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KEAM 2026 Engineering Question Paper for April 20 is available for download here. CEE Kerala conducted KEAM 2026 Engineering exam on April 20 in session 2 from 2 PM to 5 PM. KEAM 2026 Engineering exam is an online CBT with a total of 150 questions carrying a maximum of 600 marks.
- The KEAM Engineering exam is divided into 3 subjects- Physics (45 questions), Chemistry (30 questions) and Mathematics (75 questions).
- 4 marks are given for every correct answer and 1 mark is deducted for every incorrect answer
Candidates can download KEAM 2026 April 20 Engineering Question Paper with Solution PDF from the links provided below.
KEAM 2026 Engineering April 20 Question Paper with Solution PDF
| KEAM 2026 Engineering Question Paper April 20 | Download PDF | Check Solution |
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Let \(R\) be a relation in \(\mathbb{N}\) defined by \(\{(x,y): x + 3y = 10, x,y \in \mathbb{N}\}\). Then the range of \(R\) is
The domain of \(f(x) = \frac{x^2 + 1}{x^2 + x + 1}\) is
Let \(A\) and \(B\) be two sets of having 3 and 2 elements respectively. Then the number of subsets of \(A \times B\) having at least three elements is
The number of elements in the set \(\{(x,y): 2x^2 + 3y^2 = 35, x,y \in \mathbb{Z}\}\), where \(\mathbb{Z}\) is the set of all integers, is
If \(|z + 4| = 2|z + 1|\), where \(z\) is a complex number then \(|z|\) is equal to
If \(z(3 - i) = 2 + i\), then \(z^2 =\)
The imaginary part of \(\frac{1 - i\sqrt{3}}{1 + i\sqrt{3}}\) is
The sum of \(i^2 + i^4 + \cdots\) upto 25 terms is equal to
In a geometric progression of positive terms, if any term is equal to the sum of the next two terms, then the common ratio of the geometric progression is equal to
A geometric progression has an even number of terms. If the sum of all terms is five times the sum of all odd terms, then the common ratio is equal to
If \(a,b,c\) are three unequal numbers such that \(a,b,c\) are in arithmetic progression and \(b-a, c-b, a-b\) are in geometric progression, then \(a:b:c\) is
If three geometric means are inserted between 2 and 32, then the three numbers are
If \(\frac{{}^nP_{r-1}}{a} = \frac{{}^nP_r}{b} = \frac{{}^nP_{r+1}}{c}\), then
The number of ways in which we can choose a committee from 3 men and 6 women so that the committee includes at least two men and exactly twice as many women as men is
If \(\frac{1}{8!} + \frac{1}{9!} = \frac{x}{12!}\), then the value of \(x\) is equal to
There are two women participants in a badminton tournament. The number of games the men played between themselves exceeds by 12 the number of games they played with women. If each player played one game with each other, then the number of men in the tournament was
If the 17th and 18th term in the expansion of \((2 + x)^{50}\) are equal, then the value of \(x\) is equal to
Let \(f(x) = \begin{vmatrix} x & 1
\sin 2\pi x & 2x^2 \end{vmatrix}\). If \(f(x)\) is an odd function, \(f(-x)=g(x)\) and \(\lambda f(1)g(1)=4\), then the value of \(\lambda\) is equal to
The value of the determinant of the inverse of the matrix \(\begin{bmatrix} -4 & -5
2 & 2 \end{bmatrix}\) is
If \(A=\begin{bmatrix}3 & \lambda-3
-1 & 1\end{bmatrix}\) and \(B=\begin{bmatrix}3 & 2
2 & 1\end{bmatrix}\) and \(AB=\begin{bmatrix}7 & 1
-1 & -1\end{bmatrix}\), then \(\lambda\) is equal to
If \(A=\begin{bmatrix}1 & 1
0 & i\end{bmatrix}\) and \(A^{42}=\begin{bmatrix}a & b
c & d\end{bmatrix}\) then \(a+d\) is equal to
If \((x-1)(x^2 - 5x + 7) < (x-1)\), then \(x\) belongs to
The solution set of \(|x + \frac{1}{x}| > 2\) is
