List of top Mathematics Questions

Let $\alpha$ and $\beta$ be real numbers such that $-\frac{\pi}{4}<\beta<0<\alpha<\frac{\pi}{4}$. If $\sin (\alpha+\beta)=\frac{1}{3}$ and $\cos (\alpha-\beta)=\frac{2}{3}$, then the greatest integer less than or equal to $\left(\frac{\sin \alpha}{\cos \beta}+\frac{\cos \beta}{\sin \alpha}+\frac{\cos \alpha}{\sin \beta}+\frac{\sin \beta}{\cos \alpha}\right)^2$ is ____.
Let $\alpha=\displaystyle\sum_{ k =1}^{\infty} \sin ^{2 k }\left(\frac{\pi}{6}\right)$ Let $g:[0,1] \rightarrow R$ be the function defined by $g(x)=2^{\alpha x}+2^{\alpha(1-x)}$. Then, which of the following statements is/are TRUE?

Let $\alpha$ be a positive real number. Let $f: R \rightarrow R$ and $g:(\alpha, \infty) \rightarrow R$ be the functions defined by
$f(x)=\sin \left(\frac{\pi x}{12}\right) \text { and } g(x)=\frac{2 \log _e(\sqrt{ x }-\sqrt{\alpha})}{\log _e\left( e ^{\sqrt{x}}- e ^{\sqrt{\alpha}}\right)} $ 
Then the value of $\displaystyle\lim _{x \rightarrow \alpha^{+}} f( g ( x ))$ is _______.

Let $A B C$ be the triangle with $A B=1, A C=3$ and $\angle B A C=\frac{\pi}{2}$ If a circle of radius $r>0$ touches the sides $A B, A C$ and also touches internally the circumcircle of the triangle $A B C$, then the value of $r$ ___
The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct variance is equal to :
A random variable \(X\) has the following probability distribution : 
x01234
P(x)k2k4k6k8k

The value of \(P(1 < X < 4 | x ≤ 2)\) is equal to

Let x = x(y) be the solution of the differential equation 
\(2ye^{\frac{x}{y^2}}dx+(y^2−4xe^{\frac{x}{y^2}})dy=0 \)
such that x(1) = 0. Then, x(e) is equal to

If the sum of the zeroes of the quadratic polynomial kx2 +2x+3k is equal to the product of its zeroes, then the value of k is
If A and B are d is joint sets, then

Let f : R → R be a function defined by:
\(ƒ(x) = (x-3)^{n_1} (x-5)^{n_2} , n_1, n_2 ∈ N\)
Then, which of the following is NOT true?

If
\(\int_{0}^{2} (\sqrt{2x} - \sqrt{2x - x^2}) \,dx = \int_{0}^{1} \left(1 - \sqrt{1 - y^2} - \frac{y^2}{2}\right) \,dy + \int_{1}^{2} (2 - \frac{y^2}{2}) \,dy + I\)
then I equal is

if \(∫ \frac{(x^2+1)e^x}{(x+1)^2}dx = ƒ(x)e^x+C\) where \(C\) is a constant, then \(\frac{d^3ƒ}{dx^3}\) at \(x = 1\) is equal to :
\(lim _{ n → ∞}\bigg (\frac{n^2}{(n^2+1)(n+1)}+\frac{n^2}{(n^2+4)(n+2)}+\frac{n^2}{(n2+9)(n+3)}.....+ \frac{n^2}{(n^2+n^2)(n+n)}\bigg)\)is equal to
ABCD is a square whose diagonal AC is 4√2 cm. Then the circumference of its inscribed circle is
If a ∞ b and b ∞o c, then which of the following is/are correct?
Which of the following is/are correct?
For which values of 0 (0°≤θ≤ 90°), the relation 2sin2 θ-3sin θ+1=0 is satisfied?
The rationalizing factor of 5-√3 is/are,
If the ratio of the roots of the equation px2+qx+r=0 is 1 : a, then which of the following relations is/are correct?
The roots of a quadratic questions are \(\frac{1}{2}\) and \(\frac{1}{3}\). Then the square root of the difference between the coefficient of x2 and the constant term of the quadratic equations is
If 0<θ≤90°, then the minimum value of 4cot2θ +9 tan2 θ is
If sin θ=\(\frac{8}{17}\), then tan θ+secθ = 
In how many years, a sum of money becomes 4 \(\frac{2}{3}\) times of itself at a simple interest of 5 \(\frac{1}{2}\) % per annum?
A sells an umbrella to B at a loss of 20%, B sells it to C at a loss of 10% and finally C sells it to D at a loss of 5%. If D bought that umbrella at 342, at what cost had A bought it?
log4 log3, log2 x = 1, then x =