If Cos θ+ Sin θ = √2 Cos θ, find the value of (cos θ - sin θ) Sol: Shortcut Trick Formula Used:   cos θ + sin θ = x, then cos θ - sin θ = √(2 - x2)  Calculation:  Using the above formula, we get  ⇒ cos θ - sin θ = √{2 - (√2 cos θ)2}    ⇒ cos θ - sin θ = √{2 - 2cos2 θ}  ⇒ cos θ - sin θ = √2 ...

Two tap P and Q can fill a tank in 15 and 25 minutes respectively both taps are opened together. When tank is filled  8/15 a leakage tap is opened. leakage tap’s efficiency is  1/4 of the net efficiency of taps P and Q together. In how much time tank will get filled. Sol:

If compound interest on a sum for two years at 16 2/3% p.a. is Rs. 318.5, the simple interest (in Rs.) on the same sum at the same rate for years of time is a) 350 b) 367.5 c) 318.5 d) 333.5  Sol:

Find the sum of all odd factor of 840. a) 182 b) 192 c) 162 d) 172 Sol: 840 = 2³ × 3 × 5 × 7 Sum of all odd factors of 840 = (20).(30+31).(50+51).(70+71) = 1 × 4 × 6 × 8 = 192

Two numbers are in Ratio 3: 4 if 12 is subtract from each. The new numbers are in the Ratio 5:7. If 13 is added to first and 23 is added to the second number, then the ratio become. a) 5: 7 b) 3: 5 c) 7: 9 d) 29: 27 Sol:

What is the greatest positive integer that divides 554, 714 and 213 leaving the remainder 43, 57 and 67, respectively? a)            70 b)            73 ...

If a2+b2+1=2a, then the value of a4+b7 is: a) 0 b) 1 c) 2 d) 4 Sol:

In the given circle with diameter AB, find the value of X. a)            30 b)            60 c)            45 ...

(232+1) is exactly divisible by a certain number, then which of the following is also divisible by the same number a) 296+1 b) 216+1 c) 216-1 d) 7 ×232 Sol: 2⁹⁶ + 1 = (2³²) + (1)³ = (2³² + 1) (2⁶⁴ + 1 + 2³²)

The highest common factor of 108, 72 and 5a is a. What can be the least common multiple of 108, 72 and a? a) 108 b) 216 c) 72 d) 36 Sol: Given:  HCF of 108, 72 and 5a = a  Calculation:  ⇒ 108 = 72 × 1 + 36  ⇒ 72 = 36 × 2 + 0  ⇒ ...

In a class there are ‘P’ students out of them ‘Q’ are boys what part of the class is composed by girls. Sol: Total students = P Boys = Q Girls = P – Q

Atul, Chiru and Amit enter in a partnership in Ratio ¾:4/5:6/7 of their capital. After 8 months Amit increases his share of capital by 25%. If at the end of the year the profit earned is 6940 Rs. Then the share of Atul in the profit is? a) 1610 b) 2100 c) 1820 d) 1920 Sol: ...