1. Here is 15 dots. If you select 3 dots randomly, What is the probability that 3 dots make a triangle?

a. 440/455.

b. 434/455.

c. 449/455.

d. 438/455.

Answer:

Total ways of selecting 3 dots out of 15 is 15C3 = 455 If 3 dots are collinear then triangle may not be formed. Now look at the above diagram.

If we select any 3 dots from the red lines they may not form a triangle. They are 5 x 5C3 = 50. If we select the three letters from blue lines, they may
not form a triangle.

They are in total 5 ways. Also there are 6 others lines which don't form a triangle. Total = 50 + 5 + 6 = 61. So we can form a triangle in 455 - 61 = 394.
So answer could be 394/455.

2. In How many ways a team of 11 must be selected from 5 men and 11 women such that the team must comprise of not more than 3 men?

Answer: The team may consist of 0 men + 11 women, 1 men + 10 women, 2 men + 9 women, or 3 men + 8 women.

So Number of ways are = 11C11+5C1x11C10+5C2x11C9+5C3x11C8 = 2256.

3. Eesha bought 18 sharpeners for Rs.100. She paid 1 rupee more for each white sharpener than for each brown sharpener. What is the price of a white
sharpener and How many white sharpener did she buy ?

a. Rs.5, 10

b. Rs.6, 10

c. Rs.5, 8

d. Rs.6, 8

Sol: B.

Explanation:

Just check the options. If she bought 10 white sharpeners at Rs.6 per piece, She has spent Rs.60 already.

And with the remaining Rs.40, she bought 8 brown sharpeners at 40/8 = Rs.5 which is Rs.1 less than White sharpener.

4. On a 26 question test, five points were deducted for each wrong answer and eight points were added for each correct answer.

If all the questions were answered, How many were correct, if the score was zero ?

a. 10

b. 12

c. 11

d. 13

Ans: A

Explanation:

Take options and check. If 10 are correct, his score is 10 x 8 = 80. But 16 are wrong. So total negative marking is 16 x 5 = 80. So final score is zero.

5. If f(f(n))+f(n)=2n+3 and f(0)=1, What is the value of f(2012)?

a) 2011

b) 2012

c) 2013

d) 4095

Ans: Option C.

6. 1(1!)+2(2!)+3(3!)....2012(2012!) = ?

Ans: 2013!-1

1(1!)=1 => 2!-1

1(1!)+2(2!)=1+4=5 => 3!-1

1(1!)+2(2!)+3(3!)=1+4+18=23 => 4!-1

........................

.......................

1(1!)+2(2!)+3(3!)+........+2012(2012!)=>2013!-1.

7. A cow and horse are bought for Rs.2,00,000. The cow is sold at a profit of 20% and the horse is sold at a loss of 10%. The overall gain is Rs.4000, the
Cost price of cow?

a) 130000.

b) 80000.

c) 70000.

d) 120000.

Ans: Overall profit = 4000/200000x100=2%.

By applying alligation rule, we get

So cost price of the cow = 2/5 x 200000 = 80,000.

8. Ahmed, Babu, Chitra, David and Eesha each choose a large different number. Ahmed says, " My number is not the largest and not the smallest".

Babu says, "My number is not the largest and not the smallest". Chitra says, "My number is the largest".

David says, " My number is the smallest". Eesha says, " My number is not the smallest". Exactly one of the five children is lying. The others are telling
the truth. Who has the largest number?

a) Eesha.

b) David.

c) Chitra.

d) Babu.

Ans: A.

9. A beaker contains 180 liters of alcohol. On 1st day, 60 l of alcohol is taken out and replaced by water. 2nd day, 60 l of mixture iss taken out and
replaced by water and the process continues day after day. What will be the quantity of alcohol in beaker after 3 days.

Ans: 53.3.