List of top Questions asked in NATA

A class has n students, we have to form a team of the students including at least two students and also excluding at least two students. The number of ways of forming the team is

The differential equation of all non vertical lines in a plane is:

The function given by: x^myⁿ = (x + y)^m+n is:

The sum of odd integers from 1 to 2001 is:

Evaluate the integral. \(\displaystyle\int^{3}_{2}x^4dx\)

Area bounded by\( y=x^3 , y=8\) and \(x=0\) is

Let the following system of equations kx + y + z =1x + ky + z = kx + y + kz=k2Has no solution. Find

The average age of 20 students in a class is 15 years. If the teacher’s age is including, the average increases by 1. What is the teacher’s age?

You have a 9 x 9 x 9 cm box. How many cubes of side 5 cm will you be able to fit inside it?

A determinant is chosen at random from the set of order 2 with elements 0 or 1 only. The probability that the determinant chosen non zero is

The degree and order of the differential equation \((\frac{d^3y}{dx^2})^2 +(\frac{dy}{dx})^4+y^3=0\) is

A square paper is folded as shown in the figure (above). A circular hole is created in the triangular portion. Now the paper is unfolded. What will be the right diagram?

A square is drawn on 1^st quadrant of XY plane having consecutive coordinates (counter - clockwise, starting from left bottom) as P(2,3), Q(7,3), R(7,8), S(2,8) respectively. Thereafter, each side of the square is doubled considering P as a fixed point and the new square becomes PQ'R'S'. Now this new square is mirrored with respect to X axis. What will be the coordinates for the image of R'?

Let \( a, b, c \) be distinct real numbers such that
\[\Delta = \begin{vmatrix}2014 & 2015 & 2013 + a^{-1} \\2015 & 2016 & 2013 + b^{-1} \\2016 & 2017 & 2013 + c^{-1}\end{vmatrix} = 0\]
Then:

Solution of the differential equation\( \frac{dy}{dx}=y^2\) with the condition y(1)=1 is

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

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.

The points (a, 2), (0, b), (1, 1) are collinear. Then

The sum of the perpendicular distances from the origin to the planes 12x-3y+4z+26=0 and 2x-4y+4z+18=0 is

The value of \(\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} (x^2 \sin x + x^3) \, dx\) is:

Length of a solid diagonal of a cube is 6 cm. The volume of the cube is

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

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

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