List of top Mathematics Questions

If \(O(0,0,0), A(1,2,1), B(2,1,3)\), and \(C(-1,1,2)\) are the vertices of a tetrahedron, then the acute angle between its face \(OAB\) and edge \(BC\) is
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 \( y = \tanh^{-1} \left( \dfrac{1 - x}{1 + x} \right) \), then \( \dfrac{dy}{dx} = \)
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 four points (6,2,4), (1,3,5), (1,-2,3), and (6,k,2) are coplanar, then \(k =\)
If \(\theta\) is the acute angle between the asymptotes of a hyperbola \(7x^2 - 9y^2 = 63\), then \(\cos \theta =\)
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 angle between the tangents drawn from point (1, 4) to parabola \(y^2 = 4x\) is
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
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
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 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 \(\alpha + \beta = k =\)
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
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
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
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
If \(P\) is a variable point which is at a distance of 2 units from the line \(2x - 3y + 1 = 0\) and \(\sqrt{13}\) units from the point (5, 6), then the equation of the locus of \(P\) 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
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
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 \(\sigma^2 + \mu^2\)
Three dice are thrown simultaneously and the sum of the numbers is noted. If A = getting sum greater than 14 and B = getting sum divisible by 3, then \(P(A \cap B) + P(A \cup B) =\)
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
If \(\vec{a}, \vec{b}, \vec{c}\) are unit vectors and \(\vec{a} \perp \vec{b}\), and \((\vec{a} - \vec{c}) \cdot (\vec{b} + \vec{c}) = 0\), and \(\vec{c} = l\vec{a} + m\vec{b} + n(\vec{a} \times \vec{b})\), then \(n^2 =\)