m distinct animals of a circus have to be placed in m cages, one is each cage. There are n small
cages and p large animal (n < p < m). The large animals are so large that they do not fit in small
cage. However, small animals can be put in any cage. The number of putting the animals into
cage is
Previous 10 Questions — NIMCET 2017
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If (1 - x + x2 )n = a + a1x + a2x2 + ... + a2nx2n , then a0 + a2 + a4 + ... + a2n is
Topic: NIMCET 2017
The number of elements in the power set P(S) of the set S = {2, (1, 4)} is
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If = (i + 2j - 3k) and =(3i -j + 2k), then the angle between ( + ) and ( - )
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Let , and be three vector such that || = 2, || = 3, || = 5 and ++ = 0. The value o…
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Let a, b and c be three vectors having magnitudes 1, 1 and 2 respectively. If a x (a x c) - b = 0, then the acute angle…
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If , and , (a ≠ b ≠ c ≠ 1) are co-planar, then the value of is
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If $\vec{a}$, $\vec{b}$ and $\vec{c}$ are vectors such that $\vec{a}$+$\vec{b}$+$\vec{c}$…
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The equation of the hyperbola with centre at the region, length of the transverse axis is 6 and
one focus (0, 4) is
Topic: NIMCET 2017
The direction cosines of the vector a = (- 2i + j – 5k) are
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If the graph of y = (x – 2)2 – 3 is shifted by 5 units up along y-axis and 2 units to the right along
the x-axis, then …
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Let A and B two sets containing four and two elements respectively. The number of subsets of
the A × B, each having at …
Topic: NIMCET 2017
The slope of the function \[
f(x) =
\begin{cases}
x^2 \sin\!\left(\dfrac{1}{x}\right), & \text{if } x \ne 0, \…
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What is the largest area of an isosceles triangle with two edges of length 3?
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The value of $\int_{0}^{\pi}x^3 \sin x dx$
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Let f(x) be a polynomial of degree four, having extreme value at x = 1 and x = 2. If $\lim _{{x}\rightarrow0}[1+\frac{f…
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The maximum value of 4 sin2 x + 3 cos2 x + sin(x/2) + cos(x/2) is
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The solution of (ex + 1) y dy = (y + 1) ex dx is
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Evaluate $\displaystyle \int_{0}^{1}x(1-x)^ndx $
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The critical point and nature for the function f(x, y) = x2 –2x + 2y2 + 4y – 2 is
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If y = cos2 x2 , find dy/dx
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