List of practice Questions

The principal argument of the complex numb $Z=\frac{1+\sin \frac{\pi}{3}+i \cos\frac{\pi}{3} }{1+\sin \frac{\pi}{3} - i \cos\frac{\pi}{3} }$ is

The set $\{(x, y) : x + y =1\}$ in the $xy$ plane represents

The value of $\frac{\sqrt{3}}{\sin15^{\circ}} - \frac{\sqrt{1}}{\cos15^{\circ}}$ is equal to

If the mean of the numbers $a, b, 8,5,10$ is $6$ and their variance is $6.8$, then $ab$ is equal to

If the position vectors of three consecutive vertices, of a parallelogram are $ \vec{i}+\vec{j}+\vec{k}, $ $ \vec{i}+3\vec{j}+5\vec{k} $ and $ 7\vec{i}+9\vec{j}+11\vec{k}, $ then the coordinates of the fourth vertex are

If the standard deviation of $3$, $8$, $6$, $10$, $12$, $9$, $11$, $10$, $12$, $7$ is $2.71$, then the standard deviation of $30$, $80$, $60$, $100$, $120$, $90$, $110$, $100$, $120$, $70$ is

If $ \sqrt{x+iy}=\pm (a+ib), $ then $ \sqrt{-x-iy} $ is equal to

If $ x $ satisfies the in equations $ 2x-7<11 $, $ 3x+4

If $ y={{\sin }^{-1}}(3x-4{{x}^{3}})+{{\cos }^{-1}}(4{{x}^{3}}-3x) $ $ +{{\tan }^{-1}}(e), $ then $ \frac{dy}{dx} $ is equal to

Let $ \alpha $ and $ \beta $ be the roots of $ a{{x}^{2}}+bx+c=0 $ . Then, $ \underset{x\to \alpha }{\mathop{\lim }}\,\frac{1-\cos (a{{x}^{2}}+bx+c)}{{{(x-\alpha )}^{2}}} $ is equal to

Standard deviation of first $n$ odd natural numbers is

The $A$.$M$. of $9$ terms is $15$. If one more term is added to this series, then the $A$.$M$. becomes $16$. The value of the added term is

The angle between the straight lines $x-1=\frac{2y+3}{3}=\frac{z+5}{2}$ and $x-3r+2; y=-2r-1; z=2,$ where $r$ is a parameter, is

The argument of the complex number $ \left( \frac{i}{2}-\frac{2}{i} \right) $ is equal to

The locus of a point which is equidistant from the points $(1,1)$ and $(3, 3)$ is

The slope of the normal to the curve $x=t^{2}+3t-8, y=2t^{2}-2t-5$ at the point $(2,-1)$ is

If the distance between the two points $(-1, a )$ and $(-1, -4a )$ is $10$ units, then the values of $a$ are

If the mean of six numbers is $41$, then the sum of these numbers is

If $ y={{\tan }^{-1}}\left( \frac{\cos x}{1+\sin x} \right), $ then $ \frac{dy}{dx} $ is equal to

Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?

The area of the triangle formed by the points $(2, 2), (5, 5), (6, 7)$ is equal to (in square units)

If $ n=5, $ then $ {{{{(}^{n}}{{C}_{0}})}^{2}}+{{{{(}^{n}}{{C}_{1}})}^{2}}+{{{{(}^{n}}{{C}_{2}})}^{2}}+..... $ $ +{{{{(}^{n}}{{C}_{5}})}^{2}} $ is equal to

The number of words that can be formed by using all the letters of the word $PROBLEM$ only one is

The value of $\displaystyle \lim_{y \to \infty} \left[y \, sin \left(\frac{1}{y}\right) - \frac{1}{y} \right]$ is equal to