1 .If x+($1\over x$)=2 then the value of $x^7$+ ($1\over x^7$) is
A.$2^5$
B. 2
C. $2^12$
D.$2^7$
Answer & Explanation
Answer : Option B |
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Explanation : |
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x+$1\over x$=2 So, x = 1 $x^7$+ $1\over x^5$=1+$1\over1$=2 |
2 .If a shop-keeper purchases cashewnut at ` 250 per kg and sells it at ` 10 per 50 grams, then he will have ____
Answer & Explanation
Answer : Option C |
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Explanation : |
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Cost price = `250
Selling price = `(10X$1000\over50$)= `200
Loss percentage=$250-200\over250$x100=20% |
3 .The average of some natural numbers is 15. If 30 is added to first number and 5 is subtracted f rom the l ast number the average becomes 17.5 then the number of natural number is ?
Answer & Explanation
Answer : Option A |
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Explanation : |
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The average of nnatural number = 15
New average of nnatural numbers = 17.5
ATQ,
(17.5) n = (15)n+ 30 – 5
17.5n– 15n = 25
n = 10 |
4 .The total s urf ace area of a regul ar triangular pyramid with each edges of length 1 cm is ?
A. $4\sqrt3$ $cm^2$
B. $\sqrt3$ $cm^2$
C. 4 $cm^2$
D.$4\over3$$\sqrt3$ $cm^2$
Answer & Explanation
Answer : Option B |
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Explanation : |
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Each side of triangular pyramid = 1 cm Total surface area =$\sqrt3$ $a^2$
=$\sqrt3$x1x1 =$\sqrt3$ $cm^2$
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5 .The shadow of a tower standing on a level plane is found to be 40 m longer when the sun's altitude is 45°, than when it is 60°. The height of the tower is
A.30(3+$\sqrt3$)m
B.40(3+$\sqrt3$)m
C.20(3+$\sqrt3$)m
D.10(3+$\sqrt3$)m
Answer & Explanation
Answer : Option C |
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Explanation : |
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6 .Provided, sin(A – B) = sinA cosB – cosA sinB, then sin15° will be
A.$\sqrt3-3\over2\sqrt3$
B.$\sqrt3-3\over\sqrt2$
C.$\sqrt3\over2\sqrt2$
D.$\sqrt3+3\over2\sqrt3$
Answer & Explanation
Answer : Option A |
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Explanation : |
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sin (15º) = sin (45º – 30º)
= sin 45º cos30º – cos30º sin 45º
= $1\over\sqrt2$ x $\sqrt3\over2$ - $1\over2$x $1\over\sqrt2$
= $\sqrt3-1\over2\sqrt2$ |
7 .The ratio of the ages of A and B at present is 3 : 1. Four years earlier the ratio was 4 : 1. The present age of A is ?
Answer & Explanation
Answer : Option A |
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Explanation : |
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The ratio of the ages of A and B = 3 : 1 Four years ago,
The ratio of the ages of A and B = 4 : 1 ATQ,
$4x+4\over x+4 $=$3\over1$
4x+ 4 = 3x+ 12 x = 8
So, present age of A = 4x+ 4
= 4 × 8 + 4 = 36 years |
8 .If sinθ+ $sin^2$θ = 1, then value of $cos^2$ θ+ $cos^4$θ is
Answer & Explanation
Answer : Option B |
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Explanation : |
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sinθ+ $sin^2$θ = 1,
sinθ= 1-$sin^2$θ -$cos^2$θ = 1,
$cos^2$ θ+ $cos^4$θ= sinθ+ $sin^2$θ
=1 |
9 .A bus moving at 40 km per hour covers a distance in 6 hours 15 minutes. If it travels the same distance at 50 km per hour how long will it take to cover the distance ?
Answer & Explanation
Answer : Option A |
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Explanation : |
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ATQ,
Total distance = 40 × 6.25 = 250 km Speed = 50 km/hr
Required time = $250\over50$ = 5 hours |
10 .If αis an acute angle and 2sin α+ 15 cos2 α= 7, then the value of cot α is
A.$3\over4$
B.$5\over4$
C.$4\over3$
D.$4\over5$
Answer & Explanation
Answer : Option A |
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Explanation : |
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