List of top Mathematics Questions

The average age of 15 students is 18 years. If the teacher's age is added, the average increases by 1 year. What is the teacher's age?
A batsman has a certain average of runs for 11 innings. In the 12\(^{\text{th}}\) inning. He makes a score of 90 runs, thereby increasing his average by 5. His new average is:
Which of the following numbers is a perfect square?
A sum of money at simple interest doubles itself in 8 years. What is the rate of interest per annum?
A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined them after six months with an amount equal to that B. In what proportion should the profit at the end of one year be distributed among A, B and C?
If A : B = 2 : 3 and B : C = 4 : 5, find the ratio A : C.
Find the difference between the place value and the face value of the digit 7 in the number 4782.
Three numbers are in the ratio of 3 : 4 : 5, and their least common multiple (LCM) is 2400. Their highest common factor (HCF) is
The integral \[ \int \frac{x^2}{1+x^6}\,dx \] is equal to:
If the median of the following distribution is 32.5, then find the values of x and y.
In the adjoining figure, the slant height of the conical part is :
The dimensions of a window are 156 cm \(\times\) 216 cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.
Three tennis balls are just packed in a cylindrical jar. If radius of each ball is \(r\), volume of air inside the jar is
Find the value of \(k\) if the function \(f(x) = \dfrac{k\sin x}{x}\) is continuous at \(x = 0\) and \(f(0)=3\).
Let f and g be two differentiable functions satisfying $g'(5) = \frac{3}{4}$, $g(5) = 6$ and $g = f^{-1}$. Then $f'(6) =$
The coefficient of $x^{3}$ in the expansion of $(1 - \frac{3}{4}x)^{\frac{1}{2}}$ is
If $\begin{vmatrix} \alpha & \beta & \gamma \\ a & b & c \\ l & m & n \end{vmatrix} = (-1)^K \begin{vmatrix} m & n & l \\ b & c & a \\ \beta & \gamma & \alpha \end{vmatrix}$, then the least value of K is
\( T_m \) denotes the number of triangles that can be formed with the vertices of a regular polygon of \( m \) sides. If \( T_{m+1} - T_m = 15 \), then \( m = \)
If 2 and 3 are the two roots of the equation \[ 2x^3 + mx^2 - 13x + n = 0, \] then the values of \(m, n\) are respectively
If \( -1 + i \) is a root of the equation \( x^4 + 4x^3 + 5x^2 + 2x - 2 = 0 \), then the real roots of this equation are
If the system of equations \[ x + y + z = 1,\quad x + 2y + 4z = K,\quad x + 4y + 10z = K^2 \] is consistent, then \(K =\)
If CAT = 3120, then DOG = ?
To protect plants from heat, a shed of iron rods covered with green cloth is made. The lower part of the shed is a cuboid mounted by semi-cylinder as shown in the figure. Find the area of the cloth required to make this shed, if dimensions of the cuboid are \(14 \text{ m} \times 25 \text{ m} \times 16 \text{ m}\).
The probability of a shooter hitting a target is \( \frac{3}{4} \). Find the probability of hitting the target exactly 4 times in 5 shots.
One of the roots of the equation \((x + 1)^4 + 81 = 0\) is