Previous 10 Questions — NIMCET 2011
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If $ f(x)=\displaystyle \int_{0}^{x} t\sin t, dt $, then $f'(x)$ is
Topic: NIMCET 2011
$ \displaystyle \lim_{x\to 0} \frac{x+\sin x}{\sqrt{x}-\cos x} $
Topic: NIMCET 2011
Find $ \displaystyle \frac{d}{dx}\left( \sqrt{x} - \frac{5}{\sqrt{x}} \right) $
Topic: NIMCET 2011
If $a$ is a positive integer, then the number of values satisfying
$ \displaystyle \int_{0}^{\pi/2} \left[ a^{2}\left(\…
Topic: NIMCET 2011
The minimum value of $px + qy$ when $xy=r^2$ and $p,q,x,y$ are positive numbers is
Topic: NIMCET 2011
An anti-aircraft gun fires at a plane. Probabilities of hitting at slots 1,2,3,4 are $0.4,;0.3,;0.2,;0.1$.
Probability …
Topic: NIMCET 2011
The number of ways of forming different $9$-digit numbers from $223355588$ by rearranging digits so that odd digits occ…
Topic: NIMCET 2011
In a college of $300$ students, every student reads $5$ newspapers and every newspaper is read by $60$ students. The nu…
Topic: NIMCET 2011
Let $X$ be the universal set for sets $A$ and $B$. If
$n(A)=200,;n(B)=300,;n(A\cap B)=100$,
then $n(A'\cap B')=300$ pro…
Topic: NIMCET 2011
$A$ polygon has $44$ diagonals, the number of its sides is
Topic: NIMCET 2011
Next 10 Questions — NIMCET 2011
Ascending by ID
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In $\triangle ABC$, $B = 45^\circ, C = 105^\circ, c=\sqrt{2}$.
Find side $a$ and $b$.
Topic: NIMCET 2011
If $ \displaystyle \tan \theta = \frac{b}{a} $, then the value of
$ a\cos 2\theta + b\sin 2\theta $
is
Topic: NIMCET 2011
The general solution of
$ \sqrt{3}\cos x + \sin x = 3 $
is:
Topic: NIMCET 2011
$ \displaystyle \text{The value of } \frac{1 - \tan^{2} 15^\circ}{1 + \tan^{2} 15^\circ} \text{ is:} $
Topic: NIMCET 2011
$ \displaystyle \int_{0}^{1/2} \frac{dx}{\sqrt{x - x^{2}}} $
Topic: NIMCET 2011
If area between $ y=x^{2} $ and $ y=x $ is $ A $, then area between $ y=x^{2} $ and $ y=1 $ is:
Topic: NIMCET 2011
If $ a,b,c $ are coplanar, evaluate
$ [,2a - b, 2b - c,2c - a,] $
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
Lines $2x + 3y - 6 = 0$ and $9x + 6y - 18 = 0$ cut coordinate axes in concyclic points.
Center of circle is:
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
