MCA Entrance Previous Year Question Bank

If ${\int }_{-\pi /2}^{\pi /2}\frac{5^{\cos x}(1+\cos x\cos 3x+{\cos }^{2}x+{\cos }^{3}x\cos 3x)}{1+5^{\cos x}}dx=\frac{k\pi }{16}$ then $k$ is equal to:

The sum of the common terms of the following three arithmetic progressions:

$3,7,11,15,\dots ,399$

$2,5,8,11,\dots ,359$ and

$2,7,12,17,\dots ,197$

is equal to:

Number of integral solutions to the equation $x+y+z=21$, where $x\ge 1,y\ge 3,z\ge 4$, is equal to:

The total number of six digit numbers, formed using the digits $4,5,9$ only and divisible by $6$, is:

The line $x=8$ is the directrix of the ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with focus $(2,0)$. If the tangent to $E$ at point $P$ in the first quadrant passes through $(0,4\sqrt{3})$ and intersects the $x$-axis at $Q$, then $(3PQ{)}^2$ is equal to:

The point of intersection $C$ of the plane $8x+y+2z=0$ and the line joining $A(-3,-6,1)$ and $B(2,4,-3)$ divides $AB$ internally in ratio $k:1$. If $a,b,c$ are coprime direction ratios of the perpendicular from $C$ on the line $\frac{1-x}{1}=\frac{y+4}{2}=\frac{z+2}{3}$, then $|a+b+c|$ is equal to:

Let the sixth term in the binomial expansion of ${\left(\sqrt{2^{{\log }_2(10-3^x)}}+\sqrt[5]{2^{(x-2){\log }_{2}3}}\right)}^m$, in the increasing powers of $2^{(x-2){\log }_{2}3}$, be $21$. If the binomial coefficients of the second, third and fourth terms in the expansion are respectively the first, third and fifth terms of an A.P., then the sum of the squares of all possible values of $x$ is:

If the $x$-intercept of a focal chord of the parabola $y^2=8x+4y+4$ is $3$, then the length of this chord is equal to:

If the term without $x$ in the expansion of ${\left(x^{\frac{2}{3}}+\frac{a}{x^3}\right)}^{22}$ is $7315$, then $|a|$ is equal to:

Let $\alpha x+\beta y+\gamma z=1$ be the equation of a plane through the point $(3,-2,5)$ and perpendicular to the line joining the points $(1,2,3)$ and $(-2,3,5)$. Then the value of $\alpha \beta \gamma$ is equal to: