MCQ_SINGLE

If $a_{1}, a_{2}, a_3,...$ are in increasing geometric progression such that $a_{1}+a_{3}+a_{5}=21$ and $a_{1}a_{3}a_{5}=64$, then $a_{1}+a_{2}+a_{3}$ 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 .

MCQ_SINGLE

The value of $\int_{\frac{\pi}{6}}^{\pi}\frac{\pi+4x^{11}}{1-\sin(|x|+\frac{\pi}{6})}dx$ is:

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

Ellipse E: $\frac{x^{2}}{36}+\frac{y^{2}}{16}=1$. A hyperbola is confocal with the ellipse and the eccentricity of the hyperbola is equal to 5. If the principal axis of the hyperbola is the x-axis, then the length of the latus rectum of the hyperbola is:

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