List of top Mathematics Questions asked in KEAM

The angle subtended at the point $(1, 2, 3)$ by the points $P(2, 4, 5)$ and $Q(3, 3, 1)$, is:

If the line $\frac{x+1}{2} = \frac{y+1}{3} = \frac{z+1}{4}$ meets the plane $x + 2y + 3z = 14$ at $P$, then the distance between $P$ and the origin is:

The equation of the plane passing through $(-1, 5, -7)$ and parallel to the plane $2x - 5y + 7z + 11 = 0$, is:

If $\vec{a} \cdot \vec{b} = 0$ and $\vec{a} + \vec{b}$ makes an angle of $60^\circ$ with $\vec{b}$, then $|\vec{a}|$ is equal to:

If $\vec{a} + \vec{b}$ and $\vec{a} - \vec{b}$ are perpendicular and $\vec{b} = 3\hat{i} - 4\hat{j} + 2\hat{k}$, then $|\vec{a}|$ is equal to:

The straight line $\vec{r} = (\hat{i} + \hat{j} + \hat{k}) + \alpha(2\hat{i} - \hat{j} + 4\hat{k})$ meets the $xy$-plane at the point:

If $\vec{a} = 2\hat{i} - \hat{j} - m\hat{k}$ and $\vec{b} = \frac{4}{7}\hat{i} - \frac{2}{7}\hat{j} + 2\hat{k}$ are collinear, then the value of $m$ is equal to:

Let $\vec{a} = 2\hat{i} + 5\hat{j} - 7\hat{k}$ and $\vec{b} = \hat{i} + 3\hat{j} + 5\hat{k}$. Then $(3\vec{a} - 5\vec{b}) \cdot (4\vec{a} \times 5\vec{b}) =$

If $\vec{a} + 2\vec{b} - \vec{c} = \vec{0}$ and $\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a} = \lambda \, \vec{a} \times \vec{b}$, then the value of $\lambda$ is equal to:

The direction cosines of the straight line given by the planes $x=0$ and $z=0$ are:

If the eccentricity of the ellipse \( ax^2 + 4y^2 = 4a \, (a<4) \) is \( \frac{1}{\sqrt{2}} \), then its semi-minor axis is equal to:

The hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) passes through the point \( (\sqrt{6}, 3) \) and the length of the latus rectum is \( \frac{18}{5} \). Then the length of the transverse axis is equal to:

The angle between \( \vec{a} \) and \( \vec{b} \) is \( \frac{5\pi}{6} \) and the projection of \( \vec{a} \) on \( \vec{b} \) is \( \frac{-9}{\sqrt{3}} \), then \( |\vec{a}| \) is equal to:

Let \( P \) be a point on an ellipse at a distance of \( 8 \) units from a focus. If the eccentricity is \( \frac{4}{5} \), then the distance of the point \( P \) from the directrix is:

If $(-3, 0)$ is the vertex and y-axis is the directrix of a parabola, then its focus is at the point:

The foci of the ellipse $4x^2 + 9y^2 = 1$ are:

The directrix of a parabola is $x + 8 = 0$ and its focus is at $(4, 3)$. Then the length of the latus-rectum of the parabola is:

If the area of the circle $4x^2 + 4y^2 + 8x - 16y + \lambda = 0$ is $9\pi$ sq. units, then the value of $\lambda$ is:

The radius of the circle passing through the points $(2,3)$, $(2,7)$ and $(5,3)$ is:

If a diameter of the circle $x^2 + y^2 - 2x - 6y + 6 = 0$ is a chord of another circle $C$ having centre $(2, 1)$, then the radius of the circle $C$ is:

In the family of concentric circles $2(x^2 + y^2) = k$, the radius of the circle passing through $(1, 1)$ is:

The image of the origin with respect to the line $4x + 3y = 25$ is:

The slope of the straight line \( \frac{x}{10} - \frac{y}{4} = 3 \) is:

If y-intercept of the line $4x - ay = 8$ is thrice its x-intercept, then the value of $a$ is equal to:

The equation of one of the straight lines passing through the point \( (0, 1) \) and is at a distance of \( \frac{3}{5} \) units from the origin is: