List of top Mathematics Questions asked in NATA

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

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

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

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:

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

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:

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:

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

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?

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

Derivative of sinx with respect to cosx is

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