List of top Questions asked in NATA

If the points (2a, a),(a,2a), and (a, a) enclose a triangle of area 18 square units. Then the centroid of the triangle is:

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?

If \(cos2\theta+sin\theta= \sqrt{2}cos \theta,Then \ cos\theta-sin \theta=? \)

If \(tan ^{-1}(sinx)=\frac{\pi}{4}\),then the value of \(x\) is:

Area and perimeter of a rectangular field are 2000 sq.m. and 180 m respectively. What is the length and breadth?

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

A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

The curved surface area of a cylindrical pillar is \(264  m^2\)and its volume is \(924\)\( m^3\)Find the ratio of its diameter to its height

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

f \(\int_0 ^a3x^2dx=8\) then find the value of a

Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220. If the second term in it is 12, then its 4th term is :

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:

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:

A circle is inscribed within an equilateral triangle of area \(\sqrt 3\) sqm. The circumference of the circle is

Gypsum is a: