Question 1 :
The area enclosed by the curves $xy^2 =a^2(a-x)$ and $(a - x) y^2 = a^2x$ is
Question 2 :
The area of the region described by $ \begin{Bmatrix} (x,,y)/x^2 +y^2 \leq 1 and\   y^2\leq1-x\end{Bmatrix}$ is
Question 3 :
The area bounded by the circles ${ x }^{ 2 }+{ y }^{ 2 }=1, { x }^{ 2 }+{ y }^{ 2 }=4$ in the first Quadrant is 
Question 4 :
Ratio in which curve $\left| y \right| + x = 0$ divides the area bounded by curve $y = {\left( {x + 2} \right)^2}$ and coordinate axes, is-
Question 5 :
The area bounded by the graph $y=\left|\left[x-3\right]\right|$, the $x-$axis and the lines $x=-2$ and $x=3$ is ($\left[.\right]$ denotes the greatest Integer function):
Question 6 :
Let $f(x)={ x }^{ 2 }-3x+2$ then area bounded by the curve $f\left( \left| x \right| \right) $ (in square units) and x-axis is
Question 8 :
The area common to the circle ${x}^{2}+{y}^{2}=16{a}^{2}$ and the parabola ${y}^{2}=6ax$ is
Question 9 :
The area enclosed between the curves $y=a{ x }^{ 2 }$ and $x=a{ y }^{ 2 }$ $\\ (a>0)$ is $1sq.unit$. then $a=$
Question 10 :
The area enclosed by the curves<br>$f(x) = \vert sin x - cos x \vert + \vert cos x + sin x \vert \ \text {and} \ g(x) = 2\vert cos x + sin x \vert , 0 \leq x \leq \pi$
Question 12 :
Area of the region bounded by rays $|x|+y=1$ and X-axis is ___________.
Question 13 :
If the area enclosed between the curves $y=kx^2$ and $x=ky^2$, $(k > 0)$, is $1$ square unit. Then $k$ is?
Question 14 :
The area of the region bounded by the curves $ 1-y^{2}= \left | x \right | and \left | x \right |+\left | y \right |= 1 $ is
Question 15 :
If the line $y = \sqrt{2}x$ cuts the curve $x^2 + y^2 - 9 = 0$ at the points A, B then AB is
Question 16 :
The area of the region bounded by the curve $y=2x-x^2$ and the line $y=x$ is ________ square units.
Question 17 :
The area bounded by $y^{2}=4ax$ and $y=mx$ is $\displaystyle \frac{a^{2}}{3}$ sq. units then $\mathrm{m}$<span><br/></span>
Question 18 :
Tangents are drawn from a point $P$ to a parabola $y^{2}=4ax$. The area enclosed by the tangents and the corresponding chord of contact is $4a^{2}$. Then point $P$ satisfies
Question 19 :
The area of the region of the plane bounded by $max(|x|, |y|) \leq 1$ and $xy\leq \dfrac {1}{2}$ is
Question 20 :
The area of the region bounded by $y=(x-4)^2, y=16-x^2$ and the x axis,is
Question 21 :
What is the area of the region bounded by X-axis, the curve $y=f(x)$ and the two ordinates $x = \dfrac{1}{2}$ and $x=1$?
Question 22 :
The area bounded by the curve $y={ x }^{ 2 }$, X=axis and the ordinates z=1, z=3 is ____________.
Question 23 :
The area bounded by curve $y=x^{2}-1$ and tangents to it at $(2,3)$ and $y-$axis is
Question 24 :
The curves $y = x^{2} - 1, y = 8x - x^{2} - 9$ at
Question 25 :
The area bounded by the curve $y=\sqrt{x}$, the line $2y+3=x$ and the $x$-axis in the first quadrant is
Question 26 :
If the area enclosed by the parabolas $\displaystyle\ y= a-x^{2}$ and $\displaystyle\ y=x^{2}$ is $18\sqrt{2}$ sq.units. Find the value of 'a'
Question 27 :
Area bounded between the curve $x^2=y$ and the line $y=4x$ is
Question 28 :
A polynomial $P$ is positive for $x>0$ and the area of the region bounded by $P\left(x\right),$ the $x-$axis and the vertical lines $x=0$ and $x=\lambda$ is $\dfrac{{\lambda}^{2}\left(\lambda+3\right)}{3}$ sq.unit. Then polynomial $P\left(x\right)$ is:
Question 29 :
The area bounded by the curve $y={ e }^{ x }$ and the lines y = |x - 1|, x = 2 is given by :
Question 30 : Consider the curves $y = \sin x$ and $y = \cos x$.<div>What is the area of the region bounded by the above two curves and the lines $x = 0$ and $x = \dfrac {\pi}{4}$?</div>
Question 31 :
The area enclosed by the circle $x^{2} + y^{2} = 2$ is equal to
Question 32 :
The area common to the parabola $y=2{ x }^{ 2 }\quad$ and $\quad y={ x }^{ 2 }+4$
Question 33 :
The area of the figure bounded by the curves $y=\left|x-1\right|$ and $y=3-\left|x\right|$ is
Question 35 :
The area of the region bounded by the curve ${a^4}{y^2} = \left( {2a - x} \right){x^5}$ is to that curve whose radius is $a$, is given by the ration.
