List of top Mathematics Questions

The Cartesian equation of the plane $\vec{r} = (2\hat{i} - 3\hat{j}) + \lambda(\hat{i} + 2\hat{j} - \hat{k}) + \mu(2\hat{i} + 3\hat{j} + \hat{k})$ is \dots}

In L.P.P., the maximum value of objective function $Z = 6x + 3y$ subject to $x + y \leq 5, x + 2y \geq 4, 4x + y \leq 12, x, y \geq 0$ is \dots

If $\vec{b}$ and $\vec{c}$ are unit vectors and $|\vec{a}| = 7$, $\vec{a} \times (\vec{b} \times \vec{c}) + \vec{b} \times (\vec{c} \times \vec{a}) = \frac{1}{2} \vec{a}$, then angle between the vectors $\vec{a}$ and $\vec{c}$ and angle between the vectors $\vec{b}$ and $\vec{c}$ are respectively \dots
Note: The original question text displayed $\frac{1}{3}\vec{a}$, which is a known OCR/print typo in this standard exam question format. The correct standard value is $\frac{1}{2}\vec{a}$ to yield standard angular options.

The circumradius of a triangle whose sides are 10 units, 8 units and 6 units is ______.

The angle $\theta$, at which the curves $y = 3^x$ and $y = 7^x$ intersect, is given by ______.

If $\theta$ is an obtuse angle between vectors $\vec{a}$ and $\vec{b}$ such that $|\vec{a}| = 5, |\vec{b}| = 3$ and $|\vec{a} \times \vec{b}| = 5\sqrt{5}$ then $\vec{a} \cdot \vec{b} = \dots$

$\cos^4(\pi/8) + \cos^4(3\pi/8) + \cos^4(5\pi/8) + \cos^4(7\pi/8) = \dots$

The equation of the curve passing through origin and satisfying $(1 + x^2) \frac{dy}{dx} + 2xy = 4x^2$ is ______.

$\int_{\pi/4}^{\pi/2} 2\sin^{-4} x dx = \_\_\_\_\_\_.$
Note: The initial OCR showed "$23.4 \frac{/2}{/4}$". The "4" was a misread coefficient. The mathematical evaluation of the options indicates a coefficient of 2 is present in the intended question.

The eccentricity of the hyperbola which passes through the points $(3, 0)$ and $(3\sqrt{2}, 2)$ is \dots

$\int \frac{dx}{(x + a)^{9/7} (x - b)^{5/7}}$ = ______.

The length of the perpendicular drawn from the origin on the normal to the curve $x^2 + 2xy - 3y^2 = 0$ at the point $(2, 2)$ is ______.

If the vectors $\vec{a} = c (\log_7 x) \hat{i} + 2\hat{j} + 3\hat{k}$ and $\vec{b} = (\log_7 x) \hat{i} + 3c (\log_7 x) \hat{j} - 4\hat{k}$ make obtuse angle for any x > 0, then c belongs to ______.

$\int \frac{x^4 \cos(\tan^{-1} x^5)}{1 + x^{10}} dx$ equals ______.

If the lines $x = ay - 1 = z - 2$ and $x = 3y - 2 = bz - 2$ ($ab \neq 0$) are coplanar, then \dots

If $p \equiv$ The switch $S_1$ is closed, $q \equiv$ The switch $S_2$ is closed, $r \equiv$ switch $S_3$ is closed, then symbolic form of the switching circuit is equivalent to \dots

If $y = \tan^{-1} \left[ \frac{12x - 64x^3}{1 - 48x^2} \right]$, then $dy/dx = \dots$

Let $\vec{a} = \hat{i} + \hat{j} - \hat{k}$ and $\vec{c} = 5\hat{i} - 3\hat{j} + 2\hat{k}$ and if $\vec{b} \times \vec{c} = \vec{a}$ then $|\vec{b}|$ = ______.

There are 11 points in a plane of which 5 points are collinear. Then the total number of distinct quadrilaterals with vertices at these points is ______.

If a circle with centre at $(-1, 1)$ touches the line $x + 2y + 4 = 0$, then the coordinates of the point of contact are \dots

The common principal solution of the equations $\sin \theta = -1/2$ and $\tan \theta = 1/\sqrt{3}$ is \dots}

$\lim_{x \to 0} \frac{63^x - 9^x - 7^x + 1}{\sqrt{2} - \sqrt{1 + \cos x}} = \dots$

A player tosses two coins. He wins ₹10 if 2 heads appear, ₹5 if one head appears, and ₹2 if no head appears. Then variance of winning amount is ______.

Consider the probability distribution:

Then the value of $P(X > 2)$ is ______.

With usual notations in $\triangle ABC$, if $\angle B = \pi/2$, and $\tan A, \tan C$ are roots of equation $px^2 + qx + r = 0, p \neq 0$, then ______.