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 of $x_i 's$ is 48 and the standard deviation is 12, whereas the mean of $w_i 's$ is 55 and the standard deviation is 15, then the value of p and k should be
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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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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 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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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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$\lim_{x\to3} \dfrac{\sqrt{3x}-3}{\sqrt{2x-4}-\sqrt{2}}$ is equal to
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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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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 integral $\int \sqrt{1+2 cot x(cosec x+cotx)} dx$ , $(0<x<\frac{\pi}{2})$ (where C is a
constant of inte…
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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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Next 10 Questions — NIMCET 2019
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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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Equation of the tangent from the point (3,−1) to the ellipse 2x2 + 9y2 = 3 is
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The position vectors of the vertices A, B, C of a tetrahedron ABCD are \(\hat{i} + \hat{j} + \hat{k}\), \(\hat{i}\) and…
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The $sin^2 x tanx + cos^2 x cot x-sin2x=1+tanx+cotx $, $x \in (0 , \pi)$, then x
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\(\vec{a}\) and \(\vec{b}\) are non-zero non-collinear vectors such that \(|\vec{a}| = 2\), \(\vec{a}\cdot \vec{b} = 1\…
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In a chess tournament, n men and 2 women players participated. Each player plays 2 games against every other player. Al…
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Suppose A1, A2, ... 30 are thirty sets, each with five elements and B1, B2, ...., Bn are n sets each with three element…
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Let \(f(x) = \begin{cases} \cos [x], & x\geq 0\\ |x| + a, & x< 0 \end{cases}\) where \([x]\) denotes the gre…
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Let U and V be two events of a sample space S and P(A) denote the probability of an event A. Which of the following sta…
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