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List of top Mathematics Questions

An equilateral triangle is inscribed in the parabola $ y^2 = x $. One vertex of the triangle is at the vertex of the parabola. The centroid of the triangle is:

What is the general solution of the equation $ \cot\theta + \tan\theta = 2 $?

The area enclosed between the curve $ y = \sin x, y = \cos x $, $\text{ for }$ $ 0 \leq x \leq \frac{\pi}{2} $ $\text{ is:}$

Let $ A $ and $ B $ be two square matrices of the same order satisfying $ A^2 + 5A + 5I = 0 $ and $ B^2 + 3B + I = 0 $ respectively, where $ I $ is the identity matrix. Then the inverse of the matrix $ C = BA + 2B - 2A + 4I $ is:

The obtuse angle between lines $2y = x + 1$ and $y = 3x + 2$ is:

Let $ x $ be a positive real number such that \[ x^{8 \log_5(x) - 24} = 5^{-4} \] Then the product of all possible values of $ x $ is:

What is the value of $\log_{X \to \infty} \left[ -(x + 1) \left( e^{x+1} - 1 \right) \right]$?

Let $ g: \mathbb{R} \to \mathbb{R} $ and $ h: \mathbb{R} \to \mathbb{R} $ be two functions such that $ h(x) = s \cdot g \cdot n(g(x)) $, where $ \mathbb{R} $ denotes the set of all real numbers and $ s $ and $ n $ stand for the signum and the sine functions respectively. Then, select which of the following is not true?

Let the line $\frac{x}{4} + \frac{y}{2} = 1$ meet the x-axis and y-axis at A and B, respectively. M is the midpoint of side AB, and M' is the image of the point M across the line $x + y = 1$. Let the point P lie on the line $x + y = 1$ such that $\Delta ABP$ is an isosceles triangle with $AP = BP$. Then the distance between M' and P is:

The circle $ x^2 + y^2 + ax + by + \gamma = 0 $ is the image of the circle $ x^2 + y^2 - 6x - 10y + 30 = 0 $ across the line $ 3x + y = 2 $. The value of $ [\alpha + \beta + \gamma] $ is (where $ [.] $ represents the floor function)

The value of $ \frac{d}{dx} \left( \int 2 \sin x \sin x^2 e^{t^2} \right) $ at $ t = \pi $ is:

Which one of the following is NOT a correct statement?

Suppose $ t_1, t_2, t_3, \dots, t_{55} $ are in AP such that $ \sum_{l=0}^{18} t_{3l+1} = 1197 $ and $ t_7 + 3t_{22} = 174 $. If $ \sum_{l=1}^{9} t_l^2 = 947b $, then the value of $ b $ is

If $ \alpha $ and $ \beta $ are the two roots of the equation $ x^2 + ax + b = 0 $, $ ab \neq 0 $, then the quadratic equation with roots $ \frac{1}{\alpha^3 + \alpha} $ and $ \frac{1}{\beta^3 + \beta} $ is

There are 40 female and 20 male students in a class. If the average heights of female and male students are 5.15 feet and 5.66 feet, respectively, then the average height (in feet) of all the students in the class equals:

Let $ f: \mathbb{R} \to \mathbb{R} $ $\text{ be any function defined as }$ \[ f(x) = \begin{cases} x^\alpha \sin \left( \frac{1}{x^\beta} \right) & \text{for } x \neq 0, \\ 0 & \text{for } x = 0, \end{cases} \] where $ \alpha, \beta \in \mathbb{R} $. Which of the following is true? $ \mathbb{R} $ denotes the set of all real numbers.

Number of permutations of the letters of the word BANGLORE such that the string ANGLE appears together in all permutations, is:

The number of all even integers between 99 and 999 which are not multiples of 3 and 5 is

Let $ F_1, F_2 $ $\text{ be the foci of the hyperbola}$ \[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1, a > 0, \, b > 0, \] and let $ O $ be the origin. Let $ M $ be an arbitrary point on curve $ C $ and above the X-axis and $ H $ be a point on $ MF_1 $ such that $ MF_2 \perp F_1 F_2, \, M F_1 \perp OH, \, |OH| = \lambda |O F_2| $ with $ \lambda \in (2/5, 3/5) $, then the range of the eccentricity $ e $ is in:

Given the equations $ x + y = 1 $, $ x^2 + y^2 = 2 $, $ x^5 + y^5 = A $. Let N be the number of solution pairs $ (x, y) $ to this system of equations. Then $ N $ is equal to:

Number of three digit numbers that can be formed using 0, 1, 2, 3, and 5 where these digits are allowed to repeat any number of times, is equal to:

The curve $ y = \frac{x}{1 + x \tan{x}} $ attains maxima at:

The number of 3-digit integers that are multiple of 6 which can be formed by using the digits 1, 2, 3, 4, 5, 6 without repetition is:

The scores of students in a national level examination are normally distributed with a mean of 500 and a standard deviation of 100. If the value of the cumulative distribution of the standard normal random variable at 0.5 is 0.691, then the probability that a randomly selected student scored between 450 and 500 is:

Consider the matrix $ B = \begin{pmatrix} 0 & 1 & -1 \\ 1 & 0 & -1 \\ 0 & 0 & 1 \end{pmatrix} $. The sum of all the entries of the matrix $ B^{19} $ is