MCQ_SINGLE

If O is the vertex of the parabola $x^{2}=4y,$ Q is a point on the parabola. If C is the locus of the point which divides OQ in the ratio $2:3,$ then the equation of the chord of C which is bisected at the point (1,2) is: (Duplicate Question)

NUMERICAL

If the area of the region $\{(x,y):x^{2}+1\le y\le3-x\}$ is divided by the line $x=-1$ in the ratio $m : n$, where $\gcd(m,n)=1$. Then the value of $m+n$ is .

MCQ_SINGLE

If the mean and variance of observations $x, y, 12, 14, 4, 10, 2$ is 8 and 16 respectively, where $x>y$, then the value of $3x-y$ is:

MCQ_SINGLE

Value of $\int_{-\pi/2}^{\pi/2}\frac{dx}{[x]+4}$: is $-\pi/2$ where $[.]$ is GIF .

NUMERICAL

Let $\int_{1}^{x}f(t)dt=3xf(x)-x^{3}+4$, then $f(2)-f(3)$ is .

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