List of top Mathematics Questions

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) 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 .

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 .

$f(x)=\frac{|x-a|}{x-a}$ , when $x\neq a=1$ , when $x = a$ then

$f(x)=x^3 - 3x + 5 $ then $ f \left( \sin \frac{3 \pi }{ 2} \right) + f \left( \cos \frac{3 \pi}{2} \right) = $

$f(x)=\frac{\sqrt{1+px}\,-\,\sqrt{1-px}}{x}, -1\leq x\leq 0=\frac{2x+1}{x-2}, 0 \leq x \leq 1$ is continuous in the interval [-1, 1], thenp equals.

Express $50^{\circ}\, 37'\, 30''$ in radian.

Express $i^{-35}$ in the form of $a + ib$.

Express $\left(\frac{1}{3}+3i\right)^{3}$ in the form of $a +ib$.

Express $\frac{5+\sqrt{2}i}{1-\sqrt{2}i}$ in the form of $a + ib$ .

Expand $(1 - x + x^2)^4$.

Evaluate : $\int\frac{sin x}{sin 4x} dx$

Evaluate : $\int\frac{x^{3}+x}{x^{4}-9}dx$

Evaluate of the following limits. $=\displaystyle \lim_{x \to 2}$$\left\{\frac{\left(x^{2}-4\right)}{\sqrt{3x-2}-\sqrt{x+2}} \right\}=$

Evaluate: $\int\limits_{\frac{\pi}{4}}^{\frac{\pi}{2}} cos\,2x \,dx $

Evaluate: $\int\frac{sin \,2x}{sin\left(x -\frac{\pi}{3}\right) sin\left(x+\frac{\pi}{3}\right)} dx $

Evaluate: $\int\limits_{0}^{\frac{\pi}{4 }} \sqrt{1-sin\, 2x} \,\,\, dx $

Evaluate : $ \int\limits_{0}^{\pi/2}\frac{ cos \,x}{\left(cos \frac{x}{2} +sin \frac{x}{2}\right)^{3}} dx$

Evaluate: $\int\left\{\left(2x-3\right)^{5}+\frac{1}{\left(7x-5\right)^{3}}+\frac{1}{\sqrt{5x-4}}+\frac{1}{2-3x}+\sqrt{3x+2}\right\}dx$

Evaluate : $\int\left(e^{x\,log\,a} + e^{a\,log\,x} + e^{a\,log\,a} \right)dx$

Evaluate:$\int\limits_{0}^{2\pi} sin\left(\frac{\pi}{4}+\frac{x}{2}\right)dx $

Evaluate : $\int\frac{1}{sin \,x +\sqrt{3} \,cos\, x} dx$