List of top Mathematics Questions

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
Let \(S=x: x∈R\) and $\left(\sqrt{3}+\sqrt{2})^{x^2-4}+(\sqrt{3}-\sqrt{2})^{x^2-4}=10\right\}$Then $n(S)$ is equal to
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
Let $\lambda \in R , \vec{a}=\lambda \hat{i}+2 \hat{j}-3 \hat{k}, \vec{b}=\hat{i}-\lambda \hat{j}+2 \hat{k}$.If $((\vec{a}+\vec{b}) \times(\vec{a} \times \vec{b})) \times(\vec{a}-\vec{b})=8 \hat{i}-40 \hat{j}-24 \hat{k}$, then $|\lambda(\vec{a}+\vec{b}) \times(\vec{a}-\vec{b})|^2$ is equal to
$\displaystyle\lim _{n \rightarrow \infty} \frac{3}{n}\left\{4+\left(2+\frac{1}{n}\right)^2+\left(2+\frac{2}{n}\right)^2+\ldots+\left(3-\frac{1}{n}\right)^2\right\}$ is equal to
In Fig. 9.24, ∠PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR.
PQR = 100°, where P, Q and R are points on a circle with centre
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?
Find the value of:
(i) -4÷\(\frac{2}{3}\)
(ii) -\(\frac{3}{5}\)÷2
(iii) -\(\frac{4}{5}\)÷(-3)
(iv) -\(\frac{1}{8}\)÷\(\frac{3}{4}\)
(v) -\(\frac{2}{13}\)÷\(\frac{1}{7}\)
(vi) -\(\frac{7}{12}\)÷(-\(\frac{2}{13}\))
(vii) \(\frac{3}{13}\)÷(-\(\frac{4}{65}\))
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 mean and variance for the following frequency distribution.

Classes0-1010-2020-3030-4040-50
Frequencies5815166
Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3
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?

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data :

Number of cars0 - 1010 - 2020 - 3030 - 4040 - 50 50 - 60 60 -7070 - 80
Frequency71413122011158
Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6m each, what is the distance between Reshma and Mandip?
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: \(cos^{-1} \frac {12}{13} + sin^{-1} \frac 35 = sin^{-1} \frac {56}{65}\)