User Shashank Holla

4 votes

3 answers

1k views

If $ \alpha_i, i=0,1,2...n-1 $ be the nth roots of unity, the $\sum_{i=0}^{n-1} \frac{\alpha_i}{3- \alpha_i}$ is equal to?

asked Dec 4, 2016 at 16:49

2 votes

2 answers

3k views

Prove that $ \lim_{x\to0} ({1^{(1/\sin^2x)} + 2^{(1/\sin^2x)} + 3^{(1/\sin^2x)} + ....+ n^{(1/\sin^2x)})^{\sin^2(x)}} = \frac{n(n+1)}{2} $

asked Dec 8, 2016 at 16:57

2 votes

1 answer

70 views

Minimum value of $\frac{(1 + x + x^2)(1 + y + y^2)}{xy}$

asked Jan 12, 2016 at 10:38

2 votes

0 answers

175 views

Rolle's theorem and Functions

asked Oct 27, 2016 at 15:17

2 votes

1 answer

281 views

If $P$ is a monic polynomial of degree $2015$ such that $P(i)=2014-i\quad\forall i=0,...,2014$ & $P(2015)=n!-a$, find $n+a$

asked Nov 13, 2016 at 14:35

2 votes

2 answers

3k views

Tangent at any point on the hyperbola $x^2/9-y^2/16 = 1$ meets another hyperbola at $A$ and $B$.

asked Feb 26, 2017 at 4:11

2 votes

0 answers

52 views

Simplify the matrix using row-column transformations to get $2(\cos \theta)( \lambda^2 + \lambda + 1)$

asked Dec 3, 2016 at 3:43

1 vote

2 answers

179 views

Evaluate the reciprocal of the following infinite product

asked Aug 12, 2016 at 12:30

0 votes

0 answers

62 views

Limits to solve for equation of line

asked Oct 24, 2016 at 12:35

0 votes

4 answers

950 views

Let $\alpha$ be a fixed complex number such that $ |\alpha| $ < 1 and $ w = \frac{z-a}{1-a \bar z} $

asked Dec 1, 2016 at 13:17

0 votes

1 answer

91 views

Let $f(x)$ be a real value function defined by $f(x)=x^2-2|x|$

asked Dec 20, 2016 at 2:08

0 votes

2 answers

3k views

If a hyperbola whose foci are (–2, 4) and (4, 6) touches y–axis then equation of hyperbola is

asked Jan 24, 2017 at 12:00

0 votes

1 answer

508 views

$ \sec(\sec^{-1}(x)) $ when $x$ belongs to $(-1,0)$

asked Feb 24, 2017 at 13:49

0 votes

1 answer

166 views

In a triangle ABC, the real part of the equation (acosB+bcosA + i(asinB-bsinA)) ^n

asked Mar 25, 2017 at 7:44

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14 Questions

If $ \alpha_i, i=0,1,2...n-1 $ be the nth roots of unity, the $\sum_{i=0}^{n-1} \frac{\alpha_i}{3- \alpha_i}$ is equal to?

Prove that $ \lim_{x\to0} ({1^{(1/\sin^2x)} + 2^{(1/\sin^2x)} + 3^{(1/\sin^2x)} + ....+ n^{(1/\sin^2x)})^{\sin^2(x)}} = \frac{n(n+1)}{2} $

Minimum value of $\frac{(1 + x + x^2)(1 + y + y^2)}{xy}$

Rolle's theorem and Functions

If $P$ is a monic polynomial of degree $2015$ such that $P(i)=2014-i\quad\forall i=0,...,2014$ & $P(2015)=n!-a$, find $n+a$

Tangent at any point on the hyperbola $x^2/9-y^2/16 = 1$ meets another hyperbola at $A$ and $B$.

Simplify the matrix using row-column transformations to get $2(\cos \theta)( \lambda^2 + \lambda + 1)$

Evaluate the reciprocal of the following infinite product

Limits to solve for equation of line

Let $\alpha$ be a fixed complex number such that $ |\alpha| $ < 1 and $ w = \frac{z-a}{1-a \bar z} $

Let $f(x)$ be a real value function defined by $f(x)=x^2-2|x|$

If a hyperbola whose foci are (–2, 4) and (4, 6) touches y–axis then equation of hyperbola is

$ \sec(\sec^{-1}(x)) $ when $x$ belongs to $(-1,0)$

In a triangle ABC, the real part of the equation (acosB+bcosA + i(asinB-bsinA)) ^n