Question 1 :
Let $U=\left\{ 1,2,3,4,5,6,7,8,9,10 \right\}$, $A=\left\{ 1,2,5 \right\}$, $B=\left\{ 6,7 \right\}$ then $A\cap B'$ is
Question 3 : Say true or false.<div>The collection of rich people in your district is an example of a set.</div>
Question 4 :
Let $P$ be the set of points inside the square, $Q$ be the set of points inside the triangle and $R$ be the set of points inside the circle. If the triangle and circle intersect each other and are contained in the square then,<br/>
Question 5 :
If A = $\{ 1, 2, 3, 4\}$, B = $\{2, 4, 5, 6\}$ and C = $\{1, 2, 5, 7, 8,\}$ then $\displaystyle \left ( A\cup C \right )\cap B$ is equal to:
Question 7 :
Let $A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$. Then the number of subsets of $A$ containing exactly two elements is
Question 10 :
If $A = \left\{ 1,3,5,7 \right\}$, then what is the cardinality of the power set $ P\left( A \right) $?
Question 12 :
If $f(x) = {x^2} - {x^{ - 2}}$ then $f\left(\cfrac{1}{x}\right)$ is equal to
Question 13 :
Let $f(x)=x^2,g(x)=\tan x$ and $h(x)=ln\,x$.<br/>For $x=\dfrac{\sqrt{\pi}}{2}$, what is the value of $[ho(gof)(x)]?$
Question 14 :
Consider the function $f(x)=3^{x}$. At what point, the graph of $f$ will intersect $y$-axis ?
Question 16 :
Domain of the function $f\left( x \right) =\dfrac { 1 }{ \sqrt { x-\left| x \right| } }$ is
Question 18 :
Let R be the set of real numbers and the mapping $f:R\rightarrow R$ and $g:R\rightarrow R$ be defined by $f(x)=5-x^2$ and $g(x)=3\lambda-4$, then the value of $(fog)(-1)$ is
Question 19 :
If $f(x) = \dfrac{x + 1}{x - 1}$ show that f(f(x)) is an identify function.
Question 20 :
If $\displaystyle \left[ x \right] $ is the greatest integer less than or equal to $x$, what is the value of $\displaystyle \left[ -1.6 \right] +\left[ 3.4 \right] +\left[ 2.7 \right] $?
Question 21 :
Let $\dfrac {-5\pi}{12} \leq \theta \leq -\dfrac {\pi}{3}$<br>Max. Value of $\cos \left (\dfrac {\pi}{6} + \theta\right ) - \tan \left (\theta + \dfrac {\pi}{6}\right ) + \tan \left (\theta + \dfrac {2\pi}{3}\right )$ is
Question 22 :
$( \sec A + \tan A - 1 ) ( \sec A - \tan A + 1 ) =$
Question 23 :
Find the value of $\dfrac{sin (-660^o) tan (1050^o) sec (-420^o)}{cos (225^o ) cosec (315^o) cos(510^o)}$
Question 24 :
The most general solution of $tan\theta =-1 \,\,\ and \,\,\,\ cos\theta = \dfrac{1}{\sqrt{2}}$ is
Question 29 :
In which quadrant does the terminal side of the angle $420^0$ lie?<br/>
Question 30 :
Express $\displaystyle \cos { { 79 }^{ o } } +\sec { { 79 }^{ o } } $ in terms of angles between $\displaystyle { 0 }^{ o }$ and $\displaystyle { 45 }^{ o }$
Question 31 :
If $\alpha ,\beta $ are the roots of the quadratic equation $ax^{2}+bx+c=0$ and $3b^{2}=16ac$ then
Question 32 :
The product of the roots of equation $2{ m }^{ 2 }-8m=0$ is
Question 33 :
The roots of $ax^2 + bx + c = 0, a \neq 0$ are real and unequal, if $b^2- 4ac$ is ___________.
Question 34 :
The two roots of the equation $a(b - c) x^2 + b(c - a)x + c(a - b) = 0$ are 1 and:
Question 35 :
If $\displaystyle \left ( 3x+4 \right )^{2}+\left ( 3x-2 \right )^{2}=\left ( 6x+5 \right )\left ( 3x-2 \right )+12$, then the value of x is
Question 36 :
If the discriminant of the equation $3x^{2} - 4x + k = 0$ is $64$, then $k =$ _________.
Question 38 :
If the roots of $x^{3} - kx^{2} + 14x - 8 = 0$ are in geometric progression, then $k =$
Question 39 :
The sum of two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers?
Question 40 :
If $l$ and $m$ are the roots of equation ${x}^{2}-8x+15=0$, then the value of $lm$ is :
Question 42 :
Slope of the line passing through the points $C\left( 3,5 \right)$ and $ D\left( -2,-3 \right)$ is
Question 43 :
If the vertices of $\Delta MNP$ are $M(-4, 2), N(-4, 6), P(-6, 2)$ and of $\Delta QRS$ are $Q(-5, -1), R(-5, -5), S(4, -5)$, then which of the following statements is/are true?
