Let $P(E)$ denote the probability of event $E$. Given $P(A) = 1$, $P(B) = \frac{1}{2}$, the values of $P(A \mid B)$ and $P(B \mid A)$ respectively are

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If $A-B=\frac{\pi}{4}$, then $(1+\tan A)(1-\tan B)$ is equal to

Topic: NIMCET 2012

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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 $ \cos(\alpha+\beta)=\frac{4}{5}$ and  $\sin(\alpha-\beta)=\frac{5}{13},\quad 0<\alpha,\beta<\frac{\pi}{4…

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If $\mathbf{a},\; \mathbf{b},\; \mathbf{c}$ are unit vectors such that $\mathbf{a} + \mathbf{b} + \mathbf{c} = 0$, …

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Focus of the parabola $x^2 + y^2 - 2xy - 4(x + y - 1) = 0$ is:

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If the circles $ x^2 + y^2 + 2x + 2ky + 6 = 0$ and $x^2 + y^2 + 2ky + k = 0$ intersect orthogonally, then $k$ is:

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Which of the following is correct?

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If $\sin(\pi\cos\theta)=\cos(\pi\sin\theta)$, then $\sin 2\theta$ is equal to

Topic: NIMCET 2012