RTU Previous Year Question Papers and Answers

RTU previous year question papers help students understand the exam pattern and important topics for effective preparation. They provide insights into frequently asked questions and the type of answers expected. This guide compiles essential questions and answers from past RTU exams for all subjects, aiding in thorough and focused study.

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RTU Previous Year Question Papers for All Subjects

Mathematics

Question: What is the Laplace transform of e3te^{3t}e3t?

Answer:
The Laplace transform of e3te^{3t}e3t is 1s−3\frac{1}{s-3}s−31​.

Question: Solve the differential equation dydx=3×2\frac{dy}{dx} = 3x^2dxdy​=3x2.

Answer:
Integrating both sides, y=x3+Cy = x^3 + Cy=x3+C, where $C$ is the constant of integration.

Question: Evaluate the integral $\int x\sin xdx$.

Answer:
Using integration by parts, $\int x\sin xdx=-x\cos x+\sin x+C$.

Question: Find the eigenvalues of the matrix [4213]\begin{bmatrix} 4 & 2 \\ 1 & 3 \end{bmatrix}[41​23​].

Answer:
The eigenvalues are 5 and 2.

Question: Expand (1+x)5(1+x)^5(1+x)5 using the Binomial theorem.

Answer:
(1+x)5=1+5x+10×2+10×3+5×4+x5(1+x)^5 = 1 + 5x + 10x^2 + 10x^3 + 5x^4 + x^5(1+x)5=1+5x+10x2+10x3+5x4+x5.

Question: Solve lim⁡x→0sin⁡xx\lim_{x \to 0} \frac{\sin x}{x}limx→0​xsinx​.

Answer:
The limit is 1.

Question: Determine the Taylor series expansion of exe^xex about $x=0$.

Answer:
The expansion is ex=1+x+x22!+x33!+…e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \ldotsex=1+x+2!x2​+3!x3​+….

Question: What is the value of ∫01×2 dx\int_0^1 x^2 \, dx∫01​x2dx?

Answer:
The value is 13\frac{1}{3}31​.

Question: Find the determinant of the matrix [2134]\begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix}[23​14​].

Answer:
The determinant is $2(4)-1(3)=8-3=5$.

Question: State the Mean Value Theorem.

Answer:
If $f(x)$ is continuous on $[a,b]$ and differentiable on $(a,b)$, then there exists $c\in (a,b)$ such that f′(c)=f(b)−f(a)b−af'(c) = \frac{f(b) – f(a)}{b – a}f′(c)=b−af(b)−f(a)​.

Physics

Question: Define Newton’s second law of motion.

Answer:
Newton’s second law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration, $F=ma$.

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: Explain Ohm’s law.

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

Question: What is the speed of light in a vacuum?

Answer:
The speed of light in a vacuum is approximately 3×1083 \times 10^83×108 m/s.

Question: Define the term ‘work’ in physics.

Answer:
Work is done when a force is applied to an object and the object moves in the direction of the force. It is calculated as $W=F\cdot d\cdot \cos \theta$.

Question: What is the unit of frequency?

Answer:
The unit of frequency is Hertz (Hz).

Question: Write 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, m1m_1m1​ and m2m_2m2​ are masses, and $r$ is the distance between them.

Question: Explain the principle of conservation of energy.

Answer:
Energy can neither be created nor destroyed; it can only change from one form to another, but the total energy remains constant.

Question: What is Hooke’s law?

Answer:
Hooke’s law states that the force required to compress or extend a spring is proportional to the displacement, $F=-kx$.

Question: Define acceleration.

Answer:
Acceleration is the rate of change of velocity with respect to time, a=ΔvΔta = \frac{\Delta v}{\Delta t}a=ΔtΔv​.

RTU previous year question papers help students understand the exam pattern and important topics for effective preparation. They provide insights into frequently asked questions and the type of answers expected. This guide compiles essential questions and answers from past RTU exams for all subjects, aiding in thorough and focused study.

---

RTU Previous Year Question Papers for All Subjects

Mathematics

Question: What is the Laplace transform of e3te^{3t}e3t?

Answer:
The Laplace transform of e3te^{3t}e3t is 1s−3\frac{1}{s-3}s−31​.

Question: Solve the differential equation dydx=3×2\frac{dy}{dx} = 3x^2dxdy​=3x2.

Answer:
Integrating both sides, y=x3+Cy = x^3 + Cy=x3+C, where $C$ is the constant of integration.

Question: Evaluate the integral $\int x\sin xdx$.

Answer:
Using integration by parts, $\int x\sin xdx=-x\cos x+\sin x+C$.

Question: Find the eigenvalues of the matrix [4213]\begin{bmatrix} 4 & 2 \\ 1 & 3 \end{bmatrix}[41​23​].

Answer:
The eigenvalues are 5 and 2.

Question: Expand (1+x)5(1+x)^5(1+x)5 using the Binomial theorem.

Answer:
(1+x)5=1+5x+10×2+10×3+5×4+x5(1+x)^5 = 1 + 5x + 10x^2 + 10x^3 + 5x^4 + x^5(1+x)5=1+5x+10x2+10x3+5x4+x5.

Question: Solve lim⁡x→0sin⁡xx\lim_{x \to 0} \frac{\sin x}{x}limx→0​xsinx​.

Answer:
The limit is 1.

Question: Determine the Taylor series expansion of exe^xex about $x=0$.

Answer:
The expansion is ex=1+x+x22!+x33!+…e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \ldotsex=1+x+2!x2​+3!x3​+….

Question: What is the value of ∫01×2 dx\int_0^1 x^2 \, dx∫01​x2dx?

Answer:
The value is 13\frac{1}{3}31​.

Question: Find the determinant of the matrix [2134]\begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix}[23​14​].

Answer:
The determinant is $2(4)-1(3)=8-3=5$.

Question: State the Mean Value Theorem.

Answer:
If $f(x)$ is continuous on $[a,b]$ and differentiable on $(a,b)$, then there exists $c\in (a,b)$ such that f′(c)=f(b)−f(a)b−af'(c) = \frac{f(b) – f(a)}{b – a}f′(c)=b−af(b)−f(a)​.

Physics

Question: Define Newton’s second law of motion.

Answer:
Newton’s second law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration, $F=ma$.

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: Explain Ohm’s law.

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

Question: What is the speed of light in a vacuum?

Answer:
The speed of light in a vacuum is approximately 3×1083 \times 10^83×108 m/s.

Question: Define the term ‘work’ in physics.

Answer:
Work is done when a force is applied to an object and the object moves in the direction of the force. It is calculated as $W=F\cdot d\cdot \cos \theta$.

Question: What is the unit of frequency?

Answer:
The unit of frequency is Hertz (Hz).

Question: Write 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, m1m_1m1​ and m2m_2m2​ are masses, and $r$ is the distance between them.

Question: Explain the principle of conservation of energy.

Answer:
Energy can neither be created nor destroyed; it can only change from one form to another, but the total energy remains constant.

Question: What is Hooke’s law?

Answer:
Hooke’s law states that the force required to compress or extend a spring is proportional to the displacement, $F=-kx$.

Question: Define acceleration.

Answer:
Acceleration is the rate of change of velocity with respect to time, a=ΔvΔta = \frac{\Delta v}{\Delta t}a=ΔtΔv​.

Exploring previous RTU question papers with answers equips students with comprehensive knowledge for exams. Questions from different subjects provide diverse learning, ensuring clear understanding and thorough preparation. With practice, students can approach exams confidently, mastering core concepts.