If $\mathbf{a},\; \mathbf{b},\; \mathbf{c}$ are unit vectors such that $\mathbf{a} + \mathbf{b} + \mathbf{c} = 0$, then the value of $\mathbf{a}\cdot \mathbf{b} + \mathbf{b}\cdot \mathbf{c} + \mathbf{c}\cdot \mathbf{a}$ is:
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Focus of the parabola
$x^2 + y^2 - 2xy - 4(x + y - 1) = 0$ is:
Topic: NIMCET 2012
If the circles
$ x^2 + y^2 + 2x + 2ky + 6 = 0$
and
$x^2 + y^2 + 2ky + k = 0$
intersect orthogonally, then $k$ is:
Topic: NIMCET 2012
The equation of ellipse with major axis along the x–axis and passes through the point $(4,3)$ and $(-1,4)$.
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If $(4,-3)$ and $(-9,7)$ are two vertices of a triangle and $(1,4)$ is its centroid, find the area of the triangle.
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In a class of 100 students, 55 passed in Mathematics and 67 passed in Physics.The number of students who passed in Phys…
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Coefficients a, b, c of $ax^2 + bx + c = 0$ are chosen by tossing 3 fair coins.
Head means 1, Tail means 2.
Find the pr…
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The value of
$\displaystyle \int_{0}^{\sin^2 x} \sin^{-1}\sqrt{t} dt + \int_{0}^{\cos^2 x} \cos^{-1}\sqrt{t} dt$ is:
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The equation of the plane passing through the point $(1,2,3)$ and having the normal vector
$N = 3\mathbf{i} - \mathbf{j…
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If $\sin^2 x = 1 - \sin x$, then $\cos^4 x + \cos^2 x$ is equal to:
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A determinant is chosen at random from the set of all determinants of matrices of order 2 with elements 0 and 1 only.
T…
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If $ \cos(\alpha+\beta)=\frac{4}{5}$ and $\sin(\alpha-\beta)=\frac{5}{13},\quad 0<\alpha,\beta<\frac{\pi}{4…
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The number of words that can be formed by using
the letters of the word 'MATHEMATICS' that start as
well as end with T …
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If $A-B=\frac{\pi}{4}$, then $(1+\tan A)(1-\tan B)$ is equal to
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Let $P(E)$ denote the probability of event $E$.
Given $P(A) = 1$, $P(B) = \frac{1}{2}$, the values of $P(A \mid B)$ a…
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Which of the following is correct?
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