AKTU Question Paper with Detailed Answers

AKTU exams are crucial for students pursuing engineering and other courses under the university. Preparing for these exams requires an understanding of the questions and their types. In this guide, you’ll find a wide range of questions and answers for various subjects to help students ace their exams.

Subject 1: Mathematics

Question: What is the solution to the equation $2x+3=11$?

Answer: The solution to the equation is $x=4$.

Question: What is the derivative of f(x)=x2f(x) = x^2f(x)=x2?

Answer: The derivative of f(x)=x2f(x) = x^2f(x)=x2 is $2x$.

Question: What is the area of a circle with radius 5?

Answer: The area of the circle is $25\pi$ square units.

Question: What is the formula for the volume of a sphere?

Answer: The volume of a sphere is 43πr3\frac{4}{3}\pi r^334​πr3.

Question: How do you solve a quadratic equation using the quadratic formula?

Answer: The quadratic formula is x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}x=2a−b±b2−4ac​​.

Question: What is the integral of x3x^3x3?

Answer: The integral of x3x^3x3 is x44+C\frac{x^4}{4} + C4x4​+C.

Question: What is the difference between a scalar and a vector?

Answer: A scalar has only magnitude, while a vector has both magnitude and direction.

Question: What is the Pythagorean theorem?

Answer: The Pythagorean theorem states that in a right-angled triangle, a2+b2=c2a^2 + b^2 = c^2a2+b2=c2, where $c$ is the hypotenuse.

Question: What is the derivative of $\sin x$?

Answer: The derivative of $\sin x$ is $\cos x$.

Question: What is the integral of exe^xex?

Answer: The integral of exe^xex is ex+Ce^x + Cex+C.

Question: What is the limit of 1x\frac{1}{x}x1​ as $x$ approaches 0?

Answer: The limit is undefined, as 1x\frac{1}{x}x1​ tends to infinity as $x$ approaches 0.

Question: What is the equation of a line in slope-intercept form?

Answer: The equation of a line is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.

Question: What is the chain rule in calculus?

Answer: The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Question: What is the distance formula in a 2D plane?

Answer: The distance formula is d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​.

Question: What is the power rule for derivatives?

Answer: The power rule states that the derivative of xnx^nxn is nxn−1nx^{n-1}nxn−1.

Question: What is the sum of the first $n$ natural numbers?

Answer: The sum of the first $n$ natural numbers is n(n+1)2\frac{n(n+1)}{2}2n(n+1)​.

Question: What is the binomial theorem?

Answer: The binomial theorem states that (a+b)n=∑k=0n(nk)an−kbk(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k(a+b)n=∑k=0n​(kn​)an−kbk.

Question: What is the second derivative test?

Answer: The second derivative test helps to determine whether a critical point is a local maximum, local minimum, or a point of inflection.

Question: What is a matrix?

Answer: A matrix is a rectangular array of numbers arranged in rows and columns.

Question: What is the inverse of a matrix?

Answer: The inverse of a matrix is another matrix such that when multiplied by the original matrix, it gives the identity matrix.

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Subject 2: Physics

Question: What is Newton’s second law of motion?

Answer: Newton’s second law states that force is equal to mass times acceleration, $F=ma$.

Question: What is the law of conservation of energy?

Answer: The law of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another.

Question: What is the difference between speed and velocity?

Answer: Speed is a scalar quantity that refers to how fast an object is moving, while velocity is a vector quantity that includes both speed and direction.

Question: What is the formula for gravitational force?

Answer: The gravitational force is given by F=Gm1m2r2F = G\frac{m_1 m_2}{r^2}F=Gr2m1​m2​​, where $G$ is the gravitational constant.

Question: What is Ohm’s law?

Answer: Ohm’s law states that the current is directly proportional to the voltage and inversely proportional to the resistance, I=VRI = \frac{V}{R}I=RV​.

Question: What is the work-energy theorem?

Answer: The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.

Question: What is the formula for kinetic energy?

Answer: The formula for kinetic energy is KE=12mv2KE = \frac{1}{2}mv^2KE=21​mv2, where $m$ is mass and $v$ is velocity.

Question: What is the formula for potential energy?

Answer: The formula for gravitational potential energy is $PE=mgh$, where $m$ is mass, $g$ is acceleration due to gravity, and $h$ is height.

Question: What is the principle of buoyancy?

Answer: The principle of buoyancy states that an object submerged in a fluid experiences an upward force equal to the weight of the fluid displaced.

Question: What is the first law of thermodynamics?

Answer: The first law of thermodynamics states that energy cannot be created or destroyed, only transformed or transferred.

Question: What is the difference between elastic and inelastic collisions?

Answer: In elastic collisions, both momentum and kinetic energy are conserved, while in inelastic collisions, momentum is conserved, but kinetic energy is not.

Question: What is a capacitor?

Answer: A capacitor is an electrical component used to store energy in an electric field.

Question: What is the formula for Coulomb’s law?

Answer: Coulomb’s law is F=kq1q2r2F = k\frac{q_1 q_2}{r^2}F=kr2q1​q2​​, where $k$ is Coulomb’s constant, q1q_1q1​ and q2q_2q2​ are the charges, and $r$ is the distance between them.

Question: What is the principle of superposition in waves?

Answer: The principle of superposition states that when two or more waves overlap, the resulting wave is the sum of the displacements of the individual waves.

Question: What is the formula for the period of a pendulum?

Answer: The period of a simple pendulum is given by T=2πLgT = 2\pi\sqrt{\frac{L}{g}}T=2πgL​​, where $L$ is the length of the pendulum and $g$ is acceleration due to gravity.

Question: What is the concept of electric field?

Answer: An electric field is a region of space around a charged particle where other charges experience a force.

Question: What is the formula for power in an electric circuit?

Answer: The formula for power is $P=IV$, where $I$ is the current and $V$ is the voltage.

Question: What is the principle of conservation of momentum?

Answer: The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it.

Question: What is the Doppler effect?

Answer: The Doppler effect refers to the change in frequency or wavelength of a wave as the source and observer move relative to each other.

Question: What is the formula for the electric potential energy between two charges?

Answer: The formula is U=kq1q2rU = k\frac{q_1 q_2}{r}U=krq1​q2​​, where q1q_1q1​ and q2q_2q2​ are the charges and $r$ is the distance between them.

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This guide provides essential questions and answers for key subjects like Mathematics and Physics for AKTU exams. Each subject has been covered thoroughly, offering students valuable insights into exam preparation, ensuring a better understanding of concepts and efficient revision methods.