The value of k for which the equation $(k-2)x^{2}+8x+k+4=0$ has both real, distinct and negative roots is
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The foot of the perpendicular from the point (2, 4) upon $x + y = 1$ is
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If $42 (^nP_2)=(^nP_4)$ then the value of n is
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If $\vec{a}=\hat{i}-\hat{k},\, \vec{b}=x\hat{i}+\hat{j}+(1-x)\hat{k}$ and $\vec{c}=y\hat{i}+x\hat{j}+(1+x-y)\hat{k}$ ,…
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The value of the sum $\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\fr…
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If a, b, c are in geometric progression, then $log_{ax}^{a}, log_{bx}^{a}$ and $log_{cx}^{a}$ are in
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If $P=sin^{20} \theta + cos^{48} \theta $ then the inequality that holds for all values of is
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If the mean deviation of the numbers 1, 1 + d, 1 + 2d, ....., 1 + 100d from their mean is 255, then
the value of d is
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If $a+b+c=\pi$ , then the value of $\begin{vmatrix} sin(A+B+C) &sinB &cosC \\ -sinB & 0 &tanA \\ cos(A+…
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The foci of the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}=1$ and the hyperbola $\frac{x^{2}}{144}-\frac{y^{2}}{{81}…
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The value of $\int_{-\pi/3}^{\pi/3} \frac{x sinx}{cos^{2}x}dx$
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If (2, 1), (–1, –2), (3, 3) are the midpoints of the sides BC, CA, AB of a triangle ABC, then
equation of the line BC is
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If a fair dice is rolled successively, then the probability that 1 appears in an even numbered
throw is
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Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{i}-\hat{j}+\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}-\hat{k}$ be three …
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The number of bit strings of length 10 that contain either five consecutive 0’s or five consecutive
1’s is
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If $0 < x < \pi $ and $cos x + sin x = \frac{1}{2}$ , then the value of tan x is
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If $\vec{a}, \vec{b}$ and $\vec{c}$ are the position vectors of the vertices A, B, C of a triangle ABC, then the area o…
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If $\int e^{x}(f(x)-f'(x))dx=\phi(x)$ , then the value of $\int e^x f(x) dx$ is
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If $3x + 4y + k = 0$ is a tangent to the hyperbola ,$9x^{2}-16y^{2}=144$ then the value of $K$ is
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$a, b, c$ are positive integers such that $a^{2}+2b^{2}-2bc=100$ and $2ab-c^{2}=100$. Then the value of $\frac{a+b}{c}$…
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If $(– 4, 5)$ is one vertex and $7x – y + 8 = 0$ is one diagonal of a square, then the equation of the
other diagonal is
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