List of top Mathematics Questions

In a triangle \( ABC \), with usual notation, if \[ \frac{b + c}{11} = \frac{c + a}{12} = \frac{a + b}{13} \] then the ratio \( \cos A : \cos B : \cos C \) is:
Smallest angle of a triangle whose sides are \( 6 + \sqrt{12}, \sqrt{48}, \sqrt{54} \) is:
The ratio of areas bounded by curves \( y = \cos x \) and \( y = 0 \) between \( x = 0 \) to \( x = \frac{\pi}{3} \) and \( x = \frac{\pi}{3} \) to \( x = \frac{2\pi}{3} \), with the x-axis is:
A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained.

In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

Number of heartbeats per minute50-5253-5556-5859-6162-64
Number of boxs1511013511525

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

Two finite sets have m and n elements respectively. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are
If A.M. and G.M. of roots of a quadratic equation are 5 and 4 respectively, then the quadratic equation is
The enrolment in a school during six consecutive years was as follows:
1555, 1670, 1750, 2013, 2540, 2820
Find the mean enrolment of the school for this period.
The maximum volume of the right circular cone with slant height 6 units is
Verify the following:
(a) 18 × [ 7 + (–3)] = [18 × 7] + [18 × (–3)]
(b) (–21) × [(– 4) + (– 6)] = [(–21) × (– 4)] + [(–21) × (– 6)]
Let $(gof)(x) = sin x$ and $(fog)(x) = (sin \sqrt x)^2,$ Then

If area of triangle is 35 square units with vertices(2,−6), (5,4),and (k,4).Then k is

Standard deviation of the numbers 31, 32, 33, ... , 46, 47 is
Soln of \(sinx + sin 5x= sin3x\) in \((0,\frac{x}{2})\) are?

\( f(x) = 2x - 3 \quad \text{and} \quad g(x) = x^3 + 5 \), then find \( [f \circ g]^{-1}(-9) = ? \)

Find the approximate value of (25.2)1/2.

Find the differentiation of \(cot^{-1}\frac{3+4tan\,x}{4-3tan\,x}\)
If \(A=\begin{vmatrix}x&1\\1&x\end{vmatrix}\) and \(B=\begin{vmatrix}x &1&1\\1& x&1 \\1&1&x \end{vmatrix}\),then \(\frac{dB}{dx}\) is
Let f : R ⇢ R be defined by $f (x) = x^2 +1$. Then the pre images of 17 and –3 respectively are
If $S_n$ stands for sum to n-terms of a G.P. with ‘a’ as the first term and ‘r’ as the common ratio then $S_n : S_{2n}$ is
If in two circles, arcs of the same length subtend angles 30° and 78° at the centre, then the ratio of their radii is

Five letters are placed at random in five addressed envelopes. The probability that all the letters are not dispatched in the respective right envelopes is

If adj[ \(\begin{bmatrix} 1 & 0 & 2\\ -1 & 1 & -2\\ 0 & 2 & 1 \end{bmatrix}\)=  \(\begin{bmatrix} 5 & m & -2\\ 1 & 1 & 0\\ -2 & -2 & n \end{bmatrix}\) then m+n =

The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

$ \begin{vmatrix} x + 1 & x - 1 \\ x^2 + x + 1 & x^2 - x + 1 \end{vmatrix} $ is equal to: