List of top Mathematics Questions

The numbers $aₙ$ are defined by $a₀=1$ and $aₙ+1=3n²+n+aₙ$ for $n ≥ 0$. Then, $aₙ$ is equal to ________.
The range of the function $f(x)=\logₑ(3x²-4x+5)$ is ________.
If $I_{m}=\int\limits_{1}^{e}(\ln x)^{m} d x$, where $m \in N$, then $I_{10}+10 I_{9}$ is equal to -
The area of the region bounded by the curve $y=x |x|, x$-axis and the ordinates $x=1, x=$ $-1$ is given by:
If $^nC_1 + 2\, ^nC_2 + .... + n\, ^nC_n = 2n^2$, then $ n = $
The digit in the unit place of $2009! + 3^{7886}$ is
$ \sin^2 5^{\circ} + \sin^2 10^{\circ} + \sin^2 15^{\circ} +....+ \sin^2 90^{\circ} $ =
If $\log y= m \tan^{-1} x,$ then
$ \frac{1 -\tan^2 15^\circ}{1 + \tan^2 15^\circ} = $
If $|\vec{a} | = 15 , |\vec{b} | = 12$ and $|\vec{a} + \vec{b} | = 20 $ then $|\vec{a} - \vec{b} | = $
The slopes of the tangent and normal at $(0, 1)$ for the curve $y = \sin x + e^x$ are respectively
The minimum value of x⁴+y⁴+z⁴xyz for positive real numbers x,y,z is
Let f(x)=(eˣ-1)²(xa)(1+x4) for x≠0, and f(0)=12. If f(x) is continuous at x=0, then the value of a is
Which of the following functions is differentiable at x=0?
A wholesale merchant wants to start the business of cereal with ₹24000. Wheat is ₹400 per quintal and rice is ₹600 per quintal. He has capacity to store 200 quintal cereal. He earns the profit ₹25 per quintal on wheat and ₹40 per quintal on rice. If he stores x quintal rice and y quintal wheat, then maximum profit is the objective function
A flagstaff of 6 metres high placed on the top of a tower throws a shadow of 2\sqrt3 metres along the ground, when the angle (in degrees) which the sun makes with the ground is
If mean of a Poisson distribution of a random variable X is 2, then the value of P(X>1.5) is
The equation of the plane containing the line x-x₁=y-y₁m=z-z₁n is a(x-x₁)+b(y-y₁)+c(z-z₁)=0, then
The perpendicular distance of point P(1,2,3) from the line x-63=y-72=z-7-2 is
If P(A B)=23, P(A B)=16 and P(A)=13, then
What is the solution of dydx+2y=1 satisfying y(0)=0?
The solution of differential equation 2xdydx-y=3 represents a family of
If the midpoints of sides BC, CA, AB of triangle ABC are respectively D, E, F, then position vector of centre of triangle DEF, when position vectors of A, B, C are respectively i+ j, j+ k, k+ i, is
If ( a × b)² + ( a · b)² = 676 and | b| = 2, then | a| is equal to
Which one of the following is the unit vector perpendicular to both a = - i + j + k and b = i - j + k?