Let \(L\) be an arc of a circle which subtends \(45^\circ\) at the centre. If the radius of circle is \(4\) cm, then the length of \(L\) in centimeter is
If \(A = \begin{bmatrix} 1 & \sin\theta & 1
\sin\theta & 1 & \sin\theta
-1 & -\sin\theta & 1 \end{bmatrix}\), \((0 \leq \theta \leq 2\pi)\), then the minimum value of \(|A|\) is
If \(\tan\left(\frac{\pi}{4} + \theta\right) = \frac{1}{2}\) then the value of \(\sin 2\theta\) is
If \(1 + \cos x = \alpha\), \(0 \leq x \leq \frac{\pi}{2}\), then \(\sin \frac{x}{2}\) is equal to
The value of \(\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right)\) is equal to
The value of \(2\tan^{-1}\left(\frac{1}{3}\right) + \cot^{-1}\left(\frac{3}{4}\right)\) is
If \(\alpha\) and \(\beta\) are respectively the minimum and maximum values of \(\frac{\pi^2}{8} + 2\left(\sin^{-1}x - \frac{\pi}{4}\right)^2\), then \(\frac{\beta}{\alpha}\) is:
If the points \((3,-2)\), \((a,2)\), \((8,8)\) are collinear, then the value of \(a\) is:
If the slope of the line joining the points \((3,4)\) and \((-2,a)\) is equal to \(-\frac{2}{5}\), then the value of \(a\) is:
The distance of the point \(P(1,-3)\) from the line \(2y - 3x = 4\) is:
The line \(x - 1 = 0\) is the directrix of the parabola \(y^2 - kx + 8 = 0\). Then, the values of \(k\) are:
The length of the latus rectum of \(x^2 = -9y\) is equal to:
The centre and radius of the circle \(x^2 + y^2 - 2x + 4y = 8\) respectively are:
If the length of the major axis of an ellipse is thrice the length of the minor axis, then its eccentricity is equal to:
Let \(\vec{a}, \vec{b}, \vec{c}\) be such that if \(\vec{a} + \vec{b} + \vec{c} = 0\). If \(|\vec{a}| = 3, |\vec{b}| = 4, |\vec{c}| = 5\) then \(|\vec{a}\cdot\vec{b} + \vec{b}\cdot\vec{c} + \vec{c}\cdot\vec{a}|\) is:
If \(\theta\) is the angle between two vectors \(\vec{a}\) and \(\vec{b}\) such that \(|\vec{a}| = 7, |\vec{b}| = 1\) and \(|\vec{a}\times\vec{b}|^2 = k^2 - (\vec{a}\cdot\vec{b})^2\) then the value(s) of \(k\) is/are:
If \(O\) is the origin and \(C\) is the midpoint of \(A(-2,1)\) and \(B(4,-3)\), then \(\vec{OC}\) is:
If \(\vec{a} = \hat{i} + \hat{j} + \hat{k}\) and \(\vec{b} = \hat{i} - \hat{j} + \hat{k}\), then the projection of \(\vec{a}\) on \(\vec{b}\) is:
If the lines \(\frac{2x-1}{2} = \frac{3-y}{1} = \frac{z-1}{3}\) and \(\frac{x+3}{2} = \frac{y+2}{5} = \frac{z+1}{a}\) are perpendicular to each other, then the value of \(a\) is:
The equation of straight line passing through \((a,b,c)\) and parallel to x-axis is:
The equation of a line passing through the point \((1,-2,3)\) and equally inclined to the axes are:
The vector equation of the straight line \(\frac{x-2}{3} = \frac{y+1}{2} = \frac{z-3}{2}\) is:
A dice is thrown three times. If the first throw is five, the probability of getting 14 as the sum is:
If the variance of \(1,2,3,\ldots,n\) is 10, then the value of \(n\) is:
If \(P(A)=\frac{1}{4}, P(B)=\frac{1}{5}\) and \(P(A \cap B)=\frac{1}{8}\), then \(P(A' \cup B')\) is:
We have two data sets each of size 5. The variances are 4 and 5 and the corresponding means are 2 and 4 respectively. Then the variance of the combined data set is:
The value of \(\lim_{x \to 5} \left( \frac{25 - x^2}{4 - \sqrt{x^2 - 9}} \right)\) is:
The value of \(\lim_{x \to 0} \frac{\sqrt{1 - \cos 2x}}{|x|}\) is equal to
The positive integer \(n\), such that \(\lim_{x \to 3} \frac{x^n - 3^n}{x - 3} = 108\)
Let \(\lim_{x \to a} f(x)g(x) = 16\) and \(\lim_{x \to a} \frac{f(x)}{g(x)} = 4\). If both \(\lim_{x \to a} f(x)\) and \(\lim_{x \to a} g(x)\) exist, then \(\lim_{x \to a} [f(x)+g(x)]\) is
If \(f(1)=2,\ f'(1)=1\), then \(\lim_{x \to 1} \frac{x f(1) - f(x)}{x-1}\) is
