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# SSC Quiz : Quantitative Aptitude | 29 - 12 - 17

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Q. 1 – If α, β are the roots of x2 + px + 12 = 0 and α - β = 1 then its roots-

यदि α, β और x2 +px+12 = 0 और α - β = 1 के मूल है तो-

(A) ± 3

(B) ± 5

(C) ± 7

(D) ± 4

Sol. (C) –

α + β = - p
α.β = 12
α - β = 1  α2 + β2 - 2 α.β = 1
α2 + β2 = 1 + 24 = 25
(α + β)2 = α2 + β2 + 2 α.β
p2 = 25 + 24
p2 = 49
p = ± 7

Q. 2 – The HCF of (x3 + 3x2 - x - 3) and (x3 + 4x2 + x - 6) is-

(x3 + 3x2 - x - 3) और (x3 + 4x2 + x - 6) का म.स.प. है-

(A) (x2 + 2x - 3)

(B) (x + 3)

(C) (x + 2)

(D) (x - 1)

Sol. (B) –

x3 + 3x2 - x - 3 = x ( x + 3) - 1 (x + 3)
= (x + 3) (x - 1)
x3 + 4x2 + x - 6 = x3 + 3x2 + x2 +x - 6
= x3 + 3x2 + (x + 3) (x - 2)
= x2 (x + 3) + (x + 3) (x -2)
= (x + 3) (x2 + x - 2)
HCF/ म.स.प. = x + 3

Q. 3 – Find the value of (x3 +y3 + z3 - 3xyz) if x + y + z = and x2 + y2 + z2 = 62.

यदि x + y + z =12 और x2 + y2 + z2 = 62 तो (x3 + y3 + z3 - 3xyz) का मान ज्ञात कीजिये।

(A) 272

(B) 252

(C) 256

(D) 144

Sol. (B) –

(x + y + z)2 = x2 + y2 + z2 + 2 (xy + yz + zx)
xy + yz + zx =   = 41
x3 + y3 +z3 - 3xyz = (62 - 41) × 12= 21 × 12

= 252

Q. 4 – If  then the value of  will be

(A) 118

(B) 119

(C) 115

(D) 120

Sol. (C) –

Q. 5 – 2x = 4y = 8z and xyz = 288, then value of  is -

2x = 4y = 8z और xyz = 288, तो  का मान है-

(A)

(B)

(C)

(D)

Sol. (A) –

2x = 4y = 8z

Q. 6 – Mr. X invests an amount of Rs.15, 860 in the names of his three daughters A, B and C in such a way that they get the same interest after 2, 3 and 4 years respectively. If the rate of simple interest is 5% p.a., then the ratio of the amounts invested among A, B and C will be -

मि. X, 15,860 रू. अपनी तीन पुत्रियों A, B और C के नाम इस प्रकार से निवेश करता है कि वे क्रमश 2, 3 और 4 वर्ष पश्चात समान ब्याज प्राप्त करे। यदि साधारण ब्याज की दर 5% प्रतिवर्ष है तो A, B और C के बीच निवेशित राशि का अनुपात क्या होगा?

(A) 5 : 10 : 12

(B)

(C) 6 : 7 : 8

(D) 6 : 5 : 4

Sol. (B) –

Q. 7 – A goods train leaves a station at a certain time at a fixed speed. After 6 hours, an express train leaves the same station and moves in the same direction at a uniform speed of 75 km/h. This train catches the goods train in 4 hours. Find the speed of the goods train.

एक मालगाड़ी निश्चित समय से और नियत चाल से एक स्टेशन से छूटती है। 6 घंटे बाद एक मेल रेलगाड़ी भी उसी स्टेशन से, उसी दिशा में 75 किमी/घंटा एक समान चाल से छूटती है। यह रेलगाड़ी, मालगाड़ी को 4 घंटे में पकड़ लेती है। मालगाड़ी की चाल ज्ञात कीजिए।

(A) 30 kmph / (किमी. /घंटा)

(B) 36 kmph / (किमी. /घंटा)

(C) 34 kmph / (किमी. /घंटा)

(D) 32 kmph / (किमी. /घंटा)

Sol. (A) –

Let the speed of the goods train be x km/h/माना मालगाड़ी की चाल x किमी./घंटा है |
Distance covered by goods train in 10 hours/10 घंटे में मालगाड़ी द्वारा तय की  गयी दूरी
= Distance Covered by express train in 4 hours/4 घंटे में एक्सप्रेस ट्रेन द्वारा तय की गयी दूरी
10x = 4 × 75
x =  = 30 km/h/(किमी./घंटा)

Q. 8 – A two digits number is four times the sum and three times the product of its digits. Find the number?

दो अंको की एक संख्या, इसके अंको की चार गुनी और गुणनफल की तीन गुनी है। संख्या ज्ञात कीजिए।

(A) 24

(B) 28

(C) 26

(D) 32

Sol. (A) –

Let ten's digit be x and unit's digit y/माना दहाई का अंक x और इकाई का अंक y है |
10x+y = 4(x + y)
and/और 10x + y = 3xy
10x + 2x = 6x2
6x2 - 12 = 0
6x(x - 2) = 0
x = 2
y = 2x = 4
number/संख्या = 24

Q. 9 – The area of circle inscribed in an equilateral triangle of side 24 cm is -

24 सेमी भुजा वाले समबाहु त्रिभुज में खीचे गये वृत्त का क्षेत्रफल है -

(A) 24π cm2/सेमी2

(B) 36π cm2/सेमी2

(C) 48π cm2/सेमी2

(D) 18π cm2/सेमी2

Sol. (C) –

Q. 10 – The average age of committee of 12 members is 45 years. A member aged 58 years retired and his place was taken by another member aged 22 years. The average age of the present committee is -

एक कमेटी के 12 सदस्यों की औसत आयु 45 वर्ष है।एक 58 वर्ष का सदस्य सेवानिवृत्त हो जाता है, और उसके स्थान पर एक 22 वर्ष का सदस्य आ जाता है। वर्तमान में कमेटी के सदस्यों की औसत आयु क्या है?

(A) 42 years/वर्ष

(B) 43 years/वर्ष

(C) 44 years/वर्ष

(D) 41.5 years/वर्ष

Sol. (A) –

Total age of committee in present/ वर्तमान में कमेटी के सदस्यों की कुल आयु
= (12×45-58+22) = 504
average/औसत = = 42 years/वर्ष

1. (C)

2. (B)

3. (B)

4. (C)

5. (A)

6. (B)

7. (A)

8. (A)

9. (C)

10. (A)