List of practice Questions

An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point P facing east.
The ant first turns 72º anticlockwise at P, and then does the following two steps in sequence exactly FIVE times before halting. 1. Moves forward by 10 cm.
2. Turns 144º clockwise.
The pattern made by the trace left behind by the ant is:

There are 5 bags and 7 books. The books need to be distributed in the bags and any bag can get any number of books. In how many ways can these books be distributed so that 2 nd and 6th book are not put in the same bag and no bag is empty?

(112 × 5⁴) = ?

Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

Which one of the following is not a prime number?

Evaluate: $(112 \times 5^4)= ?$

A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be

The number of functions f, from the set
$A = {x∈N: x^2-10x+9≤0} $to the set $B = {n62:n∈N}$
such that
$f(x)≤(x-3)^2+1$, for every $x∈A,$
is ______.

Both the numerator and the denominator of $ \frac{3}{4} $ are increased by a positive integer, $ x $, and those of $ \frac{15}{17} $ are decreased by the same integer. This operation results in the same value for both the fractions. What is the value of $ x $?

If $ x : y : z = \frac{1}{2} : \frac{1}{3} : \frac{1}{4} $, what is the value of $ \frac{x + z - y}{y} $?

Let the minimum value v₀ of
v = |z|²+|z-3|²+|z-6i|²,z∈C
is attained at z = z₀. Then
$|2z^2_0-\overline{z}^3_0+3|^2+v^2_0$
is equal to

The movie was funny and I _________.

A double-acting hydraulic cylinder has bore and rod diameters of 76 mm and 25 mm, respectively. In extension as well as retraction strokes of the cylinder, the oil flow rate to the cylinder from the pump is 40 L min$^{-1}$. The velocity of the piston during retraction stroke in m s$^{-1}$ is _____. $\textit{[Round off to two decimal places.]}$

A single cylinder four-stroke diesel engine has an engine displacement volume of 9 L, the engine rotates at 2400 rpm and its volumetric efficiency is 88%. The actual air inducted into the cylinder in m$^3$ s$^{-1}$ is _____.

The root of the equation $ \sin x - 4x + 1 = 0 $ after its first iteration, using the Newton-Raphson method with an initial guess of $ x_0 = 0.2 $, is _____.$ \textit{[Round off to three decimal places.]}$

The slope of the function $ f(x) = 2x^4 - 3x^2 + 5x $ at $ x = 2 $ is _____. $\textit{[Answer in integer.]}$

Water from a confined aquifer having transmissivity of 1000 m$^2$ day$^{-1}$ is pumped through a fully penetrating well of 300 mm diameter at a rate of 1200 m$^3$ day$^{-1}$. If the radius of influence is 400 m, the drawdown in the well under steady-state flow condition in meter is _____.

The flow rate per unit width of a wide rectangular clean-earth channel is 20 m³ s⁻¹ m⁻¹. The calculated critical flow depth in meter will be _____. $\textit{[Round off to two decimal places]}$

A stream of 200 L s$^{-1}$ is diverted from a canal to irrigate a wheat field in 8 hours. If the runoff from the field is 500 m$^3$ and the conveyance efficiency is 75%, the application efficiency in percent is _____.

In a triple effect feed forward evaporator, pineapple juice is entering at the rate of 6.3 kg s$^{-1}$ and leaving the last effect as 50% concentrate. The system is using saturated steam of 2.48 kg s$^{-1}$ at 121.1°C. If vapour transferred from the first to the second effect, second to third effect and third to ambient are 5675, 6053 and 6416 kg h$^{-1}$, respectively, the steam economy of the evaporator is _____. $\textit{[Round off to two decimal places]}$

If an osmo-dehydrated fruit slice has 72% moisture content on wet basis, the moisture content of the same fruit slice on dry basis in percent is _____. $\textit{[Round off to one decimal place]}$

If the specific heat capacity ($c_p$) of solids in potato is 837.36 J kg⁻¹ K⁻¹, then the specific heat capacity of potatoes in J kg⁻¹ K⁻¹ with 85% moisture content (wet basis) is _____. $\textit{[Round off to two decimal places]}$

The matrix \[ \begin{bmatrix} 3 - x & 2 & 2 \\ 2 & 4 - x & 1 \\ -2 & -4 & -1 - x \end{bmatrix} \] is singular for the following values of $x$.

Work done by a moving particle in the force field $ \mathbf{F} = 6x^2 \hat{i} + (3xz + y) \hat{j} + 4z \hat{k} $, moving along the straight line from (0,0,0) to (1,2,3) is _____. $\textit{[Answer in integer]}$

The power consumption readings (in watt) by an instrument at fixed intervals of time (in seconds) are tabulated below:

\[ \begin{array}{|c|c|} \hline \text{Time (s)} & \text{Power consumption (W)} \\ \hline 0.0 & 8.6 \\ 0.6 & 9.2 \\ 1.2 & 7.8 \\ 1.8 & 6.4 \\ 2.4 & 7.2 \\ 3.0 & 8.6 \\ 3.6 & 11.2 \\ \hline \end{array} \]
Using Simpson's 1/3rd rule, the energy expenditure of the instrument in joules is _____.[Round off to two decimal places]