List of top Mathematics Questions

The value of $\:sin^{-1}\left(cos\left(\frac{33\pi }{5}\right)\right)$

A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in litres that can be stored in the tank.

milk tank

The area of a trapezium is 34 cm2 and the length of one of the parallel sides is 10 cm and its height is 4 cm. Find the length of the other parallel side.

area of a trapezium is 34 cm2

Twenty-seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S'. Find the
(i) radius r' of the new sphere,
(ii) ratio of S and S'

The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area.

A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.

If \(e^y(x+1)=1\),show that \(\frac{d^2y}{dx^2}=(\frac{dy}{dx})^2\)

Find the values of k for which the line (k – 3) x – (4 – k²) y + k² – 7k + 6 = 0 is
(a) Parallel to the x-axis
(b) Parallel to the y-axis
(c) Passing through the origin

Solve the given inequality for real x: 3x-7 > 5x-1

Given the line(s) of symmetry, find the other hole(s):

Given the line(s) of symmetry

The locus of $z$ such that $arg [(1 - 2i) z - 2 + 5i] = \frac {\pi} {4} $ is a

If \(A=\begin{bmatrix}1&0&2\\ 0&2&1\\ 2&0&3\end{bmatrix}\), prove that \(A^3-6A^2+7A+2I=0\)

y = 2 x^{3} - 2 x^{2} + 3 x - 5

x = 2

Δ x = 0.1

Δ y

Let \tan α = \frac{a}{a + 1} and \tan β = \frac{1}{2 a + 1} then α + β is

f A + B + C =,

\tan (\frac{A}{2}) \tan (\frac{B}{2}) + \tan (\frac{B}{2}) \tan (\frac{C}{2}) + \tan (\frac{C}{2}) \tan (\frac{A}{2})

The derivative of f(tan x) w.r.t. g(sec x) at x = π/4 where f`(1) = 2 and g`(√2) =4, is

The general solution of the differential equation

\log_{e} (\frac{d y}{d x}) = x + y

The approximate value of 5√33 correct to 4 decimal places is

A suitcase with measures 80 cm x 48 cm x 24 cm is to be covered with a tarpaulin cloth. How many metres of tarpaulin of width 96 cm is required to cover 100 such suitcases.

Three coins are tossed once. Find the probability of getting
(i) 3 heads (ii) 2 heads (iii) at least 2 heads
(iv) at most 2 heads (v) no head (vi) 3 tails
(vii) exactly two tails (viii) no tail (ix) at most two tails

Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.

The following table shows the ages of tha year:

Age (in years)	5 - 15	15 - 25	25 - 35	35 - 45	45 - 55	55 - 65
Number of patients	6	11	21	23	14	5

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

If mean =. (3 median - mode) fc, then the value of k is

\(If (\frac{(1+i}{1-i})^m=1, \text{then find the least positive integral value of m.}\)

AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠ BAD = ∠ ABE and ∠ EPA = ∠ DPB (see Fig). Show that

(i) ∆ DAP ≅ ∆ EBP

(ii) AD = BE

AB is a line segment and P is its mid-point. D and E