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Q.1. 66 cubic centimeters of silver is drawn into a wire of 1mm in diameter. The length of the wire in meters will be-
66 घन सेमी. चांदी से 1 मिमी. व्यास वाला एक तार खींचा जाता है। तार की लम्बाई कितने मीटर होगी?
(A) 84
(B) 128
(C) 116
(D) 96
Q.2. If x + y + z = – 1, xy + yz + zx = – 1, xyz = – 1, then x3 + y3 + z3 is-
यदि x + y + z = – 1, xy + yz + zx = – 1, xyz = – 1, तो x3 + y3 + z3 है -
(A) – 2
(B) – 1
(C) 0
(D) 1
Q.3. Rakesh get married 8 years ago. His present age is times his age at the time of his marriage. Rakesh's sister was 10 years younger to him at the time of his marriage. The age of Rakesh's sister is-
राकेश का विवाह 8 वर्ष पूर्व हुआ था। उसकी वर्तमान आयु, उसके विवाह के समय की आयु की गुना है। राकेश की बहन उसके विवाह के समय 10 वर्ष छोटी थी। राकेश की बहन की आयु है-
(A) 38 years/वर्ष
(B) 36 years/वर्ष
(C) 32 years/वर्ष
(D) 34 years/वर्ष
Q.4. A train passes through a tunnel whose length is 500 metres in 1 minute while running at a speed of 72 km per hour. The length of the train is-
एक रेलगाड़ी 500 मी. लम्बी सुरंग को 72 किमी/घंटा की चाल से 1 मिनट में पार करती है। रेलगाड़ी की लम्बाई है-
(A) 750 m./मी.
(B) 700 m./मी.
(C) 800 m./मी.
(D) 680 m./मी.
Q.5. A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture the ratio becomes 4 : 5. The quantity of alcohol in the given mixture is-
एक मिश्रण में एल्कोहल और पानी का अनुपात 4 : 3 है। यदि 5 ली. पानी इस मिश्रण में मिलाया जाता है तो अनुपात 4 : 5 हो जाता है। दिये गये मिश्रण में एल्कोहल की मात्रा है-
(A) 12 litres/लीटर
(B) 10 litres/लीटर
(C) 14 litres/लीटर
(D) 16 litres/लीटर
Q.6. If 4b2+ = 2, then the value of 8b3+ is
यदि 4b2+ = 2, तो 8b3+ का मान है
(A) 0
(B) 1
(C) 2
(D) 27
Q.7. The C.P. of two shirts taken together is Rs. 840. If by selling one at a profit of 16% and the other at a loss of 12% there is no loss or gain in the whole transaction, then the C.P. of two shirts are respectively-
दो कमीजों का एक साथ क्रय मूल्य 840 रू. है। यदि एक को 16% लाभ पर बेचा जाता है और दूसरी को 12% हानि पर, तो पूरे लेन देन में कुछ भी लाभ या हानि नहीं होती है। दोनों कमीजों का क्रमशः क्रय मूल्य है-
(A) Rs.360, Rs.480
(B) Rs.480, Rs.360
(C) Rs.380, Rs.460
(D) Rs.460, Rs.380
Q.8. The sum of five consecutive integers is 'a' and the sum of next five consecutive integers is b. Then is equal to-
पाँच क्रमिक पूर्णांकों का योग a और अगले पाँच क्रमिक पूर्णांकों का योग b है, तो के बराबर है-
(A)
(B)
(C) 4
(D) 2
Q.9. If x2 + y2 + z2 = xy + yz + zx, (x ≠ 0), then the value of is
यदि x2 + y2 + z2 = xy + yz + zx, (x ≠ 0) हो, तो का मान है-
(A) 0
(B) 1
(C)
(D)
Q.10. If x, x ≠ 0 then the value of is
यदि x, x ≠ 0 हो, तो का मान है-
(A)
(B)
(C)
(D)
ANSWER KEY:
Q1. (A)
h = 8400 cm. /सेमी. = 84 m./मी.
Q2. (D) x3+y3+ z3 - 3xyz
= (x + y + z) (x2 + y2+ z2 – xy – yz – zx)
= (x + y + z) (x + y + z)2 – 3xy – 3yz – 3zx
x33+ y3+ z3 + 3 = 1 {1 – 3(– 1)} = 4
x3 + y3 + z3 = 1
Q3. (A) 8 years ago, Rakesh age = x/8 वर्ष पहले, राकेश की आयु = x
x + 8 =
5x + 40 = 6x
x = 40
Sister's age/बहन की आयु = 40 – 10 + 8 = 38 years/वर्ष
Q4. (B) Length of train/ट्रेन की लम्बाई = x m./मी.
Speed/चाल = = 20 m./sec./मी./से.
1200 = 500 + x
x = 700 m./मी.
Q5. (B) According to the question/प्रश्नानुसार,
20x = 12x + 20
8x = 20
x = 2.5
Quantity of milk/दूध की मात्रा = 4 × 2.5 = 10 litres/लीटर
Q6. (A)
Q7. (A) Let the CP of shirt sold at gain be Rs.x and sold at a loss be Rs.y.
माना लाभ पर बेची गयी शर्ट का क्रय मूल्य x रु. और हानि पर बेची गयी शर्ट का क्रय मूल्य y रु. है ।
x: y = 3: 4
Q8. (A) Third number/तीसरी संख्या =
First number of next sequence/अगले अनुक्रम की पहली संख्या =
a+ 25 = b
25 = b –a
Q9. (C) x2 + y2 + z2 = xy + yz + zx
2x2 + 2y2 + 2z2 = 2xy + 2yz + 2zx
2x2 + 2y2 + 2z2 – 2xy – 2yz – 2zx = 0
(x – y)2 + (y – z)2 + (z – x)2 = 0
x – y = 0, x = y
y – z = 0, y =z
z – x = 0, z = x
Q10. (C)