If $f(x)=tan^{-1}\left [ \frac{sinx}{1+cosx} \right ]$ , then what is the first derivative of $f(x)$?
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In a G.P. consisting of positive terms, each term equals the sum of the next two terms. Then the
common ratio of the G.…
Topic: NIMCET 2013
If the vector $2\hat{i}-3\hat{j}$ , $\hat{i}+\hat{j}-\hat{k}$ and $3\hat{i}-\hat{k}$ form three conterminous edges of a…
Topic: NIMCET 2013
If $\omega$ is a cube root of unity, then find the value of determinant $\begin{vmatrix} 1+\omega &\omega^{2} &…
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The value of the integral $\int _0^{\pi/2} \frac{\sqrt{sinx}}{\sqrt{sinx}+\sqrt{cosx}} dx$ is
Topic: NIMCET 2013
Person A can hit a target 4 times in 5 attempts. Person B - 3 times in four attempts. Person C – 2
times in 3 attempts.…
Topic: NIMCET 2013
Let $\Delta ABC$ be a triangle whose area is $10\sqrt{3}$ units with side lengths $|AB|= 8$ units and $|AC|=5$
units. F…
Topic: NIMCET 2013
If $I_n = \int_0^{\pi/4} tan^{n} \theta d\theta$ , then $I_8 + I_6$ equals
Topic: NIMCET 2013
A six faced die is a biased one. It is thrice more likely to show an odd number than to show an even
number. It is thro…
Topic: NIMCET 2013
If the straight line ax + by + c = 0 always passes through (1, –2), then a, b, c are in
Topic: NIMCET 2013
Find the number of elements in the union of 4 sets A, B, C and D having 150, 180, 210 and 240
elements respectively, gi…
Topic: NIMCET 2013
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The solution of $\sin x +1 = \cos x $ such that $0\leq x\leq 2\pi$ is
Topic: NIMCET 2013
Let $T_n$ denote the number of triangles which can be formed by using the vertices of a regular polygon
of $n$ sides. I…
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If $\overline{X_1}$ and $\overline{X_2}$ are the means of two distributions such that
$\overline{X_1} < \overline{X_2…
Topic: NIMCET 2013
The area enclosed within the curve $|X|+|Y| = 1$ (in square units) is
Topic: NIMCET 2013
Let $f(x)$ be a polynomial function of second degree and $f(1) = f(–1)$. If $a, b, c$ are in A.P. then $f'(a), f'(b), f…
Topic: NIMCET 2013
Find the point at which, the tangent to the curve $y=\sqrt{4x-3}-1$ as its slope $\frac{2}{3}$
Topic: NIMCET 2013
Atal Speaks truth in 70% and George speaks the truth in 60% cases. In what percentage of cases they
are likely to contr…
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A man observes the angle of elevation of the top of mountain to be 30o. He walks 1000 feet nearer and
finds the angle o…
Topic: NIMCET 2013
The sum of $n$ terms of an arithmetic series is 216. The value of the first term is $n$ and the value of the
$n^{th}$ t…
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Force $3\hat{i}+2\hat{j}+5\hat{k}$ and $2\hat{i}+\hat{j}-3\hat{k}$ are acting on a particle and displace it from the po…
Topic: NIMCET 2013
