List of practice Questions

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 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

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

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

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

Standard deviation of first $n$ odd natural numbers is

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

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

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

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

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?

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

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

Factorise 

1.  \(a^ 4 - b^ 4\) 
2.  \(p^ 4 - 81\) 
3.  \(x^ 4 - (y + z)^ 4\) 
4.  \(x^ 4 - (x - z)^ 4\) 
5.  \(a ^4 - 2a ^2b^ 2 + b ^4\)

A $50\, Hz \,AC$ current of peak value $2\, A$ flows through one of the pair of coils. If the mutual inductance between the pair of coils is $150\, mH$, then the peak value of voltage induced in the second coil is

A body of mass $20\, g$ connected to spring of constant $k$ executes simple harmonic motion with a frequency of $\bigg(\frac{5}{\pi}\bigg)Hz$. The value of spring constant is

A comet orbits around Sun in an elliptical orbit. Which of the following quantities remains constant during the course of its motion?

A concave lens of focal length 20 cm produces an image half the size of the real object. The distance of the real object is

A monochromatic source of wavelength $60\, nm$ was used in Young?s double slit experiment to produce interference pattern. $I_1$ is the intensity of light at a point on the screen where the path difference is $150\, nm.$ The intensity of light at a point where the path difference is $200\, nm$ is given by

A particle of mass $m$ and charge $q$ is placed at rest in uniform electric field $E$ and then released. The kinetic energy attained by the particle after moving a distance $y$ is