Let \(f(x)\) and \(g(x)\) be twice differentiable functions defined on \([0,2]\) such that \(f''(x) - g''(x) = 0\), \(f'(1)=4,\ g'(1)=2,\ f(2)=9,\ g(2)=3\). At \(x=\frac{3}{2}\), \(f(x)-g(x)\) is
If \(y = \log \sqrt{\frac{x-1}{x+2}}\), then \(\frac{dy}{dx}\) is
If \(y = 3^x + e^x + x^x + x^3\), then \(\frac{dy}{dx}\) at \(x=3\) is equal to
If \(y = \sin x + e^x\), then \(\frac{d^2 x}{dy^2}\) is equal to
If \(y = \log_{10} x + \log_e x\), then \(\frac{dy}{dx}\) is equal to
The function \(f(x) = x^4 - 2x^2\) is strictly increasing on
If the rate of increase of the radius of a circle is \(5\) cm/sec, then the rate of increase of its area when the radius is \(20\) cm, will be
If the function \(f(x) = x^2 + ax + 1\) is increasing on \([1,2]\), then \(a\) is greater than or equal to
The absolute maximum value of the function \(f(x) = x^3 - 3x + 2\) in \([0,2]\) is
If \(\int \left(3t^2\sin\left(\frac{1}{t}\right) - t\cos\left(\frac{1}{t}\right)\right) dt = f(t)\sin\left(\frac{1}{t}\right) + c\) then \(f(2)\) is equal to
If \(\int \frac{2^{1/x}}{x^2} \, dx = k\,2^{1/x} + c\) then \(k\) is equal to
\(\int e^x \left(\frac{1 - \sin x}{1 - \cos x}\right) dx =\)
If \(u = \int e^x \cos x \, dx,\; v = \int e^x \sin x \, dx\), then \(u + v =\)
\(\int \sin^3 x \, e^{\log \cos x} \, dx =\)
If \(\int_a^b x^3 \, dx = 0\) and \(\int_a^b x^2 \, dx = \frac{2}{3}\), then the values of \(a\) and \(b\) respectively are
\(\int_{0}^{\pi/3} \frac{dx}{1 + \sqrt{\tan x}} =\)
The area of the region bounded by the lines, \(y = x + 2\), \(x = 0\), \(x = 1\) and \(y = 0\) is
\(\int_{0}^{\pi/4} \sqrt{1 + \sin 2x}\,dx =\)
The solution of \((e^y + 1)\cos x\,dx + e^y \sin x\,dy = 0\) is
The function \(y = be^x + ae^{-x}\), \(a\) and \(b\) are constants, is a solution of
Which one of the following point is not in a feasible region bounded by the inequalities \(x \leq 4\), \(y \leq 6\), \(x + y \leq 6\), \(x \geq 0\), \(y \geq 0\)
A physical quantity that has the same dimensions as those of Boltzmann constant is
Taking into consideration of significant figures, in the conversion relation \(2.0\ m s^{-2} = X\ km h^{-2}\), the value of \(X\) is
A body starts moving from the origin along a straight line at a speed of \(20\ km h^{-1}\) for \(1\) hour. Then it turns perpendicular to its path and moves with the same velocity for \(30\) minutes. Then the magnitude of its displacement is
If the angular speed of a particle moving in a circular path of radius \(1.2\) m is increased from \(2\ rad s^{-1}\) to \(4\ rad s^{-1}\) keeping its radius constant, then its linear speed is increased by
If the position vector of a particle is \(\vec{r} = 2t\hat{i} + \sqrt{3}t^2\hat{j} + 5\hat{k}\) with \(\vec{r}\) in m and \(t\) in s, then at \(t = 1\)s the angle made by the velocity vector with x-axis is
If the maximum acceleration of a moving platform to keep a box of mass \(5\) kg on it without sliding is \(3\ m s^{-1}\), then the static friction between the box and floor of the platform is (\(g = 10\ m s^{-2}\))
If \(10\) identical silver coins each of mass \(m\) are placed one over the other, then force on the \(6^{th}\) coin from the bottom is
A body initially at rest breaks up into two pieces of masses \(M\) and \(3M\) and move with a total kinetic energy of \(E\), then the kinetic energy of the piece of mass \(M\) is
If a proton, a deuteron and an \(\alpha\)-particle have the same speed, then the kinetic energy is
The moment of inertia of a system of two masses \(2\) kg and \(4\) kg lying in the x-y plane at distances, \(2\) m and \(4\) m, respectively from the origin about the z-axis is (in \(kg m^2\))
A swimmer jumps from a height is able to increase the number of loops made in air by
