List of top Mathematics Questions

Let mean and variance of 6 observations a, b, 68, 44, 40, 60 be 55 and 194. If a > b then find a + 3b

Let
\[ I(R) = \int_0^R e^{-R \sin x} \, dx, \quad R > 0. \]
Which of the following is correct?

$ABCD$ is a trapezium with $AB \parallel DC$. $AC$ and $BD$ intersect at $E$. If $\triangle AED \sim \triangle BEC$, then prove that $AD = BC$.

If tan A = 3 cot A, then the measure of the angle A is :

Let $A = \begin{bmatrix} 2 & a & 0 \\ 1 & 3 & 1 \\ 0 & 5 & b \end{bmatrix}$. If $A^3 = 4A^2 - A - 21I$, where I is the identity matrix of order $3 \times 3$, then $2a + 3b$ is equal to:

If the direction cosines of a line are \( \sqrt{3}k, \sqrt{3}k, \sqrt{3}k \), then the value of \( k \) is:

If one of the zeroes of the quadratic polynomial \((\alpha - 1)x^2 + \alpha x + 1\) is \(-3\), then the value of \(\alpha\) is:

The graph of a polynomial intersects the y-axis at one point and the x-axis at two points. The number of zeroes of this polynomial are :

Assertion (A): Zeroes of a polynomial \(p(x) = x^2 − 2x − 3\) are -1 and 3.
Reason (R): The graph of polynomial \(p(x) = x^2 − 2x − 3\) intersects the x-axis at (-1, 0) and (3, 0).

If one of the zeroes of the quadratic polynomial \((\alpha - 1)x^2 + \alpha x + 1\) is \(-3\), then the value of \(\alpha\) is:

For what value of \(k\), the product of zeroes of the polynomial \(kx^2 - 4x - 7\) is 2?

The graph of a polynomial intersects the y-axis at one point and the x-axis at two points. The number of zeroes of this polynomial are :

Assertion (A): Zeroes of a polynomial \(p(x) = x^2 − 2x − 3\) are -1 and 3.
Reason (R): The graph of polynomial \(p(x) = x^2 − 2x − 3\) intersects the x-axis at (-1, 0) and (3, 0).

For what value of \(\theta\), \(\sin^2\theta + \sin\theta + \cos^2\theta\) is equal to 2?

The diameter of a circle is of length 6 cm. If one end of the diameter is \((-4, 0)\), the other end on \(x\)-axis is at:

The distance between the points \((2, -3)\) and \((-2, 3)\) is:

The mid-point of the line segment joining the points \((-1, 3)\) and \(\left(8, \frac{3}{2}\right)\) is:

The perpendicular bisector of the line segment joining the points A(–1, 3) and B(2, 4) cuts the y-axis at :

The perpendicular bisector of the line segment joining the points A(–1, 3) and B(2, 4) cuts the y-axis at :

A card is drawn from a well-shuffled deck of 52 playing cards. The probability that drawn card is a red queen, is:

Two friends were born in the year 2000. The probability that they have the same birthday is :

A box contains cards numbered 6 to 50. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square, is :

A box contains cards numbered 6 to 50. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square, is :

Two dice are rolled together. The probability of getting a doublet is: