Mathematics Tes...

The sum of the 3^rd and the 7^th term of an A.P. is 30 and the sum of the 5^th and the 9^th term is 56. Find the sum of the 4^th and the 8^th terms of the same series.

If \(\mathrm{X}=\left\{8^{\mathrm{n}}-7 \mathrm{n}-1, \mathrm{n} \in \mathbf{N}\right\}\) and \(\mathrm{Y}=49(\mathrm{n}-1), \mathrm{n} \in \mathbf{N},\) then: \((\) given \(\mathrm{n}>1)\)

Find the value of \(\underset{{{x \rightarrow 0}}}{\lim} \frac{\tan 6 x+4 x}{4 x+\tan x}\)

In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are 35%,20% and 10%, respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is :

Let the line \(L\) pass through the point \((0,1,2)\), intersect the line \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and be parallel to the plane \(2 x+y-3 z=4\). Then the distance of the point \(P(1,-9,2)\) from the line \(L\) is:

Using principle of mathematical induction, prove that for \(n \in N\), \(3^{2 n+2}-8 n-9\) is:

Find the value of 'a' so that the volume of parallelepiped formed by \(\hat{i}+a \hat{j}+\hat{k}\); \(\hat{j} + a\hat{k}\) and \(a\hat{ i}+ \hat{k}\) becomes minimum.

If \(y=3 t^{2}-4 t-3\) and \(x=8 t+5\), find \(\frac{d y}{d x}\) at \(t=6\).

The tangent to the curve \(y=e^{2 x}\) at the point \((0,1)\) meet the \(x\)-axis at

Let \(\vec{\alpha}=3 \hat{i}+\hat{j}\) and \(\vec{\beta}=2 \hat{i}-\hat{j}+3 \hat{k}.\) If \((\vec{\beta}=\vec{\beta}_1-\vec{\beta}_2,\) where \(\vec{\beta}_1\) is parallel to \(\vec{\alpha}\) and \(\vec{\beta}_2\) is perpendicular to \(\vec{\alpha}\), then \(\vec{\beta}_1 \times \vec{\beta}_2\) is equal to: