List of top Mathematics Questions

The equation \((\cos p - 1)x^2 + \cos p \, x + \sin p = 0\) has real roots. Then \(p\) lies in

If the roots \(x^2 + ax + 9 = 0\) are complex, then

If \(a<b\), then \(a<\frac{a+b}{2}<\ldots\)

If \(a^2 + b^2 + c^2 = 1\), then \(ab + bc + ca\) lies in the interval

\(\frac{1}{\log_2 10} + \frac{1}{\log_4 10} + \frac{1}{\log_8 10} + \frac{1}{\log_{16} 10}\) is equal to 11

\(\log x + \log x^3 + \log x^5 + \dots + \log x^{2n-1}\) is equal to

\(|\frac{x}{2} - 1|<3\) implies that \(x\) lies in the interval

If \(x = \frac{2\sqrt{2}-\sqrt{7}}{2\sqrt{2}+\sqrt{7}}\), then \(x + x^{-1}\) is equal to

If \(x^{4/3} + x^{-1/3} = 1\), \(x^5 + 3x^2 - x\) is equal to

\[ 9^{-z} = \frac{1}{27^x \cdot 27^y} = (81)^{-y} \]

\[ \frac{5^{\frac{3}{2}} - 2^{\frac{3}{2}}}{\sqrt{5}-\sqrt{2}} + \frac{5^{\frac{3}{2}} + 2^{\frac{3}{2}}}{\sqrt{5}+\sqrt{2}} \]

Let $R =\{( P , Q ) | P$ and $Q$ are at the same distance from the origin $\}$ be a relation, then the equivalence class of (1,-1) is the set:

Let $A = \begin{bmatrix} \cos^2 x & \sin^2 x \\ \sin^2 x & \cos^2 x \end{bmatrix}$ and $B = \begin{bmatrix} \sin^2 x & \cos^2 x \\ \cos^2 x & \sin^2 x \end{bmatrix}$. Then the determinant of the matrix $A+B$ is ________.

The general solution of the differential equation $\frac{dy}{dx}+\frac{x}{y}=0$ is ________.

The solution of the differential equation $\frac{dx}{dy}+Px=Q$, where P and Q are constants or functions of y, is given by ________.

The equation of the tangent to the curve given by $x=a \sin^{3}t$, $y=b \cos^{3}t$ at a point where $t = \frac{\pi}{2}$ is ________.

The equation of the circle passing through the foci of the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ and having centre at (0, 3) is ________.

If $f(x)=ax^{2}+6x+5$ attains its maximum value at $x=1$, then the value of a is ________.

The area of the region bounded by the line $y=4$ and the curve $y=x^{2}$ is ________.

Let $[x^{r}]$ denotes the greatest integer of $x^{r}$ and $|x|$ denotes the modulus of x. Then $\lim_{x\rightarrow0}\frac{\sum_{r=1}^{100}[x^{r}]}{1+|x|}$ is ________.

Let $E_{1}$ and $E_{2}$ be two independent events. If $P(E_{1}' \cap E_{2}) = \frac{2}{15}$ and $P(E_{1} \cap E_{2}') = \frac{1}{6}$, then $P(E_{1})$ is ________.

A card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is either Ace or a King?

The equation $ax+by+c=0$ represents a straight line ________.

If $a = \frac{2 \sin \theta}{1 + \cos \theta + \sin \theta}$, then $\frac{1 + \sin \theta - \cos \theta}{1 + \sin \theta}$ is ________.

The value of k for which the system $x+ky+3z=0$, $4x+3y+kz=0$, $2x+y+2z=0$ has non-trivial solution is: