List of practice Questions

Theory of errors and adjustments deals with minimizing the effects of.

The side of a square land was measured as 150m and is in error by 0.05m. What is the corresponding error in the computed area of the land?

Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): A given vector \(\overrightarrow{F}\) is irrotational i.e.,\(\overrightarrow{\nabla} ×\overrightarrow{F}\) =0.
Reason (R): The vector \(\overrightarrow{F}\) is conservative.
In the light of the above statements, choose the most appropriate answer from the options given below.

What is the value of div \(\overrightarrow r\), if \(\overrightarrow r\) is the position vector of a particle?
\(\left (\overrightarrow r = x\hat i + y\hat j + z\hat k\right)\)

The general form of a central force is represented by \(\overrightarrow F = \frac{C}{r^n}\hat r\) (C = constant) known as Inverse Power law. 
A. The force represented by above equation will be attractive if C < 0.
B. The force represented by above equation will repulsive if C < 0.
C. The force represented by above equation will be repulsive if C > 0.
D. The force represented by above equation will be attractive if C > 0.
Choose the correct answer from the options given below.

There are three planets in circular orbits around a star at a distance a, 9a and 16a respectively. At time t = \(t_0\), the star and the planets are in a straight line. The period of revolution of the closest planet is T. How long after \(t_0\), will they again be in the same line?

What will be the expression for moment of inertia of a rectangular lamina (ABCD having length \(l\) and breadth b) about an axis passing through one of its corners and perpendicular to its plane?

Match List I with List II

Choose the correct answer from the options given below:

Gravitational force between two masses \(m_1\) and \(m_2\) separated by a distance r is
A. central force
B. non-central force
C. attractive force
D. repulsive force
E. directly proportional to the distance between \(m_1\) and \(m_2\)
Choose the correct answer from the options given below.

A bullet of mass 10 g moving horizontally with a speed of 500 m/s passes through a block of wood of mass 1 kg, initially at rest on a frictionless surface. The bullet comes out of the block with a speed of 200 m/s. What is the final speed of the block?

What will be the spring constant of a spring? When it is streched 10 cm, it has potential energy of 5600 J.

Two bodies of different masses are moving with the same kinetic energy. Which one has a greater momentum?

The angular speed of a motor wheel is increased from 1200 r.p.m. to 3120 r.p.m. in 16 s. What is its angular acceleration?

Given below are two statements:
Statement-I In case of bi-prism, the coherent sources are produced by the phenomenon of refraction.
Statement-II: In case of Llyod mirror, coherent sources are produced by the phenomenon of reflection.
In the light of the above statements, choose the correct answer from the options given below.

The dimension for conductivity (c) is.

Let $\lambda \in R$ and let the equation $E$ be $|x|^2-2|x|+|\lambda-3|=0$. Then the largest element in the set $S=$ $\{x+\lambda: x$ is an integer solution of $E\}$ is

The ratio of halflife and average life for a radioactive sample is_____.

An industry has two firms. They face an inverse demand function P=200-4Q and a constant unit cost of Rs.8.0. The Cournot duopoly equilibrium price (P) and Quantity (Q) will be

Suppose that for a random sample of size 10, the value of covariance between two variables X and Y is 100 and the standard deviations of X and Y are 5 and 20 respectively. What is the value of regression coefficient in regression of Y on X?

Daniel Thorner referred to colonial investment in ____ as "private investment at public risk".

A vertical triangular area with vertex downward and attitude 'h' has its baas lying on the free surface of a liquid. The center of pressure below the free surface is at distance of

An article is sold for 16500 which was bought at 18750. Find the loss percent.

Look at the series: 1224, 612, 204, 102, 34,....... Which one of the following numbers should come next in the series?

A text, according to Roland Barten, is a

If $\int_{0}^{1} $ 1/(5+2x-2x²)(1+e^(2-4x)) dx = 1/log_e (α+1/β) a, β>0, then a⁴- β⁴ is equal to