Question 44 :
If the points (-2,3), (x, y) and (-3,5) lie on a straight line then the equation of the line is______
Question 46 : <div>The bisector of the acute angle between the lines $3x-4y+7=0$ and $12x+5y-2=0$ is :</div>
Question 47 : The $x$ and $y$ intercepts of the following line is:<div>$\displaystyle y=\frac{2}{3}x-4$<br/></div>
Question 48 :
The point (x,y) lies on the line joining (3,4) and (-5,-6) if
Question 49 :
Find the $x$ and $y$ intercepts of the straight line $5x+3y-15=0.$
Question 50 :
The straight lines $x+y=1$ and $x-y=5$ are perpendicular to each other.
Question 52 :
The slope-intercept form of the equation $x + 2y - 4 = 0$ is<br/>
Question 53 : Represent the given equation in $y = mx + c$ form :<div>$\displaystyle \frac{x}{2}+\frac{y}{3}=1$</div>
Question 54 :
The equation of a straight line which makes an angle ${45}^{o}$ with the x-axis with y-intercept $101$ units is:
Question 55 :
If the coordinates of $A$ and $B$ be $(1,1)$ and $(5,7)$, then the equation of the perpendicular bisectors the line segment $AB$ is
Question 57 : <br/>Let $\mathrm{P}(\mathrm{x}_{1},\mathrm{y}_{1})\mathrm{b}\mathrm{e}$ any point on the cartesian plane then match the following lists:<br/> <br/><table class="table table-bordered"><tbody><tr><td> LIST - I </td><td> LIST - II</td></tr><tr><td> $\mathrm{A})$ The distance from $\mathrm{P}$ to X-axis</td><td>1) $0$</td></tr><tr><td> $\mathrm{B})$ The distance from $\mathrm{P}$ to Y-axis</td><td>2) $|\mathrm{y}_{1}|$</td></tr><tr><td> $\mathrm{C})$ The distance from $\mathrm{P}$ to origin is </td><td> 3) $\sqrt{x_{1}^{2}+y_{1}^{2}}$ </td></tr><tr><td> </td><td>4)$ |x_{1}|$ </td></tr></tbody></table>
Question 59 :
The equation of a line that intercepts the x-axis at x = 4 and the y-axis at y = -6 is
Question 60 :
Find the valueof c if the point $(4,5) $ pases through $y=5x+c$
Question 61 :
The mean and standard deviation of a random variable $x$ is given by $5$ and $3$ respectively. The standard deviation of $2-3x$ is _____
Question 63 :
The mean and variance of $7$ observations are $8$ and $16$ respectively. If $5$ of the observations are $2, 4, 10, 12, 14,$ find the remaining two observations.
Question 64 :
If the mean of n observations $x_1, x_2$, ....... $x_n$ is $\bar x$,then the sum of deviations of observations from mean is
Question 65 : Find the mean and standard deviation respectively for the following data.<br><table class="wysiwyg-table"><tbody><tr><td>Year</td><td>10</td><td>20</td><td>30</td><td>40</td><td>50</td><td>60</td></tr><tr><td>Number of persons (cumulative)</td><td>15</td><td>32</td><td>51</td><td>78</td><td>97</td><td>109</td></tr></tbody></table>
Question 66 :
The S.D. of 1, 2, 3, 4, 5, 6, 7 is
Question 67 :
If the median of the data $6,7,x-2,x,18,21$ written in ascending order is $16$, then the variance of the data is<br/>
Question 68 :
The algebric sum of deviations of $10$ observations measured from $15$ is $7$. The mean is
Question 71 :
The mean deviation of the data $3,10,10,4,7,10,5$ from the mean is<br>
Question 72 :
The scores of $10$ students in a class test are given as $44,54,46,63,55,42,34,48,70,38$. Calculate the mean deviation about the median.
Question 76 :
The mean of the numbers $a,b,8,5,10$ is $6$ and the variance is $6.80$, then which of the following gives possible values of $a$ and $b$
Question 77 :
The arithmetic mean of the observations $10,8,5,a,b$ is $6$ and their variance is $6.8$, then $ab=$<br/>
Question 78 :
If t is the standard deviation of x, y, z then the standard deviation of x + 5, y + 5, z + 5 is
Question 79 :
In a set of $2n$ observations, half of them are equal to '$\alpha$' and the remaining half are equal to '$-\alpha$'. If the standard deviation of all the observations is $2$, then the value of $|\alpha |$ is equal to
Question 80 :
If each observation of a dist., whose variance is $\displaystyle \sigma ^{2},$ is multiplied by $\displaystyle \lambda ,$ then the $S.D$. of the new new observations is
