List of top Mathematics Questions

$0.30300300030000\ldots$ number is:

The mean of first ten natural numbers is:

The mode of the data \(5,\ 7,\ 9,\ 7,\ 11,\ 13,\ 7,\ 15,\ 17,\ 19\) is:

If \(x-1,\ x+2\) and \(x+8\) are three consecutive terms of a Geometric Progression, then the value of \(x\) is:

Which of the following is not in Geometric Progression?

The value which occurs most frequently in a data set is called:

12 defective pens are accidentally mixed with 132 good ones. It is not possible to tell by looking at a pen whether it is defective or not. One pen is taken out at random from this lot. What is the probability that the pen taken out is a good one?

The median of the data \(13,\ 9,\ 11,\ 7,\ 17,\ 15,\ 5\) is:

In grouped frequency distribution, the formula to find median is:

The whole area surrounded by the curve with the equations $x = a \cos^3 t, y = b \sin^3 t$ is:

If $A = \begin{bmatrix} \sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha \end{bmatrix}$ and $\alpha \in (\frac{\pi}{2}, \frac{3\pi}{2})$, if $A + A^T = I$, then $\alpha =$}

The parametric equations of the circle $x^2 + y^2 - 4x - 6y - 12 = 0$ are:

Four persons can hit a target correctly with probabilities $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is:

If $n \in \mathbb{Z}$, then the expression $\frac{2^n}{(1-i)^{2n}} + \frac{(1+i)^{2n}}{2^n}$ is equal to:

If $x = a \sin t - b \cos t$ and $y = a \cos t + b \sin t$, and it is given that $\frac{d^2y}{dx^2} = 0$, then:

The value of $\int \frac{x^2 - 1}{(x^4 + 3x^2 + 1) \tan^{-1}(x + \frac{1}{x})} dx$ is:

The range of the function $y = \log(\sin x)$ where $\sin x > 0$ is:

The value of $\int_{0}^{4} \sqrt{\frac{4-x}{4+x}} dx$ is:

In the given figure, \(TP\) and \(TQ\) are tangents to a circle with centre \(M\), touching another circle with centre \(N\) at \(A\) and \(B\) respectively. It is given that \(MQ = 13 \text{ cm}\), \(NB = 8 \text{ cm}\), \(BQ = 35 \text{ cm}\) and \(TP = 80 \text{ cm}\).
(i) Name the quadrilateral MQBN. (1)
(ii) Is MN parallel to PA? Justify your answer. (1)
(iii) Find length TB. (1)
(iv) Find length MN. (2)

In the given figure, \( \triangle AHK \sim \triangle ABC \). If \( AK = 10 \text{ cm} \), \( BC = 3.5 \text{ cm} \) and \( HK = 7 \text{ cm} \), find the length of \( AC \).

In $\triangle ABC$, $(b-c)^2 \cos^2 \frac{A}{2} + (b+c)^2 \sin^2 \frac{A}{2} =$

Evaluate : \(\frac{3 \cos^2 30^{\circ} - 6 \csc^2 30^{\circ}}{\tan^2 60^{\circ}}\).

If $\frac{dy}{dx} = y + 5$ and $y(0) = 4$, then $y(\log 2)$ is equal to

Evaluate the definite integral: \( \displaystyle \int_{3}^{5} |x-4|\,dx \).

Verify that roots of the quadratic equation \((p - q)x^2 + (q - r)x + (r - p) = 0\) are equal when \(q + r = 2p\).