List of top Mathematics Questions

If \[ [2\vec{p} - 3\vec{q} \ \vec{q} \ \vec{s}] + [3\vec{p} + 2\vec{q} \ \vec{r} \ \vec{s}] = m[\vec{p} \ \vec{r} \ \vec{s}] + n[\vec{q} \ \vec{r} \ \vec{s}] + l[\vec{p} \ \vec{q} \ \vec{s}], \] then the values of \( m, n, l \) respectively are:
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:
A plane passes through the point \( (1, -2, 1) \) and is perpendicular to both the planes \[ 2x - 2y - 2z = 5 \quad \text{and} \quad x - y + 2z = 24 \] Then, the distance of the point \( (1, 2, 2) \) from this plane is:
An ellipse has \( OB \) as the semi-minor axis, and \( S \), \( S' \) as the foci. If \( \angle SBS' \) is a right angle, then the eccentricity \( e \) of the ellipse is:
A box contains 9 tickets numbered from 1 to 9 inclusive. 3 tickets are drawn from the box one at a time. What is the probability that they are alternatively either (odd, even, odd) or (even, odd, even)?
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:
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 =