का ल.स.प. उनके म.स.प. का 14 गुना है। ल.स.प. और म.स.प. का योग 600 है। यदि एक संख्या 80 है, तो दूसरी संख्या क्या है?
(A) 40
(B) 60
(C) 160
(D) 280
Q.4. What is the square root of
?
का वर्गमूल क्या है?(A)
(B)
(C)
(D)
Q.5. Two trains travel in the same direction at 50 km/h and 32 km/h respectively. A man in the slower train observes that 15 s elapse before the faster train completely passes him. What is the length of the faster train?
दो ट्रेने एक समान दिशा में क्रमशः 50 किमी/घंटा और 32 किमी/घंटा की चाल से चल रही हैं। धीमी गति वाली ट्रेन में एक आदमी प्रेक्षण करता है कि तेज गति की ट्रेन को उससे पूरी गुजरने में 15 सेकण्ड व्यतीत होते हैं। तेज गति वाली ट्रेन की लम्बाई क्या है?
(A) 75 m./मी.
(B) 125 m./मी.
(C) 150 m./मी.
(D)
m./मी.Q.6. The quantity that must be added to each term of a: b, so as to make it c: d is-
a: b के प्रत्येक पद में जोड़ी जाने वाली मात्रा जो इसे c: d बनाये है-
(A)
(B)
(C)
(D)
Q.7. If u, v, w are real numbers such that u3 - 8v3 - 27w3 = 18uvw, which one of the following is correct?
यदि u, v, w वास्तविक संख्याएं इस प्रकार हैं कि u3 – 8v3 – 27w3 = 18uvw, तो निम्न में से कौन सा एक सही है?
(A) u – v + w = 0
(B) u = 1 – v = – w
(C) u – 2v = 3w
(D) u + 2v = – 3w
Q.8. If the expression px3+3x2 - 3 and 2x3- 5x+p, when divided by x - 4 have the same remainder, then what is the value of p?
यदि व्यंजक px3 + 3x2 - 3 और 2x3 - 5x +p, जब x -4 से विभाजित किये जाते हैं तो शेषफल समान प्राप्त होता है, तो p का मान क्या है?
(A) – 1
(B) 1
(C) – 2
(D) 2
Q.9. If x + y + z = 6 and xy + yz + zx = 11 then what is the value of x3 + y3 + z3 – 3xyz?
यदि x + y + z = 6 और xy + yz + zx = 11 तो x3 + y3 + z3 – 3xyz का मान क्या है ?
(B) 66
(C) 36
(D) 54
Q.10. If
, then what is (xy + zw)2 equal to?यदि
हो, तो (xy + zw)2 के बराबर क्या है?
(A) (x2 + z2)(y2 + w2)
(B) x2y2 + z2w2
(C) x2w2 + y2z2
(D) (x2 + w2)(y2 + z2)
ANSWER:
1. Sol. (C) Let the number is x, when divided by 987/माना संख्या x है, जब इसे 987 से विभाजित किया जाता है
x = 987 × k + 59
x = 47 × 21 × k + 21 × 2 + 17
x = 21 (47k + 2) + 17
Remainder/शेषफल = 17
2. Sol. (A) 2. Sol. (A) a3b – ab3 = ab (a2 – b2)
= ab (a – b) (a + b)
a3b2 + a2b3 = a2b2 (a + b)
L.C.M. = a2b2 (a + b) (a – b)
= a2b2 (a2 – b2)
3. Sol. (D) Let the H.C.F of two numbers/माना दो संख्याओं का म.स.प. = x a3b2 + a2b3 = a2b2 (a + b)
L.C.M. = a2b2 (a + b) (a – b)
= a2b2 (a2 – b2)
and L.C.M./और ल.स.प. = 14x
According to the question/प्रश्नानुसार,
14x + x = 600
15x = 600
x = 40
and L.C.M./और ल.स.प. = 14 × 40 = 560
Now/अब, 40 × 560 = 80 × second number/दूसरी संख्या
Second number/दूसरी संख्या =
= 2804. Sol. (C)
= 
5. Sol. (A) Let x be the length of the faster train./माना तेज चलने वाली ट्रेन की लम्बाई x है ।
Time =
x =
x =
km/किमी.
m./मी. 6. Sol. (D) Let the quantity be x/माना राशि x है ।
(a + x) d = (b + x) c
ad + dx = bc + cx
ad – bc = x (c – d) 
7. Sol. (C) (u)3 + (– 2v)3 + (– 3w)3 = 3 × (– 2)( – 3) uvw
u + (– 2v) + (– 3w) = 0
u – 2v – 3w = 0
u – 2v = 3w
8. Sol. (B) Let/माना f(x) = px3 + 3x2 – 3u + (– 2v) + (– 3w) = 0
u – 2v – 3w = 0
u – 2v = 3w
and/और g(x) = 2x3 – 5x +p
put/रखिये x = 4
f(4) = p × 43 + 3 × 42 – 3
= 64p + 48 – 3 = 64p + 45
and/और g(4) = 2 (4)3 + 5(4) + p
= 128 – 20 + p = 108 + p
According to the question/प्रश्नानुसार,
f(4) = g(4)
64p + 45 = 108 + p
63p = 63
p = 1
9. Sol. (A) x + y + z = 6
and/और xy + yz + zx = 1
x3 + y3 + z3 – 3xyz
= (x + y + z)[(x + y + z)2 – 3(xy + yz + zx)]
= 6 [62 – 3 × 11]
and/और xy + yz + zx = 1
x3 + y3 + z3 – 3xyz
= (x + y + z)[(x + y + z)2 – 3(xy + yz + zx)]
= 6 [62 – 3 × 11]
= 6 × 3 = 18
10. Sol. (D)
xw = yz
(xy + zw)2 = x2y2 + z2w2 + 2(xy.yw)
= x2y2 + z2w2 + 2(zy.yz)
= x2y2 + y2z2 + z2w2 + x2w2
= y2(x2 + z2) + w2(x2 + z2)
= (x2 + z2) (y2 + w2)
= x2y2 + y2z2 + z2w2 + x2w2
= y2(x2 + z2) + w2(x2 + z2)
= (x2 + z2) (y2 + w2)