The ratio of the weights of an object of mass \(m\) at a height \(R\) and \(2R\) from the surface of earth is (\(R\) is the radius of earth)
If the magnitude of gravitational potential energy of an object of mass \(200\) kg at a height of \(3.6 \times 10^6\) m from the earth surface is \(6 \times 10^6\) J then its value at a height of \(5.6 \times 10^6\) m is (Radius of earth is \(6.4 \times 10^6\) m)
The force required to increase the length of a thin copper wire of cross-sectional area \(0.1\ cm^2\) by \(0.1%\) is (Young’s modulus of copper is \(11 \times 10^{10}\ N m^{-2}\))
If a huge tank has a small side hole at a depth of \(2\) m from the surface of water, then the velocity of water flowing through the hole is (\(g = 10\ m s^{-2}\))
Lakes and ponds freeze at the top surface with water below. This phenomenon is due to
If the temperature of \(2\) moles of krypton gas is increased from \(-11^\circ\)C to \(89^\circ\)C at constant volume, then (specific heat at constant volume of krypton is \(C_V\))
If an ideal heat engine with an efficiency of \(40%\) rejects heat at \(27^\circ\)C, then it should have absorbed heat at
Two perfect monoatomic gases at temperatures \(300\) K and \(410\) K are mixed without any loss of heat. If \(10^{24}\) and \(10^{23}\) are the number of molecules in the respective gases, then the temperature of the mixture is
If the temperature \(T\) of oxygen molecule is raised to \(9T\), then its root mean square speed \(v\) is increased to
For a particle executing simple harmonic motion with amplitude \(A\) and time period \(T\) along x-axis, the time taken by the particle to move from \(x = 0\) to \(x = A\) is
With Laplace correction in Newton’s formula for the velocity of sound in gases, the velocity of sound in monoatomic gas at STP is
\(A\), \(B\) and \(C\) are three points in space forming an equilateral triangle of side \(10\) cm. If a point charge \(8\,\mu C\) is placed at \(A\), then the work done in moving a unit charge from \(B\) to \(C\) is
Three capacitors \(A,B,C\) with respective capacitance of \(1\,\mu F\), \(2\,\mu F\) and \(3\,\mu F\) are connected as shown. For a given voltage source \(V\) connected across them, the combination that can store the maximum energy is
The equipotential surface of a system of two point charge \(5\,\mu C\) and \(-5\,\mu C\) at points \(A\) and \(B\) separated by \(80\) cm is a plane perpendicular to the line connecting \(A\) and \(B\) at
If an infinitely long uniformly charged wire produces an electric field of intensity \(E\) at a distance \(d\) from it, then the linear charge density \(\lambda\) of the wire is
The ratio of the rate of flow of electrons through three resistors connected in parallel to a voltage source \(V\) is \(3 : 2 : 1\), then the ratio of their respective resistance values is
The ratio of the heat produced in a \(2\,\Omega\) and a \(4\,\Omega\) resistor connected in series with a voltage source of \(12\) V is
Three cells of \(3\) V, \(4\) V and \(4\) V with respective internal resistances \(0.5\,\Omega\), \(0.75\,\Omega\) and \(0.75\,\Omega\) are connected in series to a resistor of \(4\,\Omega\). Then the current in the circuit is
If a current carrying circular loop is suspended in a uniform magnetic field \(\vec{B}\), then
In a uniform magnetic field \(\vec{B}\), a bar magnet of magnetic moment \(M\) is kept suspended at an angle of \(60^\circ\) with respect to \(\vec{B}\). The work done to turn it from \(60^\circ\) to \(90^\circ\) with respect to the field is
The flow of current of \(2\) A through a straight solenoid of length \(2\) m produces a magnetic field of \(2\pi \times 10^{-4}\) T at its centre. Then the number of turns in the solenoid is
