NUMERICAL

The number of real solutions of equation $x|x+4|+3|x+2|+10=0$ is equal to .

MCQ_SINGLE

The locus of the point of intersection of tangents drawn to the circle $(x-2)^{2}+(y-3)^{2}=16$ which subtends an angle of $120^{\circ}$ is:

MCQ_SINGLE

Two numbers '$a$' and '$b$' are chosen at random from the set $\{1,2,3,...,50\}$. The probability that $ab$ is divisible by 3, is :

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 .

NUMERICAL

Let $Q(5,b,c)$ be the mirror image of $P(1,3,a)$ with respect to the line $\frac{x-1}{3}=\frac{y-3}{2}=\frac{z-2}{2}$, then the value of $a^{2}+b^{2}+c^{2}$ is .

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