MCQ_SINGLE

In the binomial expansion of $(ax^{2}+bx+c)(1-2x)^{26}$, the coefficients of $x$, $x^{2}$, $x^{3}$ are 56, 0 and 0 respectively. Then the value of $(a+b+c)$ 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:

MCQ_SINGLE

Evaluate the limit: $\lim_{x\rightarrow0}\frac{sin(2x)-2~sin~x}{x^{3}}$

MCQ_SINGLE

The area enclosed by $x^{2}+4y^{2}\le4$, $y\le|x|-1$, $y\ge1-|x|$ is equal to:

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:

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