Question 36 :
If ${\int}_{0}^{1}\left(4x^{3}=f(x)\right)f(x)dx=\dfrac{4}{7}$, then the area of region bounded by $y=f(x),x-$ axis and the line $x=$ and $x=2$ is
Question 37 :
If the area enclosed between $y=m{x}^{2}$ and $x=n{y}^{2}$ is $\cfrac{1}{3}$ sq. units, then $m,n$ can be roots of (where $m,n$ are non zero real numbers)
Question 38 :
The area bounded by $y = \sin^2 x , x = \dfrac{\pi}{2} $ and $x = \pi$ is
Question 39 :
Find the area of bounded by $y=\sin x $ from $x=\dfrac{\pi}{4} $ to $x=\dfrac{\pi}{2}$
Question 40 :
The area inside the parabola $5x^2-y=0$ but outside the parabola $2x^2-y+9=0$, is
Question 41 :
The area is bounded by $x+x_1, y=y_1$ and $y=-(x+1)^2$. Where $x_1, y_1$ are the values of $x, y$ satisfying the equation $sin^{-1} x +sin^{-1} y = -\pi$ will be (nearer to origin)
Question 42 :
The area enclosed between the curve $\displaystyle y=1+{ x }^{ 2 }$, the y-axis and the straight line $\displaystyle y=5$ is given by
Question 43 :
The area bounded by the curves $y = -x^2 + 3$ and $y = 0$
Question 44 :
The area of the quadrilateral formed by the tangents at the endpoints of the latus recta to the ellipse, $\dfrac{x^{2}}{9}+\dfrac{y^{2}}{5}=1$ is 
Question 45 :
The value of $c$ for which the area of the figure bounded by the curve $y=8{x}^{2}-{x}^{5},$ the straight lines $x=1$ and $x=c$ and the $x-$axis is equal to $\dfrac{16}{3}$ is
Question 46 :
<i></i>If the area anclosed by $f\left( x \right) = \sin x + \cos x,y = a$ between two consecutive points of extremum is minimum, then the value of a is
Question 47 :
The area bounded by the x-axis, the curve<br>y =f (x ) and the lines x = 1 and x = b is equal to $ ( \sqrt { ( b^2 +1) } - \sqrt {-2} ) $for all b> 1 then f(x) is
Question 48 :
The area bounded by $\displaystyle y={ xe }^{ |X| }$ and $\displaystyle |x|=1$ is -
Question 49 :
Tangents are drawn to the ellipse $\dfrac {x^{2}}{9} + \dfrac {y^{2}}{5} = 1$ at the ends of both latus rectum. The area of the quadrilateral so formed is
Question 50 :
The area bounded by the curves $y=(x-3)^2$ and $y=x$ (in sq. units to nearest integer):
Question 51 :
<span>A factory production line is manufacturing bolts using three machines, A, B and C. Of the total output, machine A is responsible for $25$%, machine B for $35$% and machine C for the rest. It is known from previous experience with the machines that $5$% of the output from machine A is defective, $4$% from machine B and $2$% from machine C. A bolt is chosen at random from the production line and found to be defective. What is the probability that it came from </span><span>machine C? </span>
Question 52 :
There are two urns. There are $m$ white & $n$ black balls in the first urn and $p$ white & $q$ black balls in the second urn. One ball is taken from the first urn & placed into the second. Now, the probability of drawing a white ball from the second urn is
Question 53 :
A business man is expecting two telephone calls. Mr Walia may call any time between $2$ p.m and $4$ p.m. while Mr Sharma is equally likely to call any time between $2.30$ p.m. and $3.15$ p.m. The probability that Mr Walia calls before Mr Sharma is:
Question 54 :
A letter is known to have come either from TATANAGAR or from CALCUTTA. On the envelope just two Consecutive letters TA are visible. What is the probability that the letters came from TATANAGAR ? 
