MCQ_SINGLE

If $L_{1}$ and $L_{2}$ are two parallel lines and $\triangle ABC$ is an equilateral triangle as shown in the figure, then the area of triangle ABC is:

NUMERICAL

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

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 a 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:

MCQ_SINGLE

Let $M=\{1,2,3,...,16\}$ and $R=\{(x,y):4y=5x-3,x,y\in M\}$. Then the number of elements to be added in $R$ to make it symmetric is :

NUMERICAL

Find number of solutions of $\tan^{-1}4x+\tan^{-1}6x=\frac{\pi}{6}$ in $(\frac{-1}{2\sqrt{6}},\frac{1}{2\sqrt{6}})$ .

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