List of top Mathematics Questions asked in KEAM

The nearest point on the line $x + y - 3 = 0$ from the point $(3, -2)$ is:

The points $(-1, 0)$ and $(-2, 1)$ are the two extremities of a diagonal of a parallelogram. If $(-6, 5)$ is the third vertex, then the fourth vertex of the parallelogram is:

If $\tan^{-1} x + \tan^{-1} y = \frac{2\pi}{3}$, then the value of $\cot^{-1} x + \cot^{-1} y$ is equal to:

If $\tan A - \tan B = x$ and $\cot B - \cot A = y$, then the expression for $\cot(A - B)$ is:

The value of \( x \) satisfying the equation \( \tan^{-1} x + \tan^{-1} \left(\frac{2}{3}\right) = \tan^{-1} \left(\frac{7}{4}\right) \) is:

If the orthocenter, centroid, incenter and circumcentre coincide in a triangle $ABC$, and if the length of side $AB$ is $\sqrt{75}$ units, then the length of the altitude of the triangle through the vertex $A$ is:

If $A(2, 4)$ and $B(6, 10)$ are two fixed points and if a point $P$ moves so that $\angle APB$ is always a right angle, then the locus of $P$ is:

If \( \tan \theta = \frac{1}{2} \) and \( \tan \phi = \frac{1}{3} \), then the value of \( \tan(2\theta + \phi) \) is:

If \( \sin x + \cos x = \sqrt{2} \), then the value of \( \sin x \cos x \) is equal to:

The value of \( \frac{\sqrt{3}}{\sin 15^\circ} - \frac{1}{\cos 15^\circ} \) is equal to:

The value of \( \sin^2 \frac{\pi}{8} + \sin^2 \frac{3\pi}{8} + \sin^2 \frac{5\pi}{8} + \sin^2 \frac{7\pi}{8} \) is equal to:

If \( p : 3 \) is a prime number and \( q : \text{one plus one is three} \), then the compound statement “It is not that 3 is a prime number or it is not that one plus one is three” is:

Let \( A = \begin{bmatrix} 1 & \frac{-1-i\sqrt{3}}{2} \\ \frac{-1+i\sqrt{3}}{2} & 1 \end{bmatrix} \). Then \( A^{100} \) is equal to:

The least integer satisfying \( \frac{396}{10} - \frac{19-x}{10}<\frac{376}{10} - \frac{19-9x}{10} \) is:

If \( |x-1| + |x-3| \leq 8 \), then the values of \( x \) lie in the interval:

Let \( p : 57 \) is an odd prime number,
\( q : 4 \) is a divisor of 12,
\( r : 15 \) is the LCM of 3 and 5 be three simple logical statements.
Which one of the following is true?

Let \( p, q, r \) be three simple statements. Then \( \sim(p \lor q) \lor \sim(p \lor r) \equiv \)

If \( A = \begin{vmatrix} 8 & 27 & 125 \\ 2 & 3 & 5 \\ 1 & 1 & 1 \end{vmatrix} \), then the value of \( A^2 \) is equal to:

If \( A = \begin{bmatrix} x & 1 & -x \\ 0 & 1 & -1 \\ x & 0 & 7 \end{bmatrix} \) and \( \det(A) = \begin{vmatrix} 3 & 0 & 1 \\ 2 & -1 & 2 \\ 0 & 0 & 3 \end{vmatrix} \), then the value of \( x \) is:

The coefficient of \( x^2 \) in the expansion of the determinant \( \begin{vmatrix} x^2 & x^3+1 & x^5+2 \\ x^3+3 & x^2+x & x^3+x^4 \\ x+4 & x^3+x^5 & 2^3 \end{vmatrix} \) is:

If \( \begin{bmatrix} 1 & x & 1 \end{bmatrix} \begin{bmatrix} 1 & 3 & 2 \\ 0 & 5 & 1 \\ 0 & 2 & 0 \end{bmatrix} \begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix} = 0 \), then the values of \( x \) are:

The equation of the tangent to the curve $y = x^3 - 6x + 5$ at $(2,1)$ is

If a and ??are the roots of 4x2 + 2x + 1 = 0, then ??=

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

The equation of the plane which bisects the line segment joining the points $(3, 2, 6)$ and $(5,4, 8)$ and is perpendicular to the same line segment, is