List of practice Questions

A bag contains 10 balls out of which \( k \) are red and \( (10-k) \) are black, where \( 0 \le k \le 10 \). If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 red and 9 black balls is:

For two identical cells each having emf \(E\) and internal resistance \(r\), the current through an external resistor of \(6\,\Omega\) is the same when the cells are connected in series as well as in parallel. The value of the internal resistance \(r\) is ________ \(\Omega\).

For three unit vectors \( \vec a, \vec b, \vec c \) satisfying \[ |\vec a-\vec b|^2 + |\vec b-\vec c|^2 + |\vec c-\vec a|^2 = 9 \] and \[ |2\vec a + k\vec b + k\vec c| = 3, \] the positive value of \( k \) is:

Polyester fibre is manufactured by the process of:

The twist per inch (TPI) of a yarn primarily affects its:

Which fibre has the highest moisture regain under standard atmospheric conditions?

In plain weave fabric, the repeat size is:

The strength of a yarn is commonly expressed in terms of:

The main purpose of scouring in cotton processing is to remove:

Which spinning system produces yarn directly from sliver without roving?

The instrument commonly used for measuring horizontal and vertical angles in mines is:

Which one of the following is the most widely used method for coal extraction in surface mines?

In bord and pillar mining, the main load-bearing elements are:

Which gas is mainly responsible for explosions in coal mines?

The machine used for drilling blast holes in hard rock mines is:

The general solution of $\displaystyle \frac{dy}{dx} = y$ is:

If a function is analytic in a domain, then it is necessarily:

If two events $A$ and $B$ are independent, then:

Which method is commonly used to find roots of nonlinear equations?

The primary purpose of mine ventilation is to:

The Mohr–Coulomb failure criterion is mainly used to describe:

The Laplace transform of a unit step function \( u(t) \) is:

In amplitude modulation, the modulation index should be:

Let $A$ be a square matrix. If $A^2 = A$, then the matrix $A$ is called: