List of top Mathematics Questions

$\displaystyle \lim _{n \rightarrow \infty}\left[\frac{1}{1+n}+\frac{1}{2+n}+\frac{1}{3+n}+\ldots+\frac{1}{2 n}\right]$ is equal to
The mean and variance of $5$ observations are $5$ and $8$ respectively If $3$ observations are $1,3,5$, then the sum of cubes of the remaining two observations is
The sum to $10$ terms of the series $\frac{1}{1+1^2+1^4}+\frac{2}{1+2^2+2^4}+\frac{3}{1+3^2+3^4}+\ldots $ is
Let $x=(8 \sqrt{3}+13)^{13}$ and $y=(7 \sqrt{2}+9)^9$ If $[t]$ denotes the greatest integer $\leq t$, then
The parabolas : $a x^2+2 b x+c y=0$ and $d x^2+2 e x+f y=0$ intersect on the line $y=1$ If $a, b, c, d, e, f$ are positive real numbers and $a, b, c$ are in GP, then
$\displaystyle\lim _{n \rightarrow \infty} \frac{3}{n}\left\{4+\left(2+\frac{1}{n}\right)^2+\left(2+\frac{2}{n}\right)^2+\ldots+\left(3-\frac{1}{n}\right)^2\right\}$ is equal to
In a college, out of 4320 students, 2300 are girls. Find the ratio of
(a) Number of girls to the total number of students.
(b) Number of boys to the number of girls.
(c) Number of boys to the total number of students.
Cadets are marching in a parade. There are 5 cadets in a row. What is the rule which gives the number of cadets, given the number of rows? (Use n for the number of rows.)
In a village six fruit merchants sold the following number of fruit baskets in a particular season :
In a village six fruit merchants sold the following number of fruit baskets in a particular season
Observe this pictograph and answer the following questions :
  1. Which merchant sold the maximum number of baskets?
  2. How many fruit baskets were sold by Anwar?
  3. The merchants who have sold 600 or more number of baskets are planning to buy a godown for the next season. Can you name them?
Raju purchases 10 pens for Rs. 150 and Manish buys 7 pens for Rs. 84. Can you say who got the pens cheaper?
Top surface of a raised platform is in the shape of a regular octagon as shown in the figure. Find the area of the octagonal surface.
raised platform of a regular octagon
 
If the origin is shifted to the point \(\left(\frac{3}{2}, -2\right)\) by the translation of axes, then the transformed equation of \(2x^2 + 4xy + y^2 + 2x - 2y + 1 = 0\) is:
Find the inverse of each of the matrices,if it exists.\(\begin{bmatrix} 1 & 3 & -2\\ -3 & 0 & -5\\ 2&5&0 \end{bmatrix}\)
The temperature dropped 15 degree celsius in the last 30 days. If the rate of temperature drop remains the same, how many degrees will the temperature drop in the next ten days?
Find \( P(A \,|\, E_1) + P(A \,|\, E_2) \):
Evaluate: $\int sec^{4/3} \,x cosec^{8/3}\,x \,dx$

Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2): L1 is parallel to L2 }. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.  

Prove: \(cos^{-1} \frac {12}{13} + sin^{-1} \frac 35 = sin^{-1} \frac {56}{65}\)

The vector with terminal point A (2, -3, 5) and initial point B (3, -4, 7) is:
The lateral surface area of a hollow cylinder is 4224 cm2. It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet.
Write two different vectors having same magnitude.

Write two different vectors having the same direction.

For the differential equations, find the general solution:\(\frac {dy}{dx} =(1+x^2)(1+y^2)\)
Max value of x+3y subject to conditions x+y≤4, 0≤x≤3 & 0≤y≤2 is?
Area of the greatest rectangle that can be inscribed in the ellipse\( \frac{x_2 }{a_2} +\frac{ y_ 2 }{b_2} = 1\) is