List of top Questions asked in KEAM- 2026

Which of the following is not the unit of pressure ?

The value of \(\int_0^3 |3x^2 - 3| dx\) is equal to

The area of the region bounded by \(y = \sqrt{x}, y = -x\), and \(x = 4\) (in square units) is

The value of \(\int 16x^3 \log_e x dx\) is equal to

A ladder AB, of length 13m, has one end A on a levelled horizontal ground and the other end B resting against a vertical wall. If the end A begins to slip away from the wall with constant speed 0.25 m/s, and the end B slips down the wall, then the speed of the end B, when B has reached a height of 5m above the ground, is

Let \(f(x) = -x^3 + 9x^2 - \alpha x - 13\), where \(x \in \mathbb{R}\) and \(\alpha\) is a constant. If the function \(f\) is increasing only in the interval (1,5), then the value of \(\alpha\) is equal to

\(\int \frac{\sec x \sqrt{\sec x}}{\sqrt{\sin x} + \sqrt{\cos x}} dx = \)

If \(y = \sin\left(\tan^{-1}\left(\frac{1}{\sqrt{x^2 - 1}}\right)\right), x > 1\), then \(\frac{dy}{dx} =\)

If \(y = \sqrt{x} + 2\cos(\sqrt{x})\), then the value of \(\frac{dy}{dx}\) at \(x = \frac{\pi^2}{4}\) is equal to

If \(f(x) = x - 7, g(x) = 11 - x\), and \(h(x) = f(x)g(x)\), then the maximum value of \(h\) is

If \(s = \sqrt{t + 1}, x = \log s\) and \(y = 6x + 3\), then \(\frac{dy}{dt} =\)

The 10 letters of the word STATISTICS are arranged randomly. The probability that the 10-letter arrangement starts with CAT is

A committee of 4 people is selected from the members of a school council which consists of 5 students, 4 teachers and 3 administrators. The probability that the committee has no teachers is

The events A and B are such that \(P(A)=0.7, P(B')=0.8\) and \(P(A \cup B) = 0.8\). Then \(P(A' \cup B')\) is equal to

The following set of data is given: 72, 72, 74, 80, 82, 82, 86, 88, 92, 92. The mean deviation from the median is

The direction ratios of a straight line \(L_1\) are 2,-1,2 and that of another straight line \(L_2\) are 3,6,-2. Then the angle between \(L_1\) and \(L_2\) is

The projection of \(\vec{b}\) on \(\vec{a}\) is 12. If the angle between \(\vec{a}\) and \(\vec{b}\) is \(60^\circ\), then \(|\vec{b}| =\)

Let \(\vec{a} = 2\hat{i} + 2\hat{j} - 5\hat{k}\) and \(\vec{b} = 2\hat{i} + \hat{j} + \alpha\hat{k}\). If \(|\vec{a} + \vec{b}| = \sqrt{29}\). Then the possible values of \(\alpha\) are

If the equation of the straight line passing through the point \((a,1,3)\) and parallel to the vector \(\frac{2}{3}\hat{i} + \frac{3}{2}\hat{j} + \hat{k}\) is \(\frac{3x+6}{b} = \frac{2y-2}{3} = \frac{z-3}{1}\), then the value of \(a+b\) is equal to

If the position vectors of the points P and Q are, respectively, \(5\vec{a} - 6\vec{b}\) and \(\vec{a} + 2\vec{b}\), then the point R with position vector \(2\vec{a}\) divides the line segment joining P and Q internally in the ratio

The coordinates of the focus of the parabola given by the equation \(4y - x^2 + 4x - 12 = 0\) are

The equation of a circle is \(x^2 + y^2 + 6x - 8y - 24 = 0\). If a chord of the circle subtends an angle of \(60^\circ\) at the centre of the circle, then the length of the chord is

A point C lies on the perpendicular bisector of the straight-line segment joining the points A(-3,-6) and B(13,-6). If the point C lies in the first quadrant and the distance between the point C and the midpoint of AB is 8 units, then the coordinates of C are

If the eccentricity and the length of latus rectum of an ellipse are, respectively, \(\frac{1}{5}\) and \(\frac{48}{5}\), then the length of the major axis of the ellipse is

Let \(|\vec{a}| = 6\) and \(|\vec{b}| = 10\). If \(\vec{a}\) and \(\vec{b}\) make angles \(25^\circ\) and \(85^\circ\), respectively, with the x-axis, then the value of \(|\vec{a} + \vec{b}|\) is equal to