Previous 10 Questions — NIMCET 2011
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$ \text{The sum of } 11^{2} + 12^{2} + \cdots + 30^{2} \text{ is} $
Topic: NIMCET 2011
A random variable $X$ has the probability distribution:
\[\begin{array}{c|ccccccccc}
x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 …
Topic: NIMCET 2011
If the function $f:[1,\infty)\to[1,\infty)$ is defined by
$f(x)=2^{x(x-1)}$, then $f^{-1}(x)$ is:
Topic: NIMCET 2011
$ \vec{v} = 2\hat{i} + \hat{j} - \hat{k},\quad \vec{w} = \hat{i} + 3\hat{k} $
If $ \vec{u} $ is a unit vector, maximum …
Topic: NIMCET 2011
Eccentricity of ellipse
$ 9x^{2} + 5y^{2} - 30y = 0 $
Topic: NIMCET 2011
Vertex of parabola $ y^{2} - 8y + 19 = 0 $
Topic: NIMCET 2011
Number of distinct solutions of
$ x^{2} = y^{2} $
and
$ (x - a)^{2} + y^{2} = 1 $
where $a$ is any real number:
Topic: NIMCET 2011
Lines $2x + 3y - 6 = 0$ and $9x + 6y - 18 = 0$ cut coordinate axes in concyclic points.
Center of circle is:
Topic: NIMCET 2011
$ \vec{a} = x\hat{i} - 3\hat{j} - \hat{k},\quad \vec{b} = 2x\hat{i} + x\hat{j} - \hat{k} $
Angle between $ \vec{a} $ an…
Topic: NIMCET 2011
If $ a,b,c $ are coplanar, evaluate
$ [,2a - b, 2b - c,2c - a,] $
Topic: NIMCET 2011
Next 10 Questions — NIMCET 2011
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Roots of $x^{2} - 2x + 4 = 0$ are $\alpha, \beta$.
Compute $ \alpha^{6} + \beta^{6} $.
Topic: NIMCET 2011
If $ |\vec{a}\times \vec{b}| = |\vec{a}\cdot \vec{b}| $, then angle $\theta$ between $\vec{a},\vec{b}$ is:
Topic: NIMCET 2011
$ABCD$ is a parallelogram with diagonals $AC$ and $BD$.
Compute $ \overrightarrow{AC} - \overrightarrow{BD} $.
Topic: NIMCET 2011
If $\sin x,\ \cos x,\ \tan x$ are in GP, find $\cot 6x - \cot 2x$.
Topic: NIMCET 2011
Triangle sides:
$x^{2}+x+1,\ 2x+1,\ x^{2}-1$.
Largest angle?
Topic: NIMCET 2011
Solve: $ 2\sin^{2}\theta - 3\sin\theta - 2 = 0$
Topic: NIMCET 2011
System:
$3x_{1} + 7x_{2} + x_{3} = 2$
$x_{1} + 2x_{2} + x_{3} = 3$
$2x_{1} + 3x_{2} + 4x_{3} = 13$
Topic: NIMCET 2011
Correct the following equation by inter-changing two signs.
$ 3 - 9\times 27 + 9 \div 3 = 3 $
Topic: NIMCET 2011
Pushpa is twice as old as Rita was two years ago.
If the difference between their ages is $2$ years, how old is Pushpa …
Topic: NIMCET 2011
A clock is set right at $8$ a.m.
The clock gains $10$ minutes in $24$ hours.
What will be the correct time when the clo…
Topic: NIMCET 2011
