List of top Mathematics Questions

The end of a latus rectum of the ellipse \(3x^2 + 4y^2 = 12\) is lying in the third quadrant. If the normal drawn at \(L_1\) to this ellipse intersects the ellipse again at the point \(P(a,b)\), then find the value of \(a\):

The variance of the following continuous frequency distribution is:

class intervalFrequency
0 -- 42
4 -- 83
8 -- 122
12 -- 161

 

The circle \(x^2 + y^2 - 8x - 12y + \alpha = 0\) lies in the first quadrant without touching the coordinate axes. If \((6, 6)\) is an interior point to the circle, then the range of \(\alpha\) is:
If \(f(x) = \begin{cases} 2x + 3, & \text{if } x \leq 1 \\ 2ax + bx, & \text{if } x > 1 \end{cases}\) is differentiable \(\forall x \in \mathbb{R}\), then \(f(2) =\)
Let \( f: \mathbb{R} \rightarrow \mathbb{R} \) be defined by \( f(x + y) = f(x) + 12y \), for all \( x, y \in \mathbb{R} \). If \( f(1) = 6 \), then the value of \( \sum_{r=1}^n f(r) \) is:
If the line \(2x - 3y + 5 = 0\) is the perpendicular bisector of the line segment joining \(1, -2\) and \((a, b)\), then \(a + b =\)
If the origin is shifted to remove the first degree terms from the equation \(2x^2 - 3y^2 + 4xy + 4x + 4y - 14 = 0\), then with respect to this new co-ordinate system, the transformed equation of \(x^2 + y^2 - 3xy + 4y + 3 = 0\) is
If \( O(0, 0, 0), A(3, 0, 0), B(0, 4, 0) \) form a triangle then the incenter of triangle OAB is:

Evaluate the integral \( \int \frac{dx}{\sqrt{\sin^3 x \cdot \cos (x - \alpha)}} \):

If the area of the triangle formed by the straight lines \(-15x^2 + 4xy + 4y^2 = 0\) and \(x = a\) is \(200 \, {sq. units}\), then \(|a| =\)
In the interval \([0, 3]\), the function \(f(x) = |x - 1| + |x - 2|\) is:
Let \( A(2, 3), B(1, -1) \) be two points. If \( P \) is a variable point such that \( \angle APB = 90^\circ \), then the locus of \( P \) is
The probability that a man failing to hit a target is \(\frac{1}{3}\). If he fires 4 times, then the probability that he hits the target at least thrice is
In \(\triangle ABC\), if \(4r_1 = 5r_2 = 6r_3\), then \(\sin^2 \frac{A}{2} + \sin^2 \frac{B}{2} + \sin^2 \frac{C}{2} =\)
Evaluate the integral \( \int \frac{e^{2x}}{\sqrt{e^x + 1}} \, dx \):
The equation of the straight line passing through the point of intersection of the lines represented by \(x^2 + 4xy + 3y^2 - 4x - 10y + 3 = 0\) and the point \((2,2)\) is:
The number of numbers lying between 1000 and 10000 such that every number contains the digits 3 and 7 only once without repetition is:
If \([x]\) is the greatest integer function, then evaluate the integral \( \int_{0}^{5} [x] \, dx \):
The circumcentre of the triangle formed by the lines \(x + y + 2 = 0\), \(2x + y + 8 = 0\) and \(x - y - 2 = 0\) is
Evaluate the integral \( \int \frac{dx}{x(x^4 + 1)} \):
The domain of the real valued function \( f(x) = \sqrt{2 + x} + \sqrt{3 - x} \) is:
The angle between the diagonals of the parallelogram whose adjacent sides are \(2i + 4j - 5k\) and \(i + 2j + 3k\) is
If the locus of the mid points of the chords of the circle \(x^2 + y^2 = 25\) that subtend a right angle at the origin is given by \( \frac{x^2}{a^2} + \frac{y^2}{a^2} = 1\), then \(|a| =\)
If the mean deviation about the mean is \(m\) and the variance is \(\sigma^2\) for the following data, then \(m + \sigma^2 =\) % Data table \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 3 & 5 & 7 & 9 \\ \hline f & 4 & 24 & 28 & 16 & 8 \\ \hline \end{array} \]
If the roots of the equation \(x^3 + ax^2 + bx + c = 0\) are in arithmetic progression, then: