List of top Mathematics Questions

If \( y = \tanh^{-1} \left( \dfrac{1 - x}{1 + x} \right) \), then \( \dfrac{dy}{dx} = \)
If a function defined by \[ f(x) = \begin{cases} \dfrac{1 - \cos 4x}{x^2}, & x<0
a, & x = 0
\dfrac{\sqrt{x}}{\sqrt{16 + \sqrt{x} - 4}}, & x>0 \end{cases} \] is continuous at \(x = 0\), then \(a =\)
Evaluate \(\lim\limits_{x \to \infty} \dfrac{5x^3 - x^2 \sin 5x}{x^3 \cos 4x + 7|x|^3 - 4|x| + 3}\)
If \(\lim\limits_{x \to a^-} f(x) = p\), \(\lim\limits_{x \to a^+} f(x) = m\), and \(f(a) = k\), then which one of the following is true?
If the angles between the sides of triangle ABC formed by A(2,3,5), B(-1,2,3), and C(3,5,-2) are \(\alpha, \beta, \gamma\), then \(\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma =\)
If the four points (6,2,4), (1,3,5), (1,-2,3), and (6,k,2) are coplanar, then \(k =\)
The angle between the tangents drawn from point (1, 4) to parabola \(y^2 = 4x\) is
The angle between the tangents drawn from the point (2, 2) to the circle \(x^2 + y^2 + 4x + 4y + c = 0\) is \(\cos^{-1} \left( \frac{7}{16} \right)\). If two such circles exist, then the sum of values of \(c\) is
The tangents drawn to the hyperbola \(5x^2 - 9y^2 = 90\) through a variable point \(P\) make angles \(\alpha\) and \(\beta\) with its transverse axis. If \(\alpha\) and \(\beta\) are complementary angles, then the locus of \(P\) is
If (a, b) is the common point of the circles \(x^2 + y^2 - 4x + 4y - 1 = 0\) and \(x^2 + y^2 + 2x - 4y + 1 = 0\), then \(a^2 + b^2 =\)
If the circle \(S_1 = x^2 + y^2 + 2gx + 4y + 1 = 0\) bisects the circumference of circle \(x^2 + y^2 - 2x - 3 = 0\), then the radius of circle \(S_1\) is
If \(\theta\) is the acute angle between the asymptotes of a hyperbola \(7x^2 - 9y^2 = 63\), then \(\cos \theta =\)
The square of the slope of a common tangent to the circle \(4x^2 + 4y^2 = 25\) and ellipse \(4x^2 + 9y^2 = 36\) is
The equation \((2p - 3)x^2 + 2pxy - y^2 = 0\) represents a pair of distinct lines
If the intercept of a line \(L\) made between the straight lines \(5x - y - 4 = 0\) and \(3x + 4y - 4 = 0\) is bisected at the point (1, 5), then the equation of \(L\) is
The equation of chord AB of ellipse \(2x^2 + y^2 = 1\) is \(x - y + 1 = 0\). If O is the origin, then \(\angle AOB =\)
If the equation \(3x^2 + 4y^2 - xy + k = 0\) is the transformed equation of \(3x^2 + 4y^2 - xy - 5x - 7y + 2 = 0\) after shifting the origin to \((\alpha, \beta)\), then \(\alpha + \beta = k =\)
If a circle S passes through the origin and makes intercept 4 units on line \(x = 2\), then the equation of curve on which center of S lies is
A line \(L\) passes through point \(P(1, 2)\) and makes an angle of \(60^\circ\) with OX in positive direction. A and B are points on line \(L\), 4 units from P. If O is origin, then area of \(\triangle OAB\) is
A circle touches the line \(2x + y - 10 = 0\) at (3, 4) and passes through the point (1, -2). Then a point that lies on the circle is
A manufacturing company has 3 units A, B, and C which produce 25%, 35%, 40% of bulbs respectively. 5%, 4%, and 2% of their production is defective. If a bulb is found defective, the probability it came from B is
Given the PMF: \(P(X=x) = \alpha\) for \(x = 1,2\), \(= \beta\) for \(x = 4,5\), and \(= 0.3\) for \(x = 3\), with mean \(\mu = 4.2\). Find \(\sigma^2 + \mu^2\)
A student has probability \(\dfrac{2}{3}\) of getting distinction in a test. Out of 5 tests, the probability that he gets distinction in at least 3 tests is
Given \(f(x) = x^2 - 5x + 4\). Out of first 20 natural numbers, if a number \(x\) is chosen at random, then the probability that the chosen \(x\) satisfies the inequality \(f(x)>10\) is
A problem in Algebra is given to two students A and B whose chances of solving it are \(\dfrac{2}{5}\) and \(\dfrac{3}{5}\) respectively. The probability that the problem is solved if both try independently is