Out of $2n + 1$ tickets, which are consecutively numbered, three are drawn at random. Then the probability that the numbers on them are in arithmetic progression is
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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
$a, b, c$ 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 $3x + 4y + k = 0$ is a tangent to the hyperbola ,$9x^{2}-16y^{2}=144$ then the value of $K$ is
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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
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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 o…
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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
Topic: NIMCET 2015
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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…
Topic: NIMCET 2015
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 …
Topic: NIMCET 2015
A function $f : (0,\pi) \to R$
defined by $f(x) = 2 sin x + cos 2x$ has
Topic: NIMCET 2015
A matrix $M_r$ is defined as $M_r=\begin{bmatrix} r &r-1 \\ r-1&r \end{bmatrix} , r \in N$ then the value of $d…
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If $\vec{AC}=2\hat{i}+\hat{j}+\hat{k}$ and $\vec{BD}=-\hat{i}+3\hat{j}+2\hat{k}$ then the area of the quadrilateral ABC…
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The value of $sin^{-1}\frac{1}{\sqrt{2}}+sin^{-1}\frac{\sqrt{2}-\sqrt{1}}{\sqrt{6}}+sin^{-1}\frac{\sqrt{3}-\sqrt{2}}{\s…
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If two circles
$x^{2}+y^{2}+2gx+2fy=0$ and $x^{2}+y^{2}+2g'x+2f'y=0$ touch each other then whichof the following is tru…
Topic: NIMCET 2015
$\int_0^\pi [cotx]dx$ where [.] denotes the greatest integer function, is equal to
Topic: NIMCET 2015
