List of top Questions asked in KEAM- 2026

Let O be the origin and let P be a point on the line \(x + \sqrt{3}y = 10\). If OP is perpendicular to the line, then the angle between OP and the y-axis is

Let A(-4,3), B(0,5) and C(-1,2) be three points. The equation of the straight line which passes through C and bisects the straight-line segment AB is

If \(5\pi - 6 \cos^{-1}(\sqrt{3}(2x - 1)) = 0\), then the value of \(x\) is equal to

\(\sin 15^\circ \sin 45^\circ \sin 75^\circ =\)

If \(\sin \theta = \frac{3}{5}\) and \(\cos \theta < 0\), then the value of \(\tan \theta\) is

Let A and P be the area and perimeter of a rectangle respectively. The length and breadth of the rectangle are (x + 2) cm and (x - 2) cm. If \(A \leq 140 cm^2\) and \(P \geq 20 cm\), then the range of possible values of x is

The value of \(\sin(x + \frac{7\pi}{4}) + \sin(x - \frac{7\pi}{4})\) is equal to

If \(\text{cosec } t + \cot t = \frac{5}{2}\), then the value of \(\tan t\) is equal to

The set of all \(x\) satisfying the inequality \(8 + 3x > 4(x - 3) + 2\) is

Let \(A = \begin{bmatrix} 3 & 5\\ -2 & -3 \end{bmatrix}\). If \(BA^2 = A\), where \(B\) is a \(2 \times 2\) matrix, then \(B = \)

Let \(A\) and \(B\) be two square matrices each of order 3. If \(|AB| = 21\) and \(|A^{-1}| = -7\), then the value of \(|B|\) is equal to

If \(^n P_5 = 360360\), then \(^n C_5 = \)

If the homogeneous system of simultaneous equations \(AX=0\) where \(A = \begin{bmatrix} 9 & 2 & k \\ 1 & -1 & -3 \\ k-1 & 1 & 3 \end{bmatrix}\) has a nontrivial solution, then the possible values of \(k\) are

If the coefficient of \(x^4\) in the binomial expansion of \((4x + a)^7\) is -1120, then the value of \(a\) is equal to

In a business meeting, each person shakes hands with each other person once. A person arrives after 5 people have left and he shakes hands only with those present. If the total number of handshakes is exactly 100, then the initial number of people in the party, is

The first and the twentieth terms of a G.P. are 512 and \(\frac{1}{1024}\) respectively. Then the common ratio is

If \(k\), 6 and \(k+5\) are the first three terms of a geometric series, then the possible values of the common ratio are

The number of 3-digit numbers greater than 500, that can be formed using the digits 3, 4, 5, and 7, with repetition, is

In a complex plane, if two vertices of an equilateral triangle are at \(-3(1+i)\) and \(3(1-i)\), then the area of the triangle (in sq.units) is equal to

If \(z |z| = 24 + 7i\), where \(z\) is a complex number, then the value of \(|z|\) is equal to

A geometric series has common ratio \(\frac{1}{3}\). If the sum of first four terms is 200, then the first term is

The sum of the second and third terms of a G.P. is 8 and the fourth term is 4. The common ratio \(r \neq 1\) is

Let \(z = \frac{a - \frac{i}{2}}{i - 2}\), where \(a\) is a real number and \(i = \sqrt{-1}\). If \(\text{Im}(z) = 0\), then the value of \(a\) is equal to

Let \(f : [-\frac{\pi}{2}, \frac{\pi}{2}] \rightarrow (-\infty, \infty)\) be given by \(f(x) = \tan(x)\sin(x)\). Then \(f(x)\) is

Let A and B denote the sets of students in a school who play cricket and football respectively. If \(n(A) = 45, n(B) = 35\) and \(n(A \cap B) = 13\), then \(n((A \cap B)' \cap (A \cup B))\) =