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QUESTION: 1

From a container of 8 litre pure syrup 1 litre is taken out and replaced by water of equal quantity. If the same repeated again then what is the present ratio of syrup to water.

Solution:

Each time we take 1 litre from 8 litre, 7 litre is left. So, the original: remaining of syrup is

8:7

So, each tune we take out there would be 7/8th part left of the syrup.

8 lit (as two tunes done)

=49/8 litre syrup left

Therefore, water = total - remaining

Therefore, syrup left: water

*Answer can only contain numeric values

QUESTION: 2

In a family a father has three daughters and each daughter has a brother. The number of known male members in the family is___________

Solution:

QUESTION: 3

(i) The speed of your bike should not (ii) exceed more than 70 km/hr (iii) as you are driving alone (iv) No error

In the above sentene if there is any mistake, mark the corresponding part.

e.g. if there is a mistake in part (i) please mark (i) as your answer and similarly for other options. If no mistake is there mark ‘no error' (iv) as your answer

Solution:

Exceed is not followed by “more than'"

QUESTION: 4

A cricketer’s total run before the end of a senes is 750. After that he plays two more matches in the same series in which he scores 6 runs and his battmg average decreases by 2 runs. What is his batting average for the series

Solution:

Let he has played x matches

Therefore, average 750/x runs/match.

After scoring 6 mroe runs, his total is (750 + 6) = 756 runs To score 6 more runs he has played 2 more matches Therefore, total matches played = (x + 2)

Therefore, now average runs/match = 756/x+2

As per condition,

QUESTION: 5

Rain can do a work in 28 days while the same work can be done by Shyam m 35 days. They started Unseen the work together but after some days, Ram left the work and Shyam completed the remaining work in 17 days. After how many days Ram left work.

Solution:

Let total work = x

Therefore, one daywork of Ram = x/28

Therefore, one day work of Shyam= x/35

In 17 days work of Shyam =

Remaining work =

Now, in 1 day Ram and Shyam does

∴ 9x/140 = work done in 1 day

1 work done in 140 / 9x days

18x / 35 work done in = 8 days

Therefore, after working 8 days Rani left

QUESTION: 6

Ramesh standing on a platform observes tliat a train crosses him in 8 sec. Another train of same length from opposite direction crosses him in 6 secs. Running in opposite direction how much tune it would take to cross each other for the trains.

Solution:

Total distance to be covered to cross each other is the total length of both the trains. If length of both the trains are x. Then total distance to be covered = 2x First train in 8 secs goes x

First train in 1 secs goes x/8

Second train in 6 secs goes x

Second train in 1 secs goes x/6

Therefore, in 1 sec goes (as in opposite direction)

Now, 14x / 48 goes m 1 sec

Therefore, 2x goes in

*Answer can only contain numeric values

QUESTION: 7

Anil rows 30 km downstream in 10 hours. Same time is also taken to row 18 km upstream. Then, the velocity of water is __________ km/hr.

Solution:

Down stream speed = 30/10 = 3km/hr = U+V

Up stream speed = 18/10 = 1.8 km/hr = U-V

Velocity of water =

QUESTION: 8

If then value of x^{18} + x^{12} + x^{6} +1 = ?

Solution:

∴

QUESTION: 9

A Rubber ball is thrown from a height of 600 m and each time it bounces back 2/3 of the last bounce. Unseen What is the total distance covered by the ball before it stops

Solution:

Falling from 600 and again going up by

Each next term is being multiplied by 2/3

a= 1000, r = 2/3 i.e. G.P. series

Therefore, sum =

QUESTION: 10

What is the minimum value 0f 4 sec^{2 }θ + 9 cosec^{2} θ = ?

Solution:

*Answer can only contain numeric values

QUESTION: 11

Two poles of equal height are standing opposite to each other on the two sides of a 100 wide road. From a point on the road the angle of 30° and 60° are formed with the top of the two towers. The height of the first pole in metre is ________________ (upto two decmial places)

Solution:

Let us assume that we are standing at a point E somewhere on the road from where we are spectating.

Now, two poles are AB and CD; equal height i.e. AB = CD

From,

And similarly from ΔCDE,

∴

∴

QUESTION: 12

If all the circles have a radius of 10 cm, have a radius of 10 cm, then what is the area of the extrapped region between circles.

Solution:

Area in between = area of the triangles - are covered by circles

(As each side of the equilateral triangle is 20 m and as angle of total 180° is covered by circles, i.e. half of 360°)

QUESTION: 13

A metallic right circular cone of height 12 cm and base of 7 cm radius is melted and recasted to form a cuboid having breadth and height of 11cm and 2cm. What is the length of cuboid.

Solution:

Volume of cone = volume of cuboid

QUESTION: 14

Count total number of triangles in the given figure.

Solution:

Total triangles, in the upper part = 28

And in lower part is 3

therefore, total triangle is 28 + 3 = 31

QUESTION: 15

If in a certain code ‘SCHOOLS’ is written as ‘IDTPTMP’, then what will be the code for ‘SUCCESS’.

Solution:

QUESTION: 16

In how many ways a football team can be formed out of 15 players where the captain is fixed and always in the team.

Solution:

One player is always fixed, so we have to choose 10 players, out of 14,

QUESTION: 17

Some crows are cows

All cows are cats; All cats are rats; Some rats are bats Conclusions,

(1) Some bats are cats

(2) Some crows are rats

(3) Some cows are bats

Solution:

So, only intersection between crows and Rats;

Therefore, only 2 Follows.

*Answer can only contain numeric values

QUESTION: 18

Find the missing number

Based on the pattern followed above the number of inplace of Y is____________

Solution:

1^{3 }+ 2^{3} = 9

3^{3} + 4^{3} = 91

5^{3} + 6^{3} = 341

QUESTION: 19

What is the total area covered by |x|+|y|=8

Solution:

In each quadrant area is square unit

Therefore, in all four quadrants area is 32 x 4 = 128 square unit

QUESTION: 20

Find out the correct spelling

Solution:

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