List of top Mathematics Questions

A line is drawn through a fixed point $ P (\alpha,\beta) $ to cut the circle $ x^2 + y^2 = r^2$ at $A$ and $B,$ then $PA.PB$ is equal to
A letter is known to have come either from $TATANAGAR$ or $KOLKATA$. On the envelope, only the two consecutive letters $TA$ are visible. What is the probability that the letter has come from (i) $KOLKATA$, (ii) $TATANAGAR$
A ladder, $5$ meter long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of $10 \,cm/sec$, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is $2$ metres from the wall is
A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is
A ladder $10 \,m$ long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of $3\, cm/s$. The height of the upper end while it is descending at the rate of $4 \,cm/s$, is
A hyperbola having the transverse axis of length $2\, sin\, \theta$, is confocal with the ellipse $3x^2 + 4y^2 = 12$. Then its equation is
A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has (i) no girls (ii) atleast one boy and one girl (iii) atleast three girls?
A figure consists of a semi-circle with a rectangle on its diameter. Given the perimeter of the figure, find its dimensions in order that the area may be maximum.
A factory owner wants to purchase two types of machines, $A$ and $B$, for his factory. The machine $A$ requires an area of $1000 m^2$ and $12$ skilled men for running it and its daily output is $ 50$ units, whereas the machine $B$ required $1200m^ 2$ area and $8$ skilled men, and its daily output is $40$ units. If an area of $7600 m^2$ and $72$ skilled men be available to operate the machine, how many machines $A$ and $B$ respectively should be purchased to maximize the daily output?
$A$ event which has only $X$ sample point of a sample space, is called simple event. Here, $X$ refers to______.
A drawer contains 5 brown socks and 4 blue socks well mixed. A man reaches the drawer and pulls out 2 socks at random. What is the probability that they match ?
$A$ die is rolled. Let $E$ be the event "die shows $4$" and $F$ be the event "die shows even number". Then, $E$ and $F$ are
A dice is thrown twice. The probability of getting 4, 5 or 6 in the first throw and 1, 2, 3 or 4 in the second throw is
A determinant is chosen at random from the set of all determinants of order 2 with elements 0 and 1 only. The probability that the value of the determinant chosen is positive is
A dealer wishes to purchase a number of fans and sewing machines. He has only $?\, 5760$ to invest and has space for at most $20$ items. A fan and sewing machine cost $?\, 360$ and $? \,240$ respectively. He can sell a fan at a profit of $?\,22$ and sewing machine at a profit of $? \,18$. Assuming that he can sell whatever he buys, how many fans and sewing machines respectively he sell in order to maximize his profit?
A cricket club has $15$ members of which. only $5$ can bowl. If the names of $15$ members are put into a box and $11$ names are drawn at random, then the probability of obtaining $11$ member team containing exactly three bowlers is
A company has two factories located at $P$ and $Q$ and has three depots situated at $A, B$ and $C$. The weekly requirement of the depots at $A, B$ and $C$ is respectively $5, 5$ and $4$ units, while the production capacity of the factories at $P$ and $Q$ are respectively $8$ and $6$ units. The cost of transportation per unit is given below:
How many units should be transported from each factory to each depots $A, B, C$ respectively in order that the transportation cost is minimum?
A committee of $3$ persons is to be constituted from a group of $2$ men and $3$ women. In how many ways can this be done? How many of these committees would consist of $1$ man and $2$ women?
A coin is tossed twice. If the second throw result in a tail, a die is thrown. Then, the total number of the outcomes of this experiment is
The equation $x=\frac{e^t\,+\,e^{-t}}{2};y=\frac{e^1\,-\,e^{-t}}{2};t\in$ R represents
If a normal chord at a point "t" on the parabola $y^2 = 4ax$ subtends a right angle at the vertex, then t =
A card from a pack of $52$ cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both clubs. Find the probability of the lost card being a club.
A card is drawn from a well-shuffled deck of $52$ cards. Find the odds in favour of getting a face card.
A card, drawn at random from a pack of 52 cards, is noted and kept aside. Another card is then drawn from the remaining pack at random. The probability that both the cards are kings is
A boy has $3$ library tickets and $8$ books of his interest in the library. Of these $8$, he does not want to borrow Mathematics unless Mathematics is also borrowed. In how many ways can he choose the three books to be borrowed?