MCQ_SINGLE

If $\int(\cos x)^{-5/2}(\sin x)^{-11/2}dx=\frac{P_{1}}{q_{1}}(\cot x)^{9/2}+\frac{P_{2}}{q_{2}}(\cot x)^{5/2}+\frac{P_{3}}{q_{3}}(\cot x)^{1/2}-\frac{P_{4}}{q_{4}}(\cot x)^{-3/2}+C$, then $\frac{15P_{1}P_{2}P_{3}P_{4}}{q_{1}q_{2}q_{3}q_{4}}$ is equal to :

NUMERICAL

The sum of roots of the equation $|x-1|^{2}-5|x-1|+6=0$ is:

NUMERICAL

If $a_{1}=1$ and for all $n\ge1$, $a_{n+1}=\frac{1}{2}a_{n}+\frac{n^{2}-2n-1}{n^{2}(n+1)^{2}}$, then the value of $\sum_{n=1}^{\infty}(a_{n}-\frac{2}{n^{2}})$ is equal to:

NUMERICAL

Let $A$ satisfy the equation $\lambda\begin{bmatrix}1\\2\\3\end{bmatrix}=\begin{bmatrix}-1\\0\\3\end{bmatrix}$, and $|2\text{adj}(A+I)|=2^{\alpha}3^{\beta}11^{\gamma}$ then $\alpha+\beta+\gamma$ is equal to .

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 :

View All Questions