If $\vec{a}, \vec{b}$ and $\vec{c}$ are the position vectors of the vertices A, B, C of a triangle ABC, then the area of the triangle ABC is
Previous 10 Questions — NIMCET 2015
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If $0 < x < \pi $ and $cos x + sin x = \frac{1}{2}$ , then the value of tan x is
Topic: NIMCET 2015
The number of bit strings of length 10 that contain either five consecutive 0’s or five consecutive
1’s is
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Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{i}-\hat{j}+\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}-\hat{k}$ be three …
Topic: NIMCET 2015
If a fair dice is rolled successively, then the probability that 1 appears in an even numbered
throw is
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If (2, 1), (–1, –2), (3, 3) are the midpoints of the sides BC, CA, AB of a triangle ABC, then
equation of the line BC is
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The value of k for which the equation $(k-2)x^{2}+8x+k+4=0$
has both real, distinct and
negative roots is
Topic: NIMCET 2015
The foot of the perpendicular from the point (2, 4) upon $x + y = 1$ is
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If $42 (^nP_2)=(^nP_4)$ then the value of n is
Topic: NIMCET 2015
If $\vec{a}=\hat{i}-\hat{k},\, \vec{b}=x\hat{i}+\hat{j}+(1-x)\hat{k}$ and $\vec{c}=y\hat{i}+x\hat{j}+(1+x-y)\hat{k}$ ,…
Topic: NIMCET 2015
The value of the sum $\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\fr…
Topic: NIMCET 2015
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If $\int e^{x}(f(x)-f'(x))dx=\phi(x)$ , then the value of $\int e^x f(x) dx$ is
Topic: NIMCET 2015
If $3x + 4y + k = 0$ is a tangent to the hyperbola ,$9x^{2}-16y^{2}=144$ then the value of $K$ is
Topic: NIMCET 2015
$a, b, c$ are positive integers such that $a^{2}+2b^{2}-2bc=100$ and $2ab-c^{2}=100$. Then the value of $\frac{a+b}{c}$…
Topic: NIMCET 2015
If $(– 4, 5)$ is one vertex and $7x – y + 8 = 0$ is one diagonal of a square, then the equation of the
other diagonal is
Topic: NIMCET 2015
Out of $2n + 1$ tickets, which are consecutively numbered, three are drawn at random. Then the
probability that the num…
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A circle touches the X-axis and also touches another circle with centre at (0, 3) and radius 2.
Then the locus of the c…
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Let $\bar{P}$ and $\bar{Q}$ denote the complements of two sets P and Q. Then the set $(P-Q)\cup (Q-P) \cup (P \cap Q)…
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With the usual notation $\frac{d^{2}x}{dy^{2}}$
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The radius of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}$and having it centre
at …
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A function $f : (0,\pi) \to R$
defined by $f(x) = 2 sin x + cos 2x$ has
Topic: NIMCET 2015
