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

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
In a Harmonic Progression, pth term is q and the qth term is p. Then pqth term is
If the foci of the ellipse \( \frac{x^2}{25} + \frac{y^2}{b^2} = 1 \) and the hyperbola \( \frac{x^2}{144} - \frac{y^2}{81} = \frac{1}{25} \) are coincide, then the value of \( b^2 \) is
Let a be the distance between the lines \( -2x + y = 2 \) and \( 2x - y = 2 \), and b be the distance between the lines \( 4x - 3y = 5 \) and \( 6y - 8x = 1 \), then
If the roots of the quadratic equation \( x^2 + px + q = 0 \) are tan 30\(^{\circ}\) and tan 15\(^{\circ}\) respectively, then the value of \( 2 + p - q \) is
If \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) (\( a > b \)) and \( x^2 - y^2 = c^2 \) cut at right angles, then
If \( a < b \), then \( \int_a^b (|x-a| + |x-b|) dx \) is equal to
If the angle of elevation of the top of a hill from each of the vertices A, B and C of a horizontal triangle is \( \alpha \), then the height of the hill is
Which of the following is NOT true?
A straight line through the point (4, 5) is such that its intercept between the axes is bisected at A, then its equation is
\( f(x) = x + |x| \) is continuous for

The value of \( \int \frac{(x^2-1)dx}{x^3\sqrt{2x^4 - 2x^2 + 1}} \) is
 

Let \( \vec{a} = 2\hat{i} + 2\hat{j} + \hat{k} \) and \( \vec{b} \) be another vector such that \( \vec{a} \cdot \vec{b} = 14 \) and \( \vec{a} \times \vec{b} = 3\hat{i} + \hat{j} - 8\hat{k} \). The vector \( \vec{b} \) is

Inverse of the function \( f(x) = \frac{10^x - 10^{-x}}{10^x + 10^{-x}} \) is
 

If \( a_1, a_2, \ldots, a_n \) are any real numbers and n is any positive integer, then
The area enclosed within the curve \( |x| + |y| = 2 \) is
Angles of elevation of the top of a tower from three points (collinear) A, B and C on a road leading to the foot of the tower are 30\(^{\circ}\), 45\(^{\circ}\) and 60\(^{\circ}\) respectively. The ratio of AB and BC is
Solutions of the equation \( \tan^{-1}\sqrt{x^2+x} + \sin^{-1}\sqrt{x^2+x+1} = \frac{\pi}{2} \) are
In a triangle ABC, if the tangent of half the difference of two angles is equal to one third of the tangent of half the sum of the angles, then the ratio of the sides opposite to the angles is

For \( a \in \mathbb{R} \), \( a \neq -1 \), \( \lim_{n \to \infty} \frac{1^a + 2^a + \dots + n^a}{(n+1)^{a-1}[(na+1)+(na+2)+\dots+(na+n)]} = \frac{1}{60} \). Then one of the values of a is

If the volume of the parallelepiped whose adjacent edges are \( \vec{a} = 2\hat{i} + 3\hat{j} + 4\hat{k} \), \( \vec{b} = \hat{i} + \alpha\hat{j} + 2\hat{k} \), \( \vec{c} = \hat{i} + 2\hat{j} + \alpha\hat{k} \) is 15, then \( \alpha \) is equal to
The eccentricity of an ellipse, with its center at the origin is \( \frac{1}{3} \). If one of the directrices is \( x = 9 \), then the equation of ellipse is:
The function \( f(x) = \log(x + \sqrt{x^2 + 1}) \) is
If \( 0 < P(A) < 1 \) and \( 0 < P(B) < 1 \), and \( P(A \cap B) = P(A)P(B) \), then
There are two circles in xy-plane whose equations are \( x^2 + y^2 - 2y = 0 \) and \( x^2 + y^2 - 2y - 3 = 0 \). A point (x, y) is chosen at random inside the larger circle. Then the probability that the point has been taken from smaller circle is