NIMCET 2013 Previous Year Questions (PYQs) – Page 2 of 12
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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 parallelepiped, then thevolume of parallelepiped is
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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.P. is
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If $f(x)=tan^{-1}\left [ \frac{sinx}{1+cosx} \right ]$ , then what is the first derivative of $f(x)$?
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The solution of $\sin x +1 = \cos x $ such that $0\leq x\leq 2\pi$ is
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Let $T_n$ denote the number of triangles which can be formed by using the vertices of a regular polygon
of $n$ sides. If
$T_{n+1} - T_{n} = 21$
then $n$ equals
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Solution
$T_{n+1} - T_n = 21$
$\binom{n+1}{3} - \binom{n}{3} = 21$
$\frac{(n+1)n(n-1)}{6} - \frac{n(n-1)(n-2)}{6} = 21$
$\frac{n(n-1)}{6}\left[(n+1)-(n-2)\right] = 21$
$\frac{n(n-1)}{6}\times 3 = 21$
$\frac{n(n-1)}{2} = 21$
$n(n-1) = 42$
$n^2 - n - 42 = 0$
$(n-7)(n+6) = 0$
$n = 7$
$\binom{n+1}{3} - \binom{n}{3} = 21$
$\frac{(n+1)n(n-1)}{6} - \frac{n(n-1)(n-2)}{6} = 21$
$\frac{n(n-1)}{6}\left[(n+1)-(n-2)\right] = 21$
$\frac{n(n-1)}{6}\times 3 = 21$
$\frac{n(n-1)}{2} = 21$
$n(n-1) = 42$
$n^2 - n - 42 = 0$
$(n-7)(n+6) = 0$
$n = 7$
If $\overline{X_1}$ and $\overline{X_2}$ are the means of two distributions such that
$\overline{X_1} < \overline{X_2}$ and $\overline{X}$ is the mean of the combined
distribution, then
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The area enclosed within the curve $|X|+|Y| = 1$ (in square units) is
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Let $f(x)$ be a polynomial function of second degree and $f(1) = f(–1)$. If $a, b, c$ are in A.P. then $f'(a), f'(b), f'(c)$ are in.
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Find the point at which, the tangent to the curve $y=\sqrt{4x-3}-1$ as its slope $\frac{2}{3}$
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Atal Speaks truth in 70% and George speaks the truth in 60% cases. In what percentage of cases they
are likely to contradict each other in stating the same fact?
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Solution
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