List of top Mathematics Questions

If the area of the parallelogram with \(\vec {a}\) and \(\vec {b}\) as two adjacent sides is \(15\, sq.\space units\),then the area of the parallelogram having \(3\vec {a}+2\vec {b}\) and \(\vec{a}+3\vec {b}\) as two adjacent sides in sq. unit is
If $a > b > 0$, then the value of $Tan^{-1} \left(\frac{a}{b}\right)+Tan^{-1}\left(\frac {a+b}{a-b}\right) $
The remainder obtained when $(\lfloor 1)^2 + (\lfloor 2)^2 + (\lfloor 3)^2 + ... + (\lfloor 100)^2$ is divided by $10^2$ is ;
The projection of $\vec{a} = 5\hat{i} - \hat{j} + 3 \hat{k}$ on $\vec{b} = 2 \hat{i} + \hat{j} - \hat{k}$ is
In a triangle $ABC$ if $\begin{vmatrix}1&a&b\\ 1&c&a\\ 1&b&c\end{vmatrix} = 0$, then $\sin^2 A + \sin^2 B + \sin^2 C = $
If the area of triangle formed by the points $(\alpha, 0), (0, 1)$ and $(-1, 0)$ is 20 s units, then $\alpha$ is
The area of the triangle whose vertices are $A = (1, -1, 2), B = (2, 1, -1)$ and $C = (3, -1, 2)$ is
The coordinates of the circumcentre of the triangle with vertices $(2, 3), (4, -1) $ and $ (4, 3) $ are
The number of positive divisors of 67375 which are greater than 5 is
The differential equation whose general solution is $Ax^2 + By^2 = 1$, where $A$ and $B$ are arbitrary constants is of ?
If $ \sqrt{x} + \frac{1}{\sqrt{x}} = 2 \, \cos \theta $, then $x^6 + x^6 = $
If $a, b, c$ are in G.P and $x^a = y^b = z^c$, then
If the angles of a triangle are in the ratio $3 : 4 : 5$, then the sides are in the ratio
In the group $G = \{1,5,7,11\}$ under multiplication modulo $12$, the solution of $ 7^{-1} \; \otimes_{12} (x \otimes_{12} 11) = 5$ is $x$ =
The value of $\displaystyle\lim_{x \to 0} \frac {5^x-5^{-x}}{2x}=$ is :
The value of $\begin{vmatrix} x+y&y+z & z+ x \\[0.3em] x & y & z \\[0.3em] x-y & y-z & z-x \end{vmatrix}$ = is equal to :
If $Sin (x + y)+Cos(x + y) = Log (x + y),$ then $\frac {d^2y}{dx^2}$=
A point on the curve $2y^3 + x^2 = 12y$ at which the tangent to the curve is vertical is
If f (x) = min { 1, $x^2, x^3$ }, then
Let $\theta \in\Bigg(0,\frac{\pi}{4}\Bigg) and t_1=(tan \theta)^{tan \theta}, t_2=(tan \theta)^{cot \theta},t_3=(cot \theta)^{tan \theta} and t_4=(cot \theta)^{cot \theta}, then$
Let W denote the words in the English dictionary. Define the relation $R $ by : $R =\{ (x,y), \in\, W \times \,W$ : the words $x$ and $y$ have at least one letter in commona$\}$ Then R is
Internal bisector of $\angle$ A of AABC m eets side BC at D. A line drawn through D perpendicular to AD in tersects the side AC a t E an d side AB at F. If a , b, c represent sides of $\triangle$ ABC, then
In radius of a circle which is inscribed in a isosceles triangle one of whose angle is $ 2 \pi / 3, \, is \, \sqrt 3 $, then area of triangle (in sq units) is
The value of $\int \limits \frac {(x^2-1)dx}{x^3 \sqrt {2x^4-2x^2+1}} $ is
LetC be the circle with centre (0, 0)and radius 3 units. The equation of the locus of the mid points of the chords of the circle C that subtend an angle of $\frac{2 \pi}{3}$ at its centre, is :