List of top Mathematics Questions

Six pipes are fitted to a water tank. Some of these are inlet pipes and the others outlet pipes. Each inlet pipe can fill the tank in 9 h and each outlet pipe can empty the tank in 6 h. On opening all the pipes, an empty tank is filled in 9 h. The number of inlet pipes is
The total tractor population in a State is 294000, out of which 150000 are made by Mahindra & Mahindra. Out of every 1000 Mahindra tractors, 98 are red in colour. But only 5.3% of the total tractor population is red. Find the percentage of non-Mahindra tractors that are red.
The fuel indicator in a car shows \(\frac{1}{5}\)th of the fuel tank as full. When 22 more litres of fuel are poured into the tank, the indicator rests at three-fourth of the full mark. What is the capacity of the fuel tank?
Statement 1 : The only circle having radius $\sqrt{10}$ and a diameter along line $2 x+y=5 \, is\, x^{2}+y^{2}-6x+2y=0.$ Statement 2 : $2x + y = 5$ is a normal to the circle $x^{2}+y^{2}-6x+2y=0.$
A common tangent to the conics $x^{2}=6y$ and $2x^{2}-4y^{2}=9$ is:
If $ X+Y=\left[ \begin{matrix} 7 & 0 \\ 2 & 5 \\ \end{matrix} \right] $ and $ X-Y=\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right] $ , then X is equal to
If the value of mode and mean is $60$ and $66$ respectively, then the value of median is
If two vertices of an equilateral triangle are $A (- a, 0)$ and $B (a, 0), a > 0$, and the third vertex $C$ lies above x-axis then the equation of the circumcircle of $\Delta ABC$ is :
Let the equations of two ellipses be $E_{1} : \frac{x^{2}}{3}+\frac{y^{2}}{2}=1 and E_{2} : \frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}=1$, If the product of their eccentricities is $\frac{1}{2}$, then the length of the minor axis of ellipse $E_2$ is:
If the extremities of the base of an isosceles triangle are the points $(2a, 0)$ and $(0, a)$ and the equation of one of the sides is $x = 2a$, then the area of the triangle, in square units, is :
If the image of point $P(2, 3)$ in a line $L$ is $Q(4,5)$, then the image of point $R(0,0)$ in the same line is:
$ABCD$ is a trapezium such that $AB$ and $CD$ are parallel and $BC$ $\perp$ $CD$, if $\angle $ $ADB = \theta, BC = p$ and $CD = q$, then $AB$ is equal to
If the equations $x^2+2x+3=0$ and $ax^2+bx+c=0, a, b, c \in R$ have a common root, then $a : b : c$ is
If $z$ is a complex number of unit modulus and argument $\theta ,$ then $ \, arg \left(\frac{1 + z}{1 + \bar{z}}\right)$ is equal to
Let $A (-3,2)$ and $B (-2,1)$ be the vertices of a triangle $ABC$. If the centroid of this triangle lies on the line $3x + 4y+2 = 0$, then the vertex $C$ lies on the line :
A tangent to the hyperbola $\frac{x^{4}}{4}-\frac{y^{2}}{2}=1$ meets x-axis at $P$ and y-axis at $Q$. Lines $PR$ and $QR$ are drawn such that $OPRQ$ is a rectangle (where $O$ is the origin). Then $R$ lies on :
The dimensions of a room are 10m × 7m × 5m . There are 2 doors and 3 windows in the room.The dimensions of the doors are 1m × 3m. One window is of size 2m × 1.5m and the other two windows are of size 1m × 1.5m. The cost of painting the walls at ₹ 3 per m2 is
A booster pump can be used for filling as-well-as for emptying a tank. The capacity of the tank to 2400 m3. The emptying capacity of the tank i8 10 m3 per min higher than its filling capacity and the pump needs 8 min lesser to empty the tank than it needs to fill it.What is the filling capacity of the pump?
A cistern, open at the top. is to be lined with sheet lead which weights 27 𝑘𝑔 / 𝑚3. The cistern is 4.5 m long and 3 m wide and holds 50 𝑚3. The weight of lead required is
A runs 1\(\frac{2}{3}\) times as fast as B. If A gives B a start of 3 80 in. How far must the winning post be so that A and B reach it at the same time?
There are two bags, one of which contains 3 black and 4 white balls, while the other contains 4 black and 3 white balls. A dice is cast.If the face 1 or 3 turns up, a ball is taken from the first bag and if any other face turns up a ball is chosen from the second bag. The probability of choosing a black ball is
A and B walk around a circular track. They start at 8 am from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9:30 am?
The electricity bill of a certain establishment is partly fixed and partly varies with the number of units of electricity consumed. Whenin a certain month 540 units are consumed, the bill is 1800. In another month 620 units are consumed and the bill is 2040. In yetanother month 500 units are consumed. The bill for that month would be
A boat travels upstream from B to A and downstream from A to B in 3 h. If the speed of the boat in still water is 9 km/h and the speed of the current is 3 km/h, what is the distance between A and B?
The horizental distance between two towers is 60m. The angular elevation of the top of the taller tower as seen from the top of theshorter one is 30°. If the height of the taller tower is 150m, the height of the shorter one is