List of top Mathematics Questions

Determine if the following are in proportion.
(a) 15, 45, 40, 120
(b) 33, 121, 9,96
(c) 24, 28, 36, 48
(d) 32, 48, 70, 210
(e) 4, 6, 8, 12
(f) 33, 44, 75, 100

Draw the number line and represent the following rational numbers on it:
(i) \(\frac{3}{4}\)(ii) \(\frac{-5}{8}\) (iii) \(\frac{-7}{4}\) (iv) \(\frac{7}{8}\)

Examine the continuity of the function f(x) = 2x²-1 at x = 3.

Can this be a net for a die? Explain your answer.

Write the smallest 5-digit number and express it in the form of its prime factors.

Find the value of $\sqrt{(5+12i)}$, where $i=\sqrt{-1}$.

Maximam value of $:Z=10x+25$ y Subject to : $x\le 3,y\le 3,x+y\le 5,x\ge 0,y\ge 0$ at:

Maximize $Z=4x+9y$, subject to the constralnts $x=0$, y $=0,x+5y\le 200,2x+3y\le 134$.

The integrating factor of the differential equation $2y\frac{dx}{dy}+x=5y^2$ is, $(y\ne 0)$:

The differential equation of the family of curves $y=c_1{e}^x+c_2{e}^{-x}$ is:

The following table gives the weights of one hundred persons. Copute the coefficient of dispersion by the method of limits.Class-interval$40-45$$45-50$$50-55$$55-60$$60-65$$65-70$$70-75$$75-80$$80-85$$85-90$No. of persons$4$$13$$8$$14$$9$$16$$17$$9$$8$$2$

Find the position vector of the midpoint of the vector joining the points $P(2,3,4)$ and $Q(4,1,-2)$.

If $n=100!$, then what is the value of the following?$\frac{1}{{\log }_{2}n}+\frac{1}{{\log }_{3}n}+\frac{1}{{\log }_{4}n}+\dots \dots +\frac{1}{{\log }_{100}n}$

If $A=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \end{array}\right]$ then $A{A}^T$ is equal to: (where $A^T$ is the transpose of $A)$

Consider the following statements:1. If $y=\ln (\sec x+\tan x)$, then $\frac{dy}{dx}=\sec x$.2. If $y=\ln (\mathrm{cosec}x-\cot x)$, then $\frac{dy}{dx}=\mathrm{cosec}x$.Which of the above is / are correct?

Cards numbered from $107$ to $1006$ are put in a bag. A card is drawn from it at random. Find the probability that the number on the card is not divisible both by $11$ and $37$?

Direction: Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer:On a recent journey Aman drove from City A to city B to city C. His average speed for the whole journey was 60 km/hr. Find the average speed on his journey from city B to city C.Statement I:  Average speed during the journey from city A to city B is 48 km/hr Statement II: Total time taken for the entire journey is 3 hours Statement III: Ratio of distance travelled while going from A to B and B to C is 2 : 3

Find the area of the curve $y=4x^3$ between the end points $x=[-2,3]$

Direction: Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer:How much profit did the company earn in the year 2002?Statement I: The company earned 40% more profit in the year 2003 than that in the year 2001.Statement  II: The company earned a total profit of Rs. 20 crores in the years 2001 and 2002 taken together.Statement III: In the year 2003, the company earned 80% of the profit earned in 2002.

If ${\sec }^2\theta +{\tan }^2\theta =3$ then find the value of $\cot \theta$.

Find the approximate value of $f(3.01)$, where $f(x)=3x^2+3$.

General solution of $(x^2+y^2)dx-2xydy=0$ is:

If the radius of a sphere is measured as 6 m with an error of 0.02 m, then find the approximate error in calculating its surface area.