List of top Mathematics Questions

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 .

$f(x)=\frac{|x-a|}{x-a}$ , 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 : $\int\frac{1}{sin \,x +\sqrt{3} \,cos\, x} dx$

Evaluate $2\,cos\,22 \frac{1^{\circ}}{2}\cdot cos\,67 \frac{1^{\circ}}{2}$.

Evaluate $(i) 5! (ii) 7!$

Equation of $YOZ$ plane is