List of top Mathematics Questions

The numerically greatest term in the expansion of (3x - 16y)15 when x = 2⁄3 and y = 3⁄2 is ?

The vertical angle of a right circular cone is \( 60^\circ \). If water is being poured into the cone at the rate of \( \frac{1}{\sqrt{3}} \) m\(^3\)/min, then the rate (m/min) at which the radius of the water level is increasing when the height of the water level is 3m is:

If 3 dice are thrown, the probability of getting 10 as the sum of the three numbers on the top faces is ?

If \(\vec{a},\,\vec{b},\,\vec{c}\) are non-coplanar vectors. If the three points \[ \lambda \vec{a} - 2\vec{b} + \vec{c},\quad 2 \vec{a} + \lambda\vec{b} - 2\vec{c},\quad 4\vec{a} + 7\vec{b} - 8\vec{c} \] are collinear, then \(\lambda = \,?\)
If \(\vec{a},\vec{b}\) are two vectors such that \(\lvert \vec{a}\rvert =3,\;\lvert \vec{b}\rvert =4,\;\lvert \vec{a}+\vec{b}\rvert =\sqrt{37},\;\lvert \vec{a}-\vec{b}\rvert = k,\) and the angle between \(\vec{a}\) and \(\vec{b}\) is \(\theta,\) then \(\frac{4}{13}\,(k \sin \theta)^2 =\,?\)
\(\vec{r}\) is a vector perpendicular to the plane determined by \(\vec{r_1}=2\mathbf{i}-\mathbf{j}\) and \(\vec{r_2}=\mathbf{j}+2\mathbf{k}\). If the magnitude of the projection of \(\vec{r}\) on the vector \(2\mathbf{i}+\mathbf{j}+2\mathbf{k}\) is 1, then \(\lvert \vec{r}\rvert =\,?\)
If \( \vec{b} = \mathbf{i}-\mathbf{j} +2\mathbf{k},\;\vec{c} = \mathbf{i} +2\mathbf{j} -\mathbf{k} \) are two vectors and \( \vec{a} \) is a vector such that \( \cos\angle(\vec{a},\vec{b}\times \vec{c}) = \frac{2}{\sqrt{3}} \). If \( \vec{a} \) is a unit vector, then \( \lvert \vec{a}\times(\vec{b}\times \vec{c})\rvert =\,? \)
A plane \( (\pi) \) passing through the point \( (1,2,-3) \) is perpendicular to the planes \( x + y - z + 4 = 0 \) and \( 2x - y + z + 1 = 0 \). If the equation of the plane \( (\pi) \) is \( ax + by + cz + 1 = 0 \), then \( a^2 + b^2 + c^2 \) is equal to:
If \[ \frac{3x^4 - 2x^2 +1}{(x-2)^4} = A + \frac{B}{x-2} + \frac{C}{(x-2)^2} + \frac{D}{(x-2)^3} + \frac{E}{(x-2)^4}, \] then \(2A + 3B - C - D + E =\;?\)
If \( \theta \) is the acute angle between the curves \( y^2 = x \) and \( x^2 + y^2 = 2 \), then \( \tan \theta \) is:
The slope of one of the pair of lines \(2x^2 + hxy + 6y^2 = 0\) is three times the slope of the other line, \(h = ?\)
Evaluate the limit: \[ \lim_{\theta \to \frac{\pi}{2}} \frac{8\tan^4\theta + 4\tan^2\theta + 5}{(3 - 2\tan\theta)^4} \]
If \(AX = D\) represents the system of linear equations \[ 3x - 4y + 7z + 6=0,\quad 5x + 2y - 4z + 9=0,\quad 8x - 6y - z + 5=0, \] then AX = D ?
The domain of the real valued function: \[ f(x) \;=\; \sqrt[3]{\frac{x \,-\, 2}{2x^2 \,-\, 7x \,+\,5}} \;+\; \log\bigl(x^2 \,-\, x \,-\, 2\bigr). \]
f is a real valued function satisfying the relation \(f\bigl(3x + \tfrac{1}{2x}\bigr) \;=\; 9x^2 + \tfrac{1}{4x^2}\). If \(f\bigl(x + \tfrac{1}{x}\bigr) = 1\) then \(x =\) ?
Define \( f: \mathbb{R} \to \mathbb{R} \) by \[ f(x) = \begin{cases} \frac{1 - \cos 4x}{x^2}, & x < 0 \\ a, & x = 0 \\ \frac{\sqrt{x}}{\sqrt{16 + \sqrt{x}} - 4}, & x > 0 \end{cases} \] Find the value of \( a \) such that \( f \) is continuous at \( x = 0 \).

. If a random variable X has the following probability distribution, then the mean of X is:

X = xiP(X = xi)
12k²
2k
3k²

 

If are the roots of the equation \[ 2x^3 \;-\; 5x^2 \;+\; 4x \;-\; 3 \;=\; 0, \] then \[ \sum \alpha\beta(\alpha+\beta) \;=\;? \]
$$ x^5 + 4x^4 - 13x^3 - 52x^2 + 36x + 144 = 0 $$
If \( y = \frac{\tan x \cos^{-1}x}{\sqrt{1 - x^2}} \), then the value of \( \frac{dy}{dx} \) when \( x = 0 \) is:
If \( y (\cos x)^{\sin x} = (\sin x)^{\sin x} \), then the value of \( \frac{dy}{dx} \) at \( x = \frac{\pi}{4} \) is:
If \( x = \cos 2t + \log (\tan t) \) and \( y = 2t + \cot 2t \), then \( \frac{dy}{dx} \) is:
If \( y = 44x^{45} + 45x^{44} \), then \( y'' \) is:
The approximate value of \( \sqrt[3]{730} \) obtained by the application of derivatives is:
The general solution of the differential equation \[ (9x - 3y + 5) dy = (3x - y + 1) dx. \]