Question 55 :
<br>lt is given that the events $\mathrm{A}$ and $\mathrm{B}$ are such that $P(A)=\displaystyle \frac{1}{4}, P(\displaystyle \frac{A}{B})=\frac{1}{2}$ and $P(\displaystyle \frac{B}{A})=\frac{2}{3}$ then $\mathrm{P}(\mathrm{B})=$<span><br></span>
Question 56 :
Let $E, F, G$ be pairwise independent events with $P(G) > 0$ and $P(E\cap F\cap G)=0$. Then $P(E'\cap F'|G)$ equals
Question 57 :
In a certain town, $40$% of the people have brown hair, $25$% have brown eyes and $15$% have both brown hair and brown eyes. If a person selected at random from the town has brown hair, the probability that he also has brown eyes is
Question 58 :
One ticket is selected at random from $100$ tickets numbered $100,01, 02, .... 98, 99.$ If $x_{1}$ and $x_{2} $ denotes the sum and product of the digits on the tickets, then $ P((x_{1} =9)/(x_{2} =0))$ is equal to
Question 59 :
Let $A$ and $B$ be events such that $P(\overline{A})=\dfrac{4}{5}, P(B) = \dfrac{1}{3}, P\left(\dfrac{A}{B}\right) = \dfrac{1}{6}$, then:
Question 60 :
A box contains $100$ tickets numbered $1, 2, ...,100$. Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not more than $10$. The probability that the minimum number on them is $5$ is
Question 61 :
When two dice are rolled, find the probability of getting a greater number on the first die than the one on the second, given that the sum should equal 8.<br>
Question 62 :
A man and a woman appear in an interview for two vacancies in the same post. The probability of man's selection is 1/4 and that of the woman's selection is $\dfrac { 1 }{ 3 } $. What is the probability that none of them will be selected.
Question 63 :
Three numbers are chosen at random without replacement from $\left\{ 1,2,...,8. \right\} $. The probability that their minimum is $3$, given that their maximum is $6$ is
Question 64 :
In a set of $10$ coins, $2$ coins are with heads on both the sides. A coin is selected at random from this set and tossed five times. If all the five times, the result was heads, find the probability that the selected coin had heads on both the sides.  <br/>                                      <br/>
Question 65 :
A bag contains $ (2n+1)$ coins. It is known that  $n$ of these coins have a head on both sides, whereas the remaining  $(n+1)$  coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is $\dfrac{31}{42}$, then  $n$ is equal to
Question 66 :
One ticket is selected randomly from the set of $100$ tickets numbered as $\left\{00, 01, 02, 03,04,05,...,98, 99\right\}$. $E_1$ and $E_2$ denote the sum and product of the digits of the number of the selected ticket. The value of $P \left(\displaystyle \frac{E_{1}=9}{E_{2}=0} \right)$ is<br>
Question 67 : For a biased die the probabilities for different faces to turn up are given below: The die is tossed and you are told that either face 1 or 2 has turned up. Then the probability that it is face 1 is .....<br><table class="wysiwyg-table"><tbody><tr><td>Face</td><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td></tr><tr><td>Probability</td><td>0.1</td><td>0.32</td><td>0.21</td><td>0.15</td><td>0.05</td><td>0.17.</td></tr></tbody></table>
Question 68 :
A fair coin is tossed five times. If the out comes are $2$ heads and $3$ tails (in some order), then what is the probability that the fourth toss is a head?
Question 69 :
We roll a fair four-sided die. If the result is $1$ or $2$, we roll once more but otherwise, we stop. What is the probability that the sum total of our rolls is at least $4$?
Question 70 :
A lot contains 20 articles. The probability that the lot contains exactly 2 defective articles is 0.4 and the probability that it contains exactly 3 defective articles is 0.6. Articles are drawn from the lot at random one by one, without replacement and tested till all defective articles are found. The probability that the testing procedure ends at the 12th testing is
Question 71 :
The ratio of the number of trucks along a highway, on which a petrol pump is located, to the number of cars running along the same highway is 3 : 2. It is known that an average of one truck in thirty trucks and two cars in fifty cars stop at the petrol pump to be filled up with the fuel. If a vehicle stops at the petrol pump to be filled up with the fuel, find the probability that it is a car<br>
Question 72 :
Let $A$ and $B$ be two finite sets having $m$ and $n$ elements respectively such that $m \le n$. A mapping is selected at random from the set of all mappings from $A$ to $B$. The probability that the mapping selected is an injection, is
Question 73 :
In a group $14$ males and $6$ females, $8$ and $3$ of the males and females respectively are aged above $40$ years. The probability that a person selected at random from the group is aged above $40$ years, given that the selected person is female, is
Question 74 :
A pair of dice is rolled together till a sum of either $5$ or $7$ is obtained. Find the probability that $5$ comes before $7$.