A wire of length \(4\) m carrying a current of \(1\) A is bent to form a circular loop. The magnetic moment of the loop (in A m\(^2\)) is
The plane of a circular loop of area \(150\ cm^2\) is perpendicular to a uniform magnetic field of \(0.5\) T. If the loop is turned such that its plane is in the direction of the field in \(0.5\) s, then the induced emf produced is
Two identical transformers \(A\) and \(B\) each with \(\dfrac{N_p}{N_s} = 2\) are connected such that the secondary output obtained from \(A\) is given as the primary input voltage for \(B\). If the primary ac voltage of \(A\) is \(200\) V, then the secondary voltage from \(B\) is
Microwaves are
An object placed at \(10\) cm in front of a concave mirror of focal length \(8\) cm gives image of magnification of
The magnifying power of a telescope of length \(76\) cm in the normal adjustment is \(75\). Then the focal lengths of the objective and eyepiece lenses are, respectively,
The fringe width obtained in a given Young’s double slit experimental set up for red light, blue light and green light are, respectively, \(\beta_R\), \(\beta_B\) and \(\beta_G\). Then
If the de Broglie wavelength associated with an electron is \(0.1227\) nm, then its accelerating potential is
If a radiation of energy \(5.2\) eV falls on the photosensitive surfaces of Mo and Ni, they emit photoelectrons with maximum kinetic energy of \(0.5\) eV and \(1\) eV, respectively. Then the work function of
If a radioactive parent nucleus \({}^{236}_{94}X\) emits two alpha particles and two \(\beta\) particles successively to reach the daughter nucleus \({}^{a}_{b}Y\), then the values of \(a\) and \(b\) are
The difference in magnitudes of angular momentum of the electrons revolving in \(5^{th}\) Bohr’s orbit and \(3^{rd}\) Bohr’s orbit of hydrogen atom is
Intrinsic semiconductors Ge or Si doped with
Four ideal diodes are connected as shown then the current drawn from the battery is
The empirical formula of a metal oxide which has \(54%\) metal (M) and \(46%\) oxygen (O) is (Atomic mass of M = \(27\) amu and O = \(16\) amu)
The threshold wavelength of a metal is \(6000\ \AA\). The work function of the metal is (\(h = 6.62 \times 10^{-34}\) J s)
The radius of the first orbit of \(\mathrm{He^+}\) is
In Mosley experiment, the X-ray spectrum is obtained by plotting
Which of the following elements have the highest and the lowest first ionization enthalpy?
(i) Be \quad (ii) B \quad (iii) C \quad (iv) N \quad (v) O
The correct increasing order of dipole moment of the following molecules is
The number of bonding pairs and lone pairs of electrons in \(\mathrm{BrF_5}\) molecule are respectively
Which of the following bond has highest mean bond enthalpy?
The correct increasing order of enthalpy of fusion of \(\Delta_{fus}H^\circ\) (in kJ mol\(^{-1}\)) of the following compounds is
The solubility product, \(K_{sp}\) of a sparingly soluble salt, \(\mathrm{AX_2}\), is \(3.2 \times 10^{-14}\) mol\(^3\) lit\(^{-3}\). Its solubility is
Match the correct pH value with the following substances:
(a) Milk of magnesia \quad (i) pH = 6.8
(b) Black coffee \quad (ii) pH = 7.8
(c) Egg white \quad (iii) pH = 5
(d) Milk \quad (iv) pH = 10
The \(\Delta_r G^\circ\) of the galvanic cell in which the following cell reaction takes place, \[ 2\mathrm{Cr(s)} + 3\mathrm{Cd^{2+}(aq)} \rightarrow 2\mathrm{Cr^{3+}(aq)} + 3\mathrm{Cd(s)} \]
is (\(E^\circ_{\mathrm{Cr^{3+}/Cr}} = -0.74\) V and \(E^\circ_{\mathrm{Cd^{2+}/Cd}} = -0.40\) V)
The molar conductivity of a weak monobasic acid, HA at 298 K is \(70\ S cm^2 mol^{-1}\). What is the percentage ionisation of HA at 298 K?
