List of top Mathematics Questions

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

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

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

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

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

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

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 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 $C.V.$ of the following data :

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

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

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

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

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.

Fill in the blanks $ (i)$ In a $LPP$, the objective function is always $(ii)$ The feasible region for a $LPP$ is always a polygon. $(iii)$ A feasible region of a system of linear inequalities is said to be , if it can be enclosed within a circle. $(iv)$ In a $LPP$, if the objective function $Z = ax + by$ has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same value.

Fill in the blanks. (i) The number of different words that can be formed from the letters of the word such that two vowels never come together is . (ii) Three balls are drawn from a bag containing $5$ red, $4$ white and $3$ black balls. The number of ways in which this can be done if atleast $2$ are red is . (iii) The total number of ways in which six $'+'$ and four $'-'$ signs can be arranged in a line such that no two signs $'-'$ occur together, is .

Fill in the blanks. (i) The length of the latus rectum of the hyperbola $\frac{x^{2}}{16}-\frac{y^{2}}{9}=1$ is . (ii) The equations of the hyperbola with vertices $\left(\pm 2, 0\right)$, foci $ \left(\pm3, 0\right)$ is . (iii) If the distance between the foci of a hyperbola is $16$ and its eccentricity is $2$, then equation of the hyperbola is .