List of practice Questions

Find the length of latus rectum of the parabola $y^{2} = 8x$.

Find the length of perpendicular from origin to the plane $\vec{r}\cdot\left(3\hat{i}-4\hat{j}-12\hat{k}\right)+39=0$

Find the general solution for the equation $cos4x = cos2x$.

Find the identity element in the set $I^+$ of all positive integers defined by $a * b = a + b$ for all $a$, $b \in I^+$.

Find the inverse of each of the following matrices by using elementary row transformations. $\begin{bmatrix}3&3\\ 2&5\end{bmatrix}$

Find the derivative of $(x^2 + 1)\, cos\, x$.

Find the derivative of $\frac{x^{5}-cos\,x}{sin\,x}$.

Find the distance between the points $P(1, -3, 4)$ and $Q (-4,1,2)$.

Find the equation of line parallel to $y$-axis and drawn through the point of intersection of the line $x - 7y + 5 = 0$ and $3x + y = 0$.

Find the degree measure of the angle subtended at the centre of a circle of radius $100 \,cm$ by an arc of length $22 \,cm$ as shown in figure. [Use $\pi=\frac{22}{7}$]

Find the derivative of $\frac{cos\,x}{1+sin\,x}$.

Find the $C.V.$ of the following data :

Find the circular measure of the following angle $75^{\circ}$

Find the coordinates of the points which trisect the line segment $AB$ where $A(2,1, -3)$ and $B(5, -8,3)$.

Find the angle in radian through which a pendulum swings and its length is $75\, cm$ and tip describes an arc of length $21 \,cm$.

Find the area bounded by the curve $x = 2 - y - y^2$ and y-axis.

Find the area of the largest isosceles triangle having perimeter $18$ metres.

Find perpendicular distance of the line joining the points $(cos \,\theta, sin \,\theta)$ and $(cos\, \phi, sin \,\phi)$ from the origin.

Find the approximate change in the volume $V$ of a cube of side $x$ meters caused by increasing the side by $2\%$.

Find corresponding velocity-time graph for given displacement time graph

Find maximum height upto which v will move on inclined plane. All surfaces are smooth

Find out the incorrect match.

Filtration slits are formed by

Find all the points of local maxima and local minima of the function $f(x) = (x - 1)^3 (x + 1)^2$

Fill in the blanks. (i) The standard deviation of a data is of any change in origin, Put is on the change of scale. (ii) The sum of squares of the deviations of the values of the variable is when taken about their arithmetic mean. (iii) The mean deviation of the data is when measured from the median. (iv) The standard deviation is to the mean deviation taken from the arithmetic mean.