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List of top Mathematics Questions

The set of all a∈ R for which the equation x|x-1|+|x-2|+a=0 has exactly one real root is

Let $f(\theta)=3[sin^4(\frac{3\pi}{2}-\theta)+sin^4(3\pi+θ)]-2(1-sin^22\theta)$ and $S=\{\theta∈[0,\pi]:f'(\theta)=-\frac{\sqrt3}{2}\}$. If $4\beta \sum_{\theta∈S}\theta$, then $f(\beta)$ is equal to

Let $y=f(x)$ represent a parabola with focus $\left(-\frac{1}{2}, 0\right)$ and directrix $y=-\frac{1}{2}$ Then $S=\left\{x \in R : \tan ^{-1}(\sqrt{f(x)})+\sin ^{-1}(\sqrt{f(x)+1})=\frac{\pi}{2}\right\}$ :

If the radius of the largest circle with centre (2, 0) inscribed in the ellipse $x^2 + 4y^2 = 36$ is r, then $12r^2$ is equal to

Let a common tangent to the curves y² = 4x and (x – 4)² + y² = 16 touch the curves at the points P and Q. Then (PQ)² is equal to ________.

The domain of $f(x)=\frac{log_{x+1}(x-2)}{e^{2logx}-(2x+3)}$, $x∈R$ is

The perimeter of a triangle $ \triangle ABC $ is 6 times the arithmetic mean of the sines of its angles. If the side $ a $ is 1, then the angle $ A $ is:

For a group of 100 candidates, the mean and standard deviation of scores were found to be 40 and 15 respectively. Later on, it was found that the scores 25 and 35 were misread as 52 and 53 respectively. Then the corrected mean and standard deviation corresponding to the corrected figures are

The range of values of $ \theta $ in the interval $ \left( 0, \pi \right) $ such that the points $ (3, 2) $ and $ (\cos \theta, \sin \theta) $ lie on the same sides of the line $ x + y - 1 = 0 $, is:

The locus of the mid-point of all chords of the parabola $ y^2 = 4x $ which are drawn through its vertex is:

The negation of $ \sim S \vee ( \sim R \wedge S) $ $\text{ is equivalent to}$

Let $ a, b, c, d $ be non-zero numbers. If the point of intersection of the lines \[ 4ax + 2ay + c = 0 \text{and} 5bx + 2by + d = 0 \] lies in the fourth quadrant and is equidistant from the two, then the relation between $ a, b, c, d $ is

Which of the following numbers is the coefficient of $ x^{100} $ in the expansion of \[ \log_e \left( \frac{1 + x}{1 + x^2} \right), \text{where} |x| < 1? \]

Between any two real roots of the equation $ e^x \sin x = 1 $, the equation $ e^x \cos x = -1 $ has:

If \[ \int x \sin x \sec^3 x \, dx = \frac{1}{2} \left[ f(x) \sec^2 x + g(x) \left( \frac{\tan x}{x} \right) \right] + c, \] $\text{then which of the following is true?}$

If \[ \prod_{i=1}^{n} \tan (\alpha_i) = 1 \forall \alpha_i \in \left[0, \frac{\pi}{2}\right] \text{where} i = 1, 2, 3, \dots, n. \] Then the maximum value of \[ \prod_{i=1}^{n} \sin (\alpha_i) \] is

The equation of the tangent at any point of the curve \[ x = a \cos 2t, \, y = 2 \sqrt{2a} \sin t \, \text{with} \, m \, \text{as its slope is} \]

If $ \mathbf{a} $ and $ \mathbf{b} $ are unit vectors such that $ 2\mathbf{a} + \mathbf{b} = 3 $, then which of the following statement is true?

Let $ \mathbf{A} = 2\hat{i} + \hat{j} - 2\hat{k} $ and $ \mathbf{B} = \hat{i} + \hat{j} $. If $ \mathbf{C} $ is a vector such that $ |\mathbf{C} - \mathbf{A}| = 3 $ and the angle between $ \mathbf{A} \times \mathbf{B} $ and $ \mathbf{C} $ is $ 30^\circ $, then $ [(\mathbf{A} \times \mathbf{B}) \times \mathbf{C}] = 3 $, the value of $ \mathbf{A} \cdot \mathbf{C} $ is equal to:

Bag I contains 3 red, 4 black, and 3 white balls and Bag II contains 2 red, 5 black, and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball drawn is found to be black in colour. Then the probability that the transferred ball is red, is:

A point $ P $ in the first quadrant, lies on $ y^2 = 4ax $, $ a > 0 $, and keeps a distance of $ 5a $ units from its focus. Which of the following points lies on the locus of $ P $?

A bag contains different kinds of balls in which there are 5 yellow, 4 black, and 3 green balls. If 3 balls are drawn at random, then find the probability that no black ball is chosen.

Let A and B be sets. \[A \cap X = B \cap X = \varnothing \quad \text{and} \quad A \cup X = B \cup X \quad \text{for some set } X,\ \text{find the relation between } A \text{ and } B.\]

Find foci of the equation $ x^2 + 2x - 4y^2 + 8y - 7 = 0 $

In an examination of nine papers, a candidate has to pass in more papers than the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful is: