List of practice Questions

The number of solutions of the pair of equations \( 2 \sin^2 \theta - \cos 2\theta = 0 \) and \( 2 \cos^2 \theta - 3 \sin \theta = 0 \) in the interval \([0, 2\pi]\) is:

A point moves so that the sum of the squares of its distances from the six faces of a cube given by \( x = \pm 1 \), \( y = \pm 1 \), \( z = \pm 1 \) is 10 units. The locus of the point is:

A directional post is erected on a crossing. Due to heavy storm it turned in such a way that the arrow which was first showing South is now showing East. A car went in a direction thinking it is West. In what direction is the car actually moving?

Let E and F be any two sets. Which of the following statements is NOT correct?

A set P has 20 elements. The number of subsets of P containing odd number of elements is

Let P={1, 3, 5, 7, 9} and R={(1, 3), (3, 5), (1, 5), (9, 7), (7, 5), (9, 5)}. Then R

Let P={1,2,3} Q={2, 3, 4}. Then the number of elements in P×Q is

In a project, the share of material and labour costing is 3:2. In the labour component, the electrician gets 5%. What is the total project cost if an electrician gets ₹25,000/-?

From a point O, two persons A and B started their journey on XY plane. A went 7 km. along north and stopped. B went 5 km west and then 5 km south and stopped. What is the shortest distance between A and B?

Three cubes of side 2 cm are glued surface to surface horizontally such that it produces a cuboid. What is the surface area of the cuboid?

How many total number of triangles are there in the figure given below?

Which one of the following consumes least amount of electricity?

Green Architecture is promoted these days because:

World Environment Day is observed on:

Gypsum is a:

Which of the following is a scalar quantity?

A heavy ladder resting in the floor and against a vertical wall may not be in equilibrium if

The type of roof suitable in plains where rainfall is meagre and temperature is high is

The angle which an inclined plane makes with the horizontal when a body placed on it is about to slide down is known as angle of

Nurse Merry has worked more night shifts in a row than Nurse Sujata, who has worked five. Nurse Ruma has worked fifteen night shifts in a row, more than Nurses Merry and Sujata combined. Nurse Priti has worked eight night shifts in a row, less than Nurse Merry. How many night shifts in a row has Nurse Merry worked?

Unscramble and find the odd one among the following

X is 1 km northeast of Y. Y is 1 km southeast of Z. W is 1 km west of Z. P is 1 km south of W. Q is 1 km east of P. What is the distance between X and Q in km?

In a group of four children,Som is younger to Riaz.Shiv is elder to Ansu.Ansu is youngest in the group.Which of the following statements is/are required to find the eldest child in the group?
Statements:
1. Shiv is younger to Riaz.
2. Shiv is elder to Som

Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows.
Statements:
I. All film stars are playback singers.
II. All film directors are film stars.
Conclusions:
I. All film directors are playback singers.
II. Some film stars are film directors.

A truncated (horizontally cut in mid-way) hexagonal pyramid has following numbers of surfaces, edges and vertices respectively.