In an examination of nine papers, a candidate has to pass in more papers than the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful is
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The perimeter of a $\Delta ABC$ is 6 times the arithmetic mean of the sines of its angles. If the side a is 1, then the…
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The mean of 5 observation is 5 and their variance is 12.4. If three of the observations are 1, 2 and 6; then the mean d…
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A computer producing factory has only two plants $T_1$ and $T_2$. Plant $T_1$ produces 20% and plant $T_2$ produces 80%…
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A circle touches the x–axis and also touches the circle with centre (0, 3) and radius 2. The locus of the centre of the…
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For a group of 100 candidates, the mean and standard deviation of scores were found to be 40 and 15
respectively. Later…
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Consider the following frequency distribution table. Class interval 10-20 20-3030-40 40-50 &nb…
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The sum of infinite terms of decreasing GP is equal to the greatest value of the function $f(x) = x^3
+ 3x – 9$ in the…
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If $f(x)=\lim _{{x}\rightarrow0}\, \frac{{6}^x-{3}^x-{2}^x+1}{\log _e9(1-\cos x)}$ is a real number then $\lim _{{…
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The value of $\int ^{\pi/3}_{-\pi/3}\frac{x\sin x}{{\cos }^2x}dx$ is
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The equation of the tangent at any point of curve $x=a cos2t, y=2\sqrt{2} a sint$ with $m$ as its slope is
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If $\prod ^n_{i=1}\tan ({{\alpha}}_i)=1\, \forall{{\alpha}}_i\, \in\Bigg{[}0,\, \frac{\pi}{2}\Bigg{]}$ where i=1,2,3,..…
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A speaks truth in 60% and B speaks the truth in 50% cases. In what percentage of cases they are likely incontradict eac…
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If $\overrightarrow{{a}}$ and $\overrightarrow{{b}}$ are vectors in space, given by $\overrightarrow{{a}}=\frac{\hat{i}…
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Let $\vec{A} = 2\hat{i} + \hat{j} – 2\hat{k}$ and $\vec{B} = \hat{i} + \hat{j}$, If $\vec{C}$ is a vector such that $|\…
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