List of top Mathematics Questions asked in NIT MCA Common Entrance Test

There are two sets A and B with \( |A| = m \) and \( |B| = n \). If \( |P(A)| - |P(B)| = 112 \) then choose the wrong option (where \( |A| \) denotes the cardinality of A, and P(A) denotes the power set of A)
If \( \csc\theta - \cot\theta = 2 \), then the value of \( \csc\theta \) is
Suppose that the temperature at a point (x, y) on a metal plate is \( T(x, y) = 4x^2 - 4xy + y^2 \). An ant, walking on the plate, traverses a circle of radius 5 centered at the origin. What is the highest temperature encountered by the ant?

If \( (\vec{a} \times \vec{b}) \times \vec{c} = \vec{a} \times (\vec{b} \times \vec{c}) \), then
 

If \( x^m y^n = (x+y)^{m+n} \), then \( \frac{dy}{dx} \) is
 

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively is
The 10th and 50th percentiles of the observation 32, 49, 23, 29, 118 respectively are
The first three moments of a distribution about 2 are 1, 16, -40 respectively. The mean and variance of the distribution are
Which term of the series \( \frac{\sqrt{3}}{9}, \frac{1}{3\sqrt{3}}, \frac{1}{9}, \ldots \) is \( \frac{1}{2187} \)?
If \( \alpha, \beta \) are the roots of \( x^2 - x - 1 = 0 \), and \( A_n = \alpha^n + \beta^n \), then Arithmetic mean of \( A_{n-1} \) and \( A_n \) is
Let a, b, c be distinct non-negative numbers. If the vectors \( a\hat{i} + a\hat{j} + c\hat{k} \), \( \hat{i} + \hat{k} \) and \( c\hat{i} + c\hat{j} + b\hat{k} \) lie in a plane, then c is
The value of \( 3^{3-\log_3 5} \) is
A survey is done among a population of 200 people who like either tea or coffee. It is found that 60% of the population like tea and 72% of the population like coffee. Let x be the number of people who like both tea & coffee. Let \( m \leq x \leq n \), then choose the correct option.
The correct expression for \( \cos^{-1}(-x) \) is
The solutions of the equation \( 4\cos^2x + 6\sin^2x = 5 \) are
The value of \( \cot(\csc^{-1}\frac{5}{3} + \tan^{-1}\frac{2}{3}) \) is
A particle is at rest at the origin. It moves along the x -axis with an acceleration \( x - x^2 \), where x is the distance of the particle at time t. The particle next comes to rest after it has covered a distance
If \( \cos^{-1}\frac{x}{2} + \cos^{-1}\frac{y}{3} = \phi \), then \( 9x^2 - 12xy\cos\phi + 4y^2 \) is equal to

The function \( f(x) = \begin{cases} (1+2x)^{1/x}, & x \neq 0 \\ e^2, & x=0 \end{cases} \) is
 

If \( \vec{a} = \lambda\hat{i} + \hat{j} - 2\hat{k} \), \( \vec{b} = \hat{i} + \lambda\hat{j} - 2\hat{k} \), \( \vec{c} = \hat{i} + \hat{j} + \hat{k} \) and \( [\vec{a}\vec{b}\vec{c}] = 7 \), then the values of \( \lambda \) are
Coordinate of focus of the parabola \(4y^2 + 12x - 20y + 67 = 0\) is

If \( D = \begin{vmatrix} 1 & 1 & 1 \\ 1 & 2+x & 1 \\ 1 & 1 & 2+y \end{vmatrix} \) for \( x \neq 0, y \neq 0 \), then D is

The domain of the function \( f(x) = \frac{\cos^{-1}x}{[x]} \) is
 

The mean of 25 observations was found to be 38. It was later discovered that 23 and 38 were misread as 25 and 36, then the mean is
If \( a_1, a_2, \ldots, a_n \) are in Arithmetic Progression with common difference d, then the sum \( (\sin d) (\csc a_1 \csc a_2 + \csc a_2 \csc a_3 + \dots + \csc a_{n-1} \csc a_n) \) is equal to