The value of $sin^{-1}\frac{1}{\sqrt{2}}+sin^{-1}\frac{\sqrt{2}-\sqrt{1}}{\sqrt{6}}+sin^{-1}\frac{\sqrt{3}-\sqrt{2}}{\sqrt{12}}+...$ to infinity , is equal to
Previous 10 Questions — NIMCET 2015
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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…
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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A function $f : (0,\pi) \to R$
defined by $f(x) = 2 sin x + cos 2x$ has
Topic: NIMCET 2015
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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With the usual notation $\frac{d^{2}x}{dy^{2}}$
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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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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
Out of $2n + 1$ tickets, which are consecutively numbered, three are drawn at random. Then the
probability that the num…
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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
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$a, b, c$ are positive integers such that $a^{2}+2b^{2}-2bc=100$ and $2ab-c^{2}=100$. Then the value of $\frac{a+b}{c}$…
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Next 10 Questions — NIMCET 2015
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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
In a right angled triangle, the hypotenuse is four times the perpendicular drawn to it from the opposite vertex. The va…
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A is targeting B, B and C are targeting A. Probability of hitting the target by A, B and C are $\frac{2}{3}, \frac{1}{2…
Topic: NIMCET 2015
If the angles of a triangle are in the ratio 2 : 3 : 7, then the ratio of the sides opposite to these
angles is
Topic: NIMCET 2015
Suppose that A and B are two events with probabilities $P(A) =\frac{1}{2} \, P(B)=\frac{1}{3}$ Then which of the
follo…
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The number of one-to-one functions from {1, 2, 3} to {1, 2, 3, 4, 5} is
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A harbour lies in a direction 60° South of West from a fort and at a distance 30 km from it, a ship sets out from the h…
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If $x, y, z$ are three consecutive positive integers, then $log (1 + xz)$ is
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A professor has 24 text books on computer science and is concerned about their coverage of the topics (P) compilers, (Q…
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