The value of $\cot\!\left(cosec^{-1}\dfrac{5}{3} + \tan^{-1}\dfrac{2}{3}\right)$ is
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A bird is flying in a straight line with velocity vector 10i+6j+k, measured in km/hr. If the starting point is (1,2,3),…
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Forces $4\hat{i} - 3\hat{j} + 7\hat{k}$ and $-2\hat{i} + 2\hat{j} - 8\hat{k}$ are acting on a particle and displaced it…
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The vector $\vec{a} = \alpha\hat{i} + 2\hat{j} + \beta\hat{k}$ lies in the plane of the vector $\vec{b} = \hat{i} + \ha…
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If $\vec{a}, \vec{b}$ and $\vec{c}$ are unit vectors, then $|\mathbf{a} - \mathbf{b}|^2 + |\mathbf{b} - \mathbf{c}|^2 +…
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$f(x) = x + |x|$ is continuous for
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Differential coefficient of $\log_{10} x$ with respect to $\log_{x} 10$ to
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If and , then the value of is
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How many natural numbers smaller than $2 \times 10^8$ can be formed using the digits 1 and 2 only?
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If $\sin\theta = 3\sin(\theta + 2\alpha)$, then value of $\tan(\theta + \alpha) + 2\tan\alpha$ is
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In a triangle ABC, angle A=90° and D is the midpoint of AC. What is the value of equal to?
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Through any point (x, y) of a curve which passes through the origin, lines are drawn parallel to the coordinate axes. T…
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A line passing through (4, 2) meets the x and y-axis at P and Q respectively. If O is the origin, then the locus of the…
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In a city 40% of the adults are illiterate while 85% of the children are literate If the ratio of the adults to that of…
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There are 50 students admitted to a nursery class. Some students can speak only English and so…
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The last digit of the number obtained by multiplying the numbers 81 x 82 x 83 x 84 x 85 x 86 x 87 x 88 x 89 is
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It has been reported in recent years that a very large number of seats in the engineering colleges in the country remai…
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At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?
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If $\log_3 2,\ \log_3(2^x - 5),\ \log_3\!\left(2^x - \dfrac{7}{2}\right)$ are in arithmetic progression, then the value…
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