Question 75 :
One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is 
Question 76 :
There is a three-volume dictionary among 43 books arranged on a shelf in random order. Three books are drawn at random from the shelf. The probability that all the three volumes of the dictionary will be drawn, is
Question 77 :
For three events $A, B$ and $C$, $P$ (Exactly one of $A$ or $B$ occurs) $= P$ (Exactly one of $B$ or $C$ occurs) $=P$(Exactly one of $C$ or $A$ occurs) $=\displaystyle\frac{1}{4}$and $P$ (All the three events occur simultaneously)$=\displaystyle\frac{1}{16}$. Then the probability that at least one of the events occurs, is.
Question 78 :
A bag contains $4$ red and $6$ black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is
Question 79 :
The contents of urn I and II are as follows, <br>Urn I: 4 white and 5 black balls<br>Urn II : 3 white and 6 black balls<br>One urn is chosen at random and a ball is drawn and its colour is noted and replaced back to the urn. Again a ball is drawn from the same urn,<br>colour is noted and replaced. The process is repeated 4 times and as a result one ball of white colour and 3 of black colour are noted. The probability that the chosen urn was I is<br>
Question 80 :
A candidate takes three tests in succession and the probability of passing the first test is P. The probability of passing each succeeding test is P or $\frac{P}{2}$ according as he passes or fails in the preceding one. The candidate is selected if he passes at least two tests. The probability that the cndidate is selected is
Question 81 :
Two non-negative integers are chosen at random from the set of non-negative integers with replacement. The probability that the sum of their squares is divisible by $10$ is <br>
Question 82 :
If the integers $'m'$ and $'n'$ are chosen at random from $1$ to $100$ then the probability that $7^{m}+7^{n}$ is divisible by $5$ is ?<br/>
Question 83 :
A signal which can be green or red with probability $\displaystyle \frac{4}{5}$ and $\displaystyle \frac{1}{5}$ respectively, is received by station $\mathrm{A}$ and then transmitted to station $\mathrm{B}$. The probability of each station receiving the signal correctly is $\displaystyle \frac{3}{4}$. If the signal received at station $\mathrm{B}$ is green, then the probability that the original signal was green is<span><br></span>
Question 84 :
A sample of size $4$ is drawn with replacement (without replacement )from an urn containing $12$ balls, of which $8$ are white, what is the conditional probability that the ball drawn on the third draw was white, given that the sample contains $3$ white balls ?
Question 85 :
If the integers $m$ and $n$ are chosen at random from $1$ to $100$ then the probability that ${7}^{m}+{7}^{n}$ is divisible by $5$ is  ?<br/>
Question 86 :
A certain party consists of four different group of people - 30 students, 35 politicians, 20 actors and 27 leaders. On a particular function day, the total cost spent on party members was Rs. 9000. It was found that 6 students spent as much as 7 politicians, 15 politicians spent as much as 12 actors and 10 actors spent as much as 9 leaders. How much did students spent ?
Question 87 :
Two events $A$ and $B$ are such that $P(A)=\cfrac{1}{4},P(B)=\cfrac{1}{2}$ and $P(B| A)=\cfrac{1}{2}$<br/>Consider the following statements<br/>$(I)$ $P(\overline { A } |\overline { B } )=\cfrac { 3 }{ 4 } $<br/>$(II)$ $A$ and $B$ are mutually exclusive<br/>$(III)$ $P(\overline { A } |\overline { B } )+P(A|\overline { B } )=1$<br/>Then
Question 88 :
There are 5 students S1,S2,S3,S4,S5 in a music class and for them there are 5 seats in a row. On examination day, all five students are randomly allotted the five seats. Let Ti denote the event that Si and Si+1 do NOT sit adjacent to each other on examination day. (i=1,2,3,4) What is the probability that T1,T2,T3,T4,T5 all occur simultaneously on examination day? If the probability is of the form A/B, find A+B
Question 89 :
A boy has a collection of blue and green marbles. The number of blue marbles belong to the sets ${2,3,4,13}$. If two marbles are chosen simultaneously and at random from his collection, then the probability that they have different colour is $1/2$. Possible number of blue marbles is:
