The integral $\int \sqrt{1+2 cot x(cosec x+cotx)} dx$ , $(0<x<\frac{\pi}{2})$ (where C is a
constant of integration) is equal to
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The tangent at the point (2, -2) to the curve $x^2 y^2-2x=4(1-y)$ does not passes through the point
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If A > 0, B > 0 and A + B = $\frac{\pi}{6}$ , then the minimum value of $ \tan A + \tan B$
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A computer producing factory has only two plants T1 and T2 produces 20% and plant T2 produces …
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If $|z|<\sqrt{3}-1$, then $|z^{2}+2z cos \alpha|$ is
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Number of onto (surjective) functions from A to B if n(A)=6 and n(B)=3, is
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The sum of infinite terms of a decreasing GP is equal to the greatest value of the function $f(x)=x^3+3x-9$ in the…
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Number of real solutions of the equation $\sin\!\left(e^x\right) = 5^x + 5^{-x}$ is
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A force of 78 grams acts at the point (2,3,5). The direction ratios of the line of action being 2,2,1 . The magnit…
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The value of non-zero scalars α and β such that for all vectors $\vec{a}$ and $\ve…
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In a beauty contest, half the number of experts voted Mr. A and two thirds voted for Mr. B 10 voted for both and 6 did …
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If all the words, with or without meaning, are written using the letters of the word QUEEN add are arranged a…
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The curve satisfying the differential equation ydx-(x+3y2)dy=0 and passing through the point (1,1) also passe…
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$\lim_{x\to3} \dfrac{\sqrt{3x}-3}{\sqrt{2x-4}-\sqrt{2}}$ is equal to
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If S and S' are foci of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, B is the end of the minor axis and B…
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The equation of the circle passing through the point (4,6) and whose diameters are along x + 2y - 5 =0 and 3x…
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In a parallelogram ABCD, P is the midpoint of AD. Also, BP and AC intersect at Q. Then AQ : QC =
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The median AD of ΔABC is bisected at E and BE is extended to meet the side AC in F. The AF : FC =
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Let $X_i, i = 1,2,.. , n$ be n observations and $w_i = px_i +k, i = 1,2,
,n$ where p and k are constants. If the mean o…
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If x is real, then the minimum value of $\dfrac{x^2-x+1}{x^2+x+1}$is:
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If , then the values of A1, A2, A3, A4 are
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