4
Q:

# 5 sin(x)+ 12 cos(x) + r is always greater than or equal to zero. What is the smallest value satisfied by 'r' ?

 A) -13 B) 11 C) 13 D) -11

Answer:   C) 13

Explanation:

Given,

5sinx + 12cosx ≥ -r

cosx) ≥ -r

$\frac{5}{13}$= cosA => sinA =$\frac{12}{13}$

=> 13(sinx cosA + sinA cosx) ≥ -r

=> 13(sin(x + A)) ≥ -r

we know that , -1 ≤ sin (angle) ≤ 1

=> 13sin (x + A) ≥ -13

Q:

Simplify

39.96% of 649.85 $\mathbf{÷}$13.07 = 45.14 - ?

 A) 25 B) 26 C) 27 D) 28

Answer & Explanation Answer: A) 25

Explanation:

This can be easily simplified by Approximation process

Given 39.96% of 649.85 $÷$13.07 = 45.14 - ? can be written as

40% of 650 $÷$13 = 45 - ?

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0 239
Q:

Simplify the fraction?

5 (2/7) - 3 (1/14) - 2 (1/14) - 1 (1/7) = ? + 3 (1/17)

 A) -4 (1/17) B) 5 (2/17) C) -2 (1/17) D) 3 (3/17)

Answer & Explanation Answer: A) -4 (1/17)

Explanation:

Given fraction is 5 (2/7) - 3 (1/14) - 2 (1/14) - 1 (1/7) = ? + 3 (1/17)

It can be written as

(5 - 3 - 2 - 1) + (2/7 - 1/14 - 1/14 - 1/7) = ? +  3 (1/17)

-1 + 0 - 3 (1/17) = ?

=> ? = -4 (1/17)

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2 277
Q:

5 + 2 x 10/2 = ?

 A) 15 B) 35 C) 10 D) 20

Answer & Explanation Answer: A) 15

Explanation:

Using BODMAS Rule,

First solve division, mutiplication and Addition

So here 10/2 = 5

Then 2 x 5 =  10

Now, 5 + 10 = 15.

Hence, 5 + 2 x 10/2 = 15.

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4 458
Q:

Simplify the following :

 A) 10 B) 24 C) 36 D) 40

Answer & Explanation Answer: A) 10

Explanation:

Given equation can be written as

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0 379
Q:

Simplify the following expression?

40% of () = 48

 A) 24 B) 22 C) 20 D) 18

Answer & Explanation Answer: C) 20

Explanation:

We know that

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1 372
Q:

Derivative of sinx by first principle?

 A) -sinx B) -cosx C) cosx D) sinx

Answer & Explanation Answer: C) cosx

Explanation:

Thus, the derivative of sinx by first principle is cosx.

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2 401
Q:

Simplify the following and find the value of ?

 A) 1134 B) 1237 C) 1187 D) 1249

Answer & Explanation Answer: A) 1134

Explanation:

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5 991
Q:

Simplify

 A) 10 47/60 B) 11 45/73 C) 11 47/36 D) 10 35/48

Answer & Explanation Answer: A) 10 47/60

Explanation:

The given equation is in Mixed fraction.

Now to solve this type of fractions,

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8 608