List of practice Questions

The area bounded by the curve \(y=x^3, y=0, x=1\) is

The left most figure below shows the top view of an object. Identify the correct elevation from amongst the answer figures, looking in the direction of arrow.

How many surfaces are there in the model? Consider all seen and unseen surfaces.

The value of \(\lambda\) for which the straight line (2x+3y+4)+\(\lambda\)(6x-y+12)=0 is parallel to y-axis is 

Derivative of sinx with respect to cosx is

Value of the determinant \[\begin{vmatrix}1 & w & w^2 \\w & w^2 & 1 \\w^2 & 1 & w\end{vmatrix}\] where \( w \) is the cube root of unity is:

The system of linear equations -2x+y+2=a, x-2y+z=b, x+y-2z=c have infinitely many solutions if

The monthly rate of sales for the first 11 months of the year of a certain salesman was ₹12,000. But due to his illness during the last month, the average sales for the whole year came down to ₹11,375. The value of the sale during the last month was

The probability that a man will live for 10 more years is 1/4 and the probability that his wife will live for 10 more years is 1/3. The probability that neither the husband nor the wife will be alive after 10 years is

If \(^nc_7=^nc_4\), then the value of n is

If \( a, b, c \) are non-zero, then the number of solutions of \[\frac{2x^2}{a^2} - \frac{y^2}{b^2} - \frac{z^2}{c^2} = 0,\]\[-\frac{x^2}{a^2} + \frac{2y^2}{b^2} - \frac{z^2}{c^2} = 0\]is:

If \( A = \begin{bmatrix} -\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ -\frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} & 0 \\ 0 & 0 & 1 \end{bmatrix} \), then \( A^{-1} \) is:

\( m \) men and \( w \) women are to be seated in a row so that all women sit together. The number of ways in which they can be seated is:

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?