1. Express A Speed Of 36 Kmph In Meters Per Second ?

36 * 5/18 = 10 mps

2. A Boy Has Nine Trousers And 12 Shirts. In How Many Different Ways Can He Select A Trouser And A Shirt?

The boy can select one trouser in nine ways.

The boy can select one shirt in 12 ways.

The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways.

3. The Number Of Permutations Of The Letters Of The Word ‘mesmerise’ Is_.

n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.

The letter pattern ‘MESMERISE’ consists of 10 letters of which there are 2M’s, 3E’s, 2S’s and 1I and 1R.

Number of arrangements = 9!/(2!)2 3!

4. Twice The Speed Of A Boat Downstream Is Equal To Thrice The Speed Upstream. The Ratio Of Its Speed In Still Water To The Speed Of Current Is

Let the boat speed in still water be b.

Let the stream speed be x.

2(b+ x) = 3(b-x)

5x=b

b/x=5/1

5. The Difference Between The Simple Interest And Compound Interest On A Certain Sum Of Money For 2 Years At 15% P. A. Is Rs. 4

Since we know that the interest rate is 0.15, and knowing that the difference between two years of compound interest is nothing but interest on interest, we can find the first year’s interest as –

45/0.15 = 300.

Now if the interest is 300 at the end of one year, then the principal is 300 / 0.15 = 2,000

6. In Order To Obtain An Income Of Rs. 650 From 10% Stock At Rs. 96, One Must Make An Investment Of

To obtain Rs. 10, investment = Rs. 96.

To obtain Rs. 650, investment = Rs.96/10x 650 = Rs. 6240.

7. India Plays Two Matches Each With West Indies And Australia. In Any Match The Probabilities Of India Getting Points 0, 1, 2 Are 0.45, 0.05 And 0.50 Respectively. Assuming That Outcomes Are Independent

Getting 7 points is possible in 2 cases.

**Case 1:** India wins all 4 matches.

Probability: (.5)4 = .0625.

**Case 2:** India wins any of the 3 matches and draws the remaining match. This can happen in total 4 ways. Probability: 4 x (.50)3 x (.05) = .025.

So, required probability: .0625 + .025 = .0875

8. Express 25 Mps In Kmph?

25 * 18/5 = 90 kmph

9. Using All The Letters Of The Word “nokia”, How Many Words Can Be Formed, Which Begin With N And End With A ?

There are five letters in the given word.

Consider 5 blanks .

The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.

The number of words = 3! = 6.

10. A Person Has A Chemical Of Rs. 25 Per Litre. In What Ratio Should Water Be Mixed With That Chemical So That After Selling The Mixture At Rs. 20/litre He May Get A Profit Of 25% ?

This can be solved using alligation.

What is required at the end of mixing is a price of 20/1.25 = 16.

So the alligation would look like this –

Water/0 Mixture/16 Chemical/25

Hence the ratio would be (25 – 16) : 16 = 9 : 16

Hence required ratio of Water : Chemical is 9:16.

11. A Bottle Is Full Of Dettol. One-third Of It Is Taken Out And Then An Equal Amount Of Water Is Poured Into The Bottle To Fill It. This Operation Is Done Four Times. Find The Final Ratio Of Dettol And W

As in denominator we have to take 1/3 four times so, we start by assuming 81 ml of dettol in the bottle. After the first iteration you will be left with

2/3 × 81 = 54 ml. After the second iteration you will be left with

2/3 × 54 = 36 ml. After the third iteration you will be left with

2/3 × 36 = 24 ml. After the fourth iteration you will be left with

2/3 × 24 = 16 ml. So the required ratio will be 16 : (81 – 16) = 16 : 65

12. How Many Terms Are There In An A.p. Whose First And Fifth Terms Are -14 And 2, Respectively, And The Sum Of Terms Is 40 ?

Now the common difference of this AP is 16/4 = 4.

The sum of an AP is n/2 {2a + (n – 1)d}

Substituting we get, 40 = n/2 {2×-14 + (n – 1)4}

The best way to solve this is by plugging options. Put in n = 10 and get the RHS as 40.

13. The Number Of Arrangements That Can Be Made With The Letters Of The Word Meadows So That The Vowels Occupy The Even Places ?

The word MEADOWS has 7 letters of which 3 are vowels.

-V-V-V-

As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.

Hence the total ways are 24 * 6 = 144.

14. In A Class, 50 Students Play Cricket, 20 Students Play Football And 10 Play Both Cricket And Football. How Many Play At Least One Of These Two Games ?

The required wer is 50 + 20 – 10 = 60.

15. In A Survey Of Defaulted Payments Of Electrical Bills Of A Residential Complex Of 125 Houses, It Is Found That 50 Houses Defaulted On Their Payment Of Electrical Bills In January, 60 In February And 4

We use formula for intersection of three sets, keeping in mind that Jan ∩ Mar does not exist, since they are not consecutive months.

Let x be the number of people defaulting in all 3 months.

We get the equation as : 125 = 50 + 60 + 40 – 20 – 10 + x. Solving we get x = 5.