A.1

B.2

C.3

D.4

Explanation: log₄ √(a + b + c) = log₄ √(4 + 5 + 7) = = log₄ √16 == log₄ 4 = 1

A.   100

B.   110

C.   120

D.   130

Explanation: LCM of 20,30 and 40 = 120

HCF of 20,30 and 40 = 10

Difference between L.C.M and H.C.F is 120-10 = 110.

A.6

B.24

C.120

D.720

Explanation: six different books on a shell can be arranged in 6P6 6! Ways = 720 ways

A. 26.66%

B. 12%

C. 30%

D. 13.33%

Explanation: Let principal be rs. p

Then simple interest after 15 years will be 2p

Now, Simple Interest = Principal × Rate × Time

2p = p × Rate × 15

2 = Rate × 15

Rate × 15 = 2

Rate = 2/15

rate = 0.1333

So, rate of interest = 13.33%

Explanation: The largest power of 20 contained in 100 factorials.

20=5×2×2

The highest prime factor 20 is 5.

So, number of powers of 20 will only depend on power of 5.

Also, 1005=20,10025=4.

Therefore, the power of 5 is 20+4=24

Hence, the largest power of 20 contained in 100 factorial is 24.

Explanation: The distance travelled by Rajesh from home to office by metro train = 4/5

The distance travelled by auto = 3/20

The distance travelled on Foot = 1 km

Let x be the total distance from the home to the office

Distance travelled

x = [(4/5)x + (3/20)x] + 1

x [1 – (4/5) – (3/20)] =1

x (1/20)=1

x = 20 km

Thus, the total distance travelled by Rajesh from home to the office is 20 km.

Explanation: The LCM is 120

Now to find the smallest square number divisible by 120:

Factors of 120 = 2*2*2*3*5

Now, to form pairs, you have to multiply it by 2*3*5 or 30

120*30 = 3600

Hence, the smallest perfect square number that is divisible by 24, 30, and 60? is 3600 (it is the square of 60).

Explanation: Let the no. of hen be H1, no. of eggs E1, no. days D1 separately

Thus,                               

H1=50, E1=200, D1= 2

We are supposed to find what amount of time will 20 hens require to give 400 eggs

Allow x to be the no. of days

So,

H2= 20, E2= 400, D2=x

Therefore, the formula here will be

                                         (H1 * D1)/E1 = (H2 * D2)/ E2

                                         (50 * 2)/200 = (20 * x)/400

                                         (50 * 2) * 400/(200 * 20) = x

                                           Hence, x = 10

So, we can conclude that 20 hens will take 10 days to lay 400 eggs.

Consequently 20 hens require 10 days to give 400 eggs.

Explanation: Going through option verification

Option A – 21 and 35 , L.C.M =105 , Hence wrong option

Option b – 35 and 49 , L.C.M =245 , Hence wrong option

Option c – 49 and 63, L.C.M =441 , and H.C.F is 7 and difference between numbers is 14, hence option C

Explanation: cp = x

Sold at Rs. 50000 less than Rs. x

so, sp = x - 50000

Also, 50000 is 8% of x

so, 50000 = 8/100 of x

or, 50000 = 0.08x

or, x = 50000/0.08 = 625000

So, Piya bought at Rs. 625000.

To gain what she lost in her first transaction I.e., Rs 50000 she should have sold the car at

Rs. 625000 + 50000 = Rs. 6,75,000

Explanation: The permutations and combinations of abcd taken 3 at a time are respectively 4P3 and 4C3

4P3 = 4! /1! = 24

4C3 = 4!/3! = 4

Explanation: Average = sum of elements / no. of elements.

average age of cricket team = sum of ages of players/ no of players

22 = sum of ages of players/ no of players

22 × 11 = sum of ages of players

242 = sum of ages of players

as average age gets increased by 1 year when the coach age is also included

23 = sum of ages of players + age of coach / no of players + 1

23 ( 11 + 1 ) = sum of ages of players + age of coach

23 × 12 = sum of ages of players + age of coach

276 = sum of ages of players + age of coach

Now,

age of coach = sum of ages of players + age of coach - sum of ages of players

age of coach = 276 – 242= 34

Hence, the age of the coach is 34

Explanation: 16,800 = 168 * 100 = 2⁵ * 7 *3 *5² =2* 2⁴ * 7 *3 *5², hence 2,7 and 3 are the one’s which are not perfect squares , hence the product of 2*3*7 = 42 should be divided