List of top Mathematics Questions

The number of distinct real roots of the equation x5(x3 – x2 – x + 1) + x (3x3 – 4x2 – 2x + 4) – 1 = 0 is ______ .

A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If \(σ^2 \) is the variance of X, then 100 σ2 is equal to ____.
The value of the integral \(\begin{array}{l} \displaystyle\int\limits_0^{\frac{\pi}{2}}60\frac{\sin\left(6x\right)}{\sin x}dx \end{array}\) is equal to ______.

The number of solutions of |cos x| = sinx, such that –4π ≤ x ≤ 4π is :

Let the relation R is defined in N by \(a \mathbb{R} b\), if \(3a+2b = 27\) , then R is
A line, with a slope greater than one, passes through point A(4, 3) and intersects the line x – y – 2 = 0 at the point B. If the length of the line segment AB is \(\frac{\sqrt{29}}{3}\) then B also lies on the line :

If α, β are the roots of the equation
\(x^2-(5+3^{\sqrt{log_35}}-5^{\sqrt{log_53}})+3(3^{(log_35)^{\frac{1}{3}}}-5^{(log_53)^{\frac{2}{3}}}-1) = 0\)
then the equation, whose roots are α + 1/β and β + 1/α , is

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is
Which of the following is not an irrational number?
Let m1, m2 be the slopes of two adjacent sides of a square of side a such that \(a^2 + 11a + 3(m_1^2 + m_2^2) = 220\). If one vertex of the square is \((10(\cos \alpha - \sin \alpha), 10(\sin \alpha + \cos \alpha))\), where \(\alpha \in \left(0, \frac{\pi}{2}\right)\)and the equation of one diagonal is \((\cos \alpha - \sin \alpha)x + (\sin \alpha + \cos \alpha)y = 10\), then \(72(\sin^4 \alpha + \cos^4 \alpha) + a^2 - 3a + 13\) is equal to :

A circle C1 passes through the origin O and has diameter 4 on the positive x-axis. The line y = 2x gives a chord OA of circle C1. Let C2 be the circle with OA as a diameter. If the tangent to C2 at the point A meets the x-axis at P and y-axis at Q, then QA :AP is equal to

If sin2(10°)sin(20°)sin(40°)sin(50°)sin(70°) 
\(=α−\frac{1}{16}sin⁡(10^∘),\)
 then 16 + α–1 is equal to _______

Let the lines\( \begin{array}{l} \frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2}\ \text{and}\ \frac{x+26}{-2}=\frac{y+18}{3}=\frac{z+28}{\lambda}\end{array}\)be coplanar and P be the plane containing these two lines. Then which of the following points does NOT lie on P?
Let \(\alpha, \beta\) be the roots of the equation \(x^2 - 4\lambda x + 5 = 0\) and α, γ be the roots of the equation \(x^2 - (3\sqrt{2} + 2\sqrt{3})x + 7 + 3\lambda\sqrt{3} = 0\). If \(\beta + \gamma = 3\sqrt{2}\) then \((\alpha + 2\beta + \gamma)^2\) is equal to _______.
The equations of the lines which cut off an intercept 1 from the y-axis and are equally inclined to the axes are:

If the sum of all the roots of the equation \(e^{2x} - 11e^x - 45e^{-x} + \frac{81}{2} = 0\)
 is logeP, then p is equal to _____.

The line y = x + 1 meets the ellipse \(\frac{x^2}{4}+\frac{y^2}{2}=1\) at two points P and Q. If r is the radius of the circle with PQ as diameter then (3r)2 is equal to
A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2:1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be (α, β). Then, the value of \(7α + 3β\) is equal to ________ .
If the equation of the parabola, whose vertex is at \((5, 4)\) and the directrix is \(3x + y – 29 = 0\), is \(x^2 + ay^2 + bxy + cx + dy + k = 0\), then \(a + b + c + d + k\) is equal to

If the circle
x2+y2-2gx+6y-19c = 0,g,c∈R
passes through the point (6, 1) and its centre lies on the line x – 2cy = 8, then the length of intercept made by the circle on x-axis is

The number of real solutions of the equation e4x + 4e3x - 58e2x + 4ex + 1 = 0 is _____.

If
\(0 < x< \frac{1}{\sqrt2}\ and\ \frac{\sin^{-1}x}{α} = \frac{\cos^{-1}x}{β} \)
then a value of 
\(sin(\frac{2πα}{α+β}) \)
is

The number of points, where the function $f: \mathbb{R} \to \mathbb{R}$, $$ f(x) = |x - 1|\cos|x - 2|\sin|x - 1| + (x - 3)|x^2 - 5x + 4|, $$ is NOT differentiable, is 
Let S={z=x+iy:|z–1+i|≥|z|,|z|<2,|z+i|=|z–1|}.
Then the set of all values of x, for which w = 2x + iy ∈ S for some y ∈ R is

If the sum of the first ten terms of the series
 \(\frac{1}{5} + \frac{2}{65} + \frac{3}{325} + \frac{4}{1025} + \frac{5}{2501}\)+… is \(\frac{m}{n}\), 
where m and n are co-prime numbers, then m + n is equal to __________.