List of top Mathematics Questions

PQ and RS are two perpendicular chords of the rectangular hyperbola xy=c2. If C is the centre of the rectangular hyperbola, then the product of the slopes of CP,CQ,CR and CS is equal to:
In the triangle ABC with vertices A (2, 3), B (4, –1) and C (1, 2), find the equation and length of altitude from the vertex A.
Find the following integral: \(\int (ax^2+bx+c)dx\)
In Class XI of a school 40% of the student's study Mathematics and 30% study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.
Find the distance between parallel lines
(i) \(15x + 8y – 34 = 0\) and \(15x + 8y + 31 = 0\)
(ii) \(l (x + y) + p = 0\) and \(l (x + y) – r = 0.\)
(i) If z = 10, find the value of z3 – 3(z – 10) 
(ii) If p = – 10, find the value of p2 – 2p – 100
Solution of the equation $x^2 dy + y (x + y) dx = 0$ is
For the following statements, write True (T) or False (F). If the statement is false, correct the statement.
(a) – 8 is to the right of – 10 on a number line.
(b) – 100 is to the right of – 50 on a number line.
(c) Smallest negative integer is – 1.
(d) – 26 is greater than – 25.
Prove that cos 4x =1-8 sin2 x cos2 x
If $cos x = -\frac{4}{5}$, where $x\in\left[0, \pi\right]$, then the value of $cos \left(\frac{x}{2}\right)$ is equal to
If $x=sin^{-1}\left(3t-4t^{3}\right)$ and $y=cos^{-1}\left(\sqrt{1-t^{2}}\right)$, then $\frac{dy}{dx}$ is equal to
If $log_e\,5$, $log_e(5^x-1)$ and $log_e$ $\left(5^{x}-\frac{11}{5}\right)$ are in $A.P.$, then the values of $x$ are
The domain and range of relation $R = \{ (x , y ) /x , y \in N , x + 2y = 5\}$ is
Let f : R $\rightarrow$ R be function defined by f(x) = sin (2x -3), then f is
Order of $\left(3x + 2y\right) \left(\frac{dy}{dx}\right)^{2} +5x \frac{d^{2}y}{dx^{2}} = 0 $ is
By using the properties of definite integrals, evaluate the integral: \(∫_0^π log(1+cosx)dx\)

Solve the following pair of linear equations by the substitution method. 
(i) x + y = 14 
    x – y = 4   

(ii) s – t = 3 
    \(\frac{s}{3} + \frac{t}{2}\) =6 

(iii) 3x – y = 3 
      9x – 3y = 9

(iv) 0.2x + 0.3y = 1.3 
     0.4x + 0.5y = 2.3 

(v)\(\sqrt2x\) + \(\sqrt3y\)=0
    \(\sqrt3x\) - \(\sqrt8y\) = 0

(vi) \(\frac{3x}{2} - \frac{5y}{3}\) =-2,
    \(\frac{ x}{3} + \frac{y}{2}\) = \(\frac{ 13}{6}\)

The circle x2+y2+4x−7y+12=0 cuts an intercept on y -axis of length
The derivative of sec-1 12x2-1 with respect to 1-x2 at x=12 is:
The rate of change of volume of a sphere with respect to its surface area when the radius is 4 cm is:
If A = {1, 2, 3, 4, 6} and R is a relation on A such that R = {(a, b) : a, b ∈ A and b is exactly divisible by a} then find the number of elements present in the range of R?
The number of terms of an AP is even. The sum of the odd terms is 24 and of the even terms is 30. The last term exceeds the first by 1012. Then the number of terms in the series is ______.

 If \(\frac{d}{dx}f(x) = 4x^3-\frac{3}{x^4}\) such that \(f(2)=0\), then \(f(x)\) is

If |x + 1||x + 3| – 4|x + 2| + 5 = 0, then sum of squares of solutions is
Find \(x\) in the following figures.
Polygon a   Polygon b