MCA Entrance Previous Year Question Bank

Equation of pair of lines $ y = px $ , $ y = qx $ written as $ (y - px)(y - qx) = 0 $ . Find the equation of the pair of angle bisectors of the lines $ x^2 - 4xy - 5y^2 = 0 $ .

A matrix $ A $ is both symmetric and skew-symmetric matrix. Then:

Assertion: $ A(BA) $ and $ (AB)A $ are symmetric matrices.

Reason: $ AB $ is symmetric matrix, if matrix multiplication of $ A $ with $ B $ is commutation.

Assertion: $ \frac{1}{3}, -\frac{1}{2}, \frac{3}{4}, -\frac{9}{8} $ form an AP.

Reason: The constant sequence is the only sequence which is both AP as well as GP.

$ \int_{0}^{\frac{\pi}{2}} \frac{\sin^2 x}{1 + \sin x \cos x} dx $

Let $ f $ be function $ f(x) = \begin{cases} \frac{\tan x}{x} & x \neq 0 \\ 1 & x = 0 \end{cases} $

Assertion: $ x = 0 $ is point of minima of $ f $

Reason: $ f'(0) = 0 $

The foci of a hyperbola coincide with the foci of the ellipse $ \frac{x^2}{25} + \frac{y^2}{9} = 1 $ . Find the equation of the hyperbola if its eccentricity $ e = 2 $ .

The curves $ x = y^2 $ and $ xy = k $ cut at right angles. Find the value of $ k $ .

$ S $ and $ T $ are symmetric matrices of the same order, then which of the following statements are true?

(A) $ S + T $ is a symmetric matrix

(B) $ ST - TS $ is a skew-symmetric matrix

(C) $ ST + TS $ is a symmetric matrix

(D) $ ST - TS $ is a symmetric matrix

Match the following columns: