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यदि x = 2015, y = 2014 और z = 2013, तो x2 + y2 + z2 – xy – yz – zx का मान है
(A) 2
(B) 3
(C) 4
(D) 6
Sol. (B) - x2 + y2 + z2 – xy – yz – zx =
=
=
= 3Ques. 2 - If P3 + 3P2 + 3P = 7, then the value of P2 + 2P is
यदि P3 + 3P2 + 3P = 7, तो P2 + 2P का मान है
(A) 3
(B) 4
(C) 5
(D) 6
Sol. (A) – (P + 1)3 = P3 + 1 + 3P2 + 3P
(P + 1)3 = 7 + 1 = 8
(P + 1) = 2
P = 1
P2 + 2P = 1 + 2 = 3
Ques. 3 - If 3a2 = b2 ≠ 0, then the value of
यदि 3a2 = b2 ≠ 0, तो
का मान है (A)
(B) b
(C)
(D)
Sol. (A) –
Ques. 4 - If tan θ =
, then the value of 
is equal to यदि tan θ =
, तो 
का मान बराबर है (A)
(B)
(C)
(D)
Sol. (A) –
Ques. 5 - If
and 
then 
is equal to यदि
और 
तो 
बराबर है (A)
(B)
(C)
(D)
Sol. (C) –
,
Ques. 6 - If p + q + r = 0, then the value of (p + q – r) 2 + (q + r – p) 2 + (r + p – q) 2 is
यदि p + q + r = 0, तो (p + q – r) 2 + (q + r – p) 2 + (r + p – q) 2 का मान है
(A) 0
(B) 8pqr
(C) 4(pq + qr + rp)
(D) 4(p2 + q2 + r2)
Sol. (D) – p + q + r = 0
p + q = - r, q + r = - p, r + p = - q
(p + q - r) 2 + (q + r - p) 2 + (r + p - q) 2
= 4r2 + 4p2 + 4q2
= 4 (p2 + q2 + r2)
Ques. 7 - A certain sum in certain time becomes Rs.500 at the rate of 8% per annum simple interest and the same sum amounts to Rs.200 at the rate of 2% simple interest in the same duration. Find the time.
एक निश्चित धनराशि निश्चित समय में 8% प्रति वर्ष साधारण ब्याज की दर पर 500 रू.हो जाती है और यही धनराशि 2% प्रतिवर्ष साधारण ब्याज की दर पर इसी समान समय में 200 रू. हो जाती है। समय ज्ञात कीजिए।
(A) 25 years/वर्ष
(B) 30 years/वर्ष
(C) 40 years/वर्ष
(D) 50 years/वर्ष
Sol. (D) –
Again for 8% rule/पुनः 8% नियम से,
Sum/धनराशि = 500 – 400 = रु. 100
PT = 5000
T =
= 50 years/वर्षQues. 8 - A shopkeeper sells an article at a profit of 20%. If he had bought it at 20% less and sold for Rs.10 less, he would have gained 25%. Find the cost price of the article.
एक दुकानदार एक वस्तु को 20% लाभ पर बेचता है। यदि यह इसे 20% कम में खरीदे और 10 रू.कम में बेचे तो उसे 25% लाभ प्राप्त होगा। वस्तु का क्रय मूल्य ज्ञात कीजिए।
(A) Rs. /रु. 40
(B) Rs. /रु. 50
(C) Rs. /रु. 60
(D) Rs. /रु. 70
Sol. (B) –
C.P./क्रय मूल्य S.P./विक्रय मूल्य Profit/लाभ
Case – I 100% 120% 20%
Case – I 80% 100% 25%
According to the question/प्रश्नानुसार,
20% = Rs. /रु. 10
100% = Rs. /रु. 50
Ques. 9 - Raj can row a certain distance downstream in 12 hr and can retern the same distance in 18 hr. If the stream flows at the rate of 6 km/hr, find the speed of Raj in still water.
राज अनुप्रवाह में एक निश्चित दूरी को तैरने में 12 घंटे और उसी दूरी से वापस आने में 18 घंटे लगाता है। यदि प्रवाह की दर 6 किमी/ घंटा हो, तो राज की शांत जल में चाल क्या है?
(A) 15 kmph/ किमी/घंटा
(B) 20 kmph/ किमी/घंटा
(C) 25 kmph/ किमी/घंटा
(D) 30 kmph/ किमी/घंटा
Sol. (D) – Let the speed of Raj in still water be x kmph/माना राज की स्थिर जल में चाल x किमी/घं. है |
speed in downstream/अनुप्रवाह चाल = (x + 6)
and speed in upstream/और ऊर्ध्वप्रवाह चाल = (x - 6)
12(x + 6) = 18(x - 6)
2x + 12 = 3x - 18
x = 30 kmph/ किमी/घं.
Ques. 10 - A train overtakes two persons walking along a railway track. The first one walks at 4.5 kmph and the other one walks at 5.4 km/hr. The train needs 8.4 sec and 8.5 sec. respectively to overtake them. What is the speed of the train if both the person are walking in the same direction as the train?
एक रेलगाड़ी दो व्यक्ति जो रेलवे पथ के अनुदिश चल रहे हैं, को पार करती है। पहला 4.5 किमी/घंटा और दूसरा 5.4 किमी/घंटा की चाल से चल रहा है। रेलगाड़ी द्वारा उनको पार करने में लगा समय क्रमशः 8.4 सेकण्ड और 8.5 सेकण्ड हैं। रेलगाड़ी की चाल क्या है, यदि व्यक्ति रेलगाड़ी की ही दिशा में चल रहे हैं?
(A) 66 kmph/ किमी/घंटा
(B) 72 kmph/ किमी/घंटा
(C) 78 kmph/ किमी/घंटा
(D) 81 kmph/ किमी/घंटा
Sol. (D) –
Speed of first man/पहले आदमी की चाल =
= 1.25 m/sec (मी./से.)and speed of second man/और दूसरे आदमी की चाल =
= 1.5 m/sec (मी./से.)Let the speed of the train be x km/hr./माना ट्रेन की चाल x किमी./घंटा है |
According to the question/प्रश्नानुसार,
(x – 1.25) × 8.4 = (x – 1.5) × 8.5
8.4x – 10.5 = 8.5x – 12.75
0.1x = 2.25
x = 22.5
Speed in km/hr./किमी./घंटा की चाल = 22.5 ×
= 81 km/hr./किमी./घंटाAnswer Key:
Q1. (B)
Q2. (A)
Q3. (A)
Q4. (A)
Q5. (C)
Q6. (D)
Q7. (D)
Q8. (B)
Q9. (D)
Q10. (D)
