List of practice Questions

Find the number of arrangements of the letters of the word when words begin with $I$ and end in $P$.

Find the number of different $8$ - letter arrangements that can be made from the letters of the word so that (i) all vowels occur together (ii) all vowels do not occur together.

Find the number of different signals that can be generated by arranging at least $2$ flags in order (one below the other) on a vertical staff, if five different flags are available.

Find the multiplicative inverse of $2 - 3i$.

Find the new coordinates of the point $(1, 1)$ if the origin is shifted to the point $(-3, -2)$ by a translation of axes.

Find the new coordinates of the point $(5, 0)$ if the origin is shifted to the point $(-3, -2)$ by a translation of axes

Find the number of $4$ letter words, with or without meaning, which can be formed out of the letters of the word , where the repetition of the letters is not allowed.

Find the mean of first $10$ multiples of $3$.

Find the median of $18, 35, 10, 42, 21 $

Find the magnifying power of a compound microscope whose objective has a focal power of 100 D and eyepiece has a focal power of 16 D when the object is placed at a distance of 1.1 cm from the objective. Assume that the final image is formed at the least distance of distinct vision, 25 cm.

Find the maximum and minimum values of $6sinx\, cosx + 4cos2x$.

Find the maximum profit that a company can make, if the profit function is given by $P(x) = 41 + 24x - 18x^2$.

Find the maximum value of $f(x) = sin(sinx)$ for all $x \in R$

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 :