Let 
, 
and 
be three vector such that || = 2, || = 3, || = 5 and ++ = 0. The value of .+.+. is
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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…
Topic: NIMCET 2017
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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The equation of the tangent line to the curve y = 2x sin x at the point (π/2, π), is
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If x2 + 3xy + 2y2 – x – 4y – 6 = 0 represents a pair of straight lines, their point of intersection is
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In a triangle ABC, let angle C = π/2. If R is the inradius and R is circumradius of the triangle ABC,
then 2(r + R) equ…
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If the lines x + (a – 1)y + 1 = 0 and 2x + a2y – 1 = 0 are perpendicular, then the condition satisfies by a is
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Next 10 Questions — NIMCET 2017
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If = (i + 2j - 3k) and =(3i -j + 2k), then the angle between ( + ) and ( - )
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 (1 - x + x2 )n = a + a1x + a2x2 + ... + a2nx2n , then a0 + a2 + a4 + ... + a2n is
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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 anim…
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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 …
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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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