At infinite dilution \(\lambda^\circ_{H^+} = 340\ S cm^2 mol^{-1}\) and \(\lambda^\circ_{A^-} = 80\ S cm^2 mol^{-1}\)
The percentage of helium present in air used by scuba divers is
A first order reaction follows the equation \(k = (4 \times 10^{10}\ s^{-1}) e^{-2000/T}\). The value of \(E_a\) for the reaction is about (\(R = 8.314\ J K^{-1} mol^{-1}\))
In a pseudo first order reaction, the following results were obtained.
\begin{tabular{|c|c|c|c|c|c|c|c|
\hline
Time / s & 0 & 10 & 20 & 30 & 40 & 50 & 60
\hline \([A]\)/mol lit\(^{-1}\) & 0.65 & 0.55 & 0.46 & 0.38 & 0.26 & 0.20 & 0.13
\hline
\end{tabular
Average rate of the reaction between 20 and 40 seconds is
Which of the following compound of manganese is a mixed oxide?
The formula of pentaamminecarbonatocobalt(III) chloride is
The correct increasing order of wavelength of absorption of the following complexes is
(i) \([\mathrm{CoCl(NH_3)_5}]^{2+}\) \quad (ii) \([\mathrm{Co(NH_3)_5(H_2O)}]^{3+}\) \quad (iii) \([\mathrm{Co(NH_3)_6}]^{3+}\) \quad (iv) \([\mathrm{Co(CN)_6}]^{3-}\)
When sodium fusion extract is treated with sodium nitroprusside, the appearance of violet colour is due to the formation of
Which of the following gives 2-methylbutane on hydrogenation?
(i) 2-methylbut-1-ene \quad (ii) 3-methylbut-1-yne \quad (iii) 2-methylbut-2-ene
(iv) 3-methylbut-1-ene \quad (v) pent-2-ene
An alkene, \(\mathrm{C_3H_6}\) (X), on treatment with HBr in presence of peroxide gives (Y). The compound (Y) on treatment with \(\mathrm{AgNO_2}\) in ethanol gives (Z). The compounds (X), (Y) and (Z) are respectively
The reaction \(\mathrm{CH_3Br + AgF \rightarrow CH_3F + AgBr}\) is termed as
When 2-methylbutan-2-ol is treated with Lucas reagent (conc. HCl and \(\mathrm{ZnCl_2}\)) at room temperature, the product obtained is
The relative ease of dehydration of the following alcohols is
(i) Propan-2-ol \quad (ii) Propan-1-ol \quad (iii) 2-Methylpropan-2-ol
Which of the following is a commercial method of manufacture of benzaldehyde?
Vigorous oxidation of n-propylbenzene with alkaline potassium permanganate (\(\mathrm{KMnO_4/KOH/\Delta}\)) followed by hydrolysis gives
The descending order of basic strength of the following amines is
(i) N-Methylbenzenamine \quad (ii) N,N'-Dimethylbenzenamine \quad (iii) Benzenamine \quad (iv) Phenylmethanamine
Benzene diazonium chloride on treatment with HCl in the presence of copper powder gives chlorobenzene. This reaction is termed as
Which of the following statements are true about sucrose?
(i) It is a disaccharide
(ii) It is a reducing sugar
(iii) It is laevorotatory
(iv) Sucrose on hydrolysis gives equimolar mixture of D(+) glucose and D(-)-fructose
(v) In sucrose, two monosaccharides are held together by a glycosidic linkage
KEAM 2026 Exam Pattern
| Particulars | Details |
|---|---|
| Paper | Engineering |
| Mode of Exam | Online CBT |
| Subjects | Physics- 45 questions Chemistry- 30 questions Mathematics- 75 questions |
| Type of Question | Objective Type |
| Total Number of questions | 150 |
| Marks are awarded for each correct answer | 4 marks |
| Marks are awarded for each incorrect answer | 1 marks |
| KEAM total marks for Engineering | 600 marks |
| Duration of KEAM Engineering exam | 3 hours |
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