List of practice Questions

Perspective view of an object is shown below. The object is successively rotated 180 degrees clockwise about x-axis, 90 degrees clockwise about y-axis and 90 degrees anticlockwise about z-axis. All rotations have to be viewed from a point on the positive axis facing towards the origin. Which one of the following perspective view options will be the result of the rotations?

P and Q are two grids, in which white squares are transparent. P is rotated 90 degrees counter-clockwise and Q is rotated 90 degrees clockwise. What would be the resulting figure if the rotated grids are overlapped?

Four transparent planes A, B, C and D are shown in front view on the left. But when viewed in perspective, they appear like the image shown on the right. Which plane is the farthest from the viewer?

Which set of pieces can form a full circle, if rotation of pieces is not permitted?

Consider the following sentences from the Nobel Lecture of the writer Doris Lessing:
"That poor girl trudging through the dust dreaming of an education for her children, do we think that we are better than she is - we, stuffed full of food, our cupboards full of clothes, stifling in our superfluities?
I think it is that girl, and the women who were talking about books and an education when they had not eaten for three days, that may yet define us."
Which of the option(s) is/are implied by the quote?

In order to fit a metal rim to the wooden wheel of a bullock cart, the metal rim is ______________________________________ and placed on the wooden wheel and ______________________________________. This process works because ______________________________________.

How many fonts have been used in the words given below?

The figure shows an urban road map of a city. The boundary of the city is a perfect rectangle as indicated by the black dotted line. The grey lines indicate the major roads that run parallel to the edges of the city. The red line shows the route taken by a bus from point P to point Q. If the perimeter of the boundary is 68 km, what is the distance travelled by the bus in kilometres?

The image shows a swinging pendulum. As it swings, it reaches an extreme position and then reverses its motion. In animation, what is this commonly referred to as?

Which option is the correct logo?

If $ A = \begin{pmatrix} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{pmatrix} $ and $ M = A + A^2 + A^3 + \cdots + A^{20} $, then the sum of all the elements of the matrix $ M $ is equal to ________.

Let $ f : [0, \infty) \rightarrow [0, 3] $ be a function defined by
\[ f(x) = \begin{cases} \max\{\sin t : 0 \le t \le x\}, & 0 \le x \le \pi \\ 2 + \cos x, & x > \pi \end{cases} \] Then which of the following is true ?

Let the mean and variance of the frequency distribution be 6 and 6.8 respectively.
x : $ x_1 = 2,\; x_2 = 6,\; x_3 = 8,\; x_4 = 9 $
f : $ 4,\; 4,\; \alpha,\; \beta $
If $ x_3 $ is changed from 8 to 7, then the mean for the new data will be:

Given below are two statements :
Statement I : Penicillin is a bacteriostatic type antibiotic.
Statement II : The general structure of Penicillin is :
Choose the correct option :

What is A in the following reaction ?

Consider the above reaction, and choose the correct statement :

Match List - I with List - II :

Choose the correct answer from the options given below :

A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30$^\circ$ with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle $\theta$ with the line AB should be ________ $^\circ$, so that the swimmer reaches point B.

In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic energy, the ratio of rotational inertias $(\frac{I_1}{I_2})$ will be x : 1. The value of x will be ________ .

Figure A and B show two long straight wires of circular cross-section (a and b with a<b), carrying current I which is uniformly distributed across the cross-section. The magnitude of magnetic field B varies with radius r and can be represented as :

Match List I with List II.

Choose the correct answer from the options given below:

Find the truth table for the function Y of A and B represented in the following figure.

Let n be a non-negative integer. Then the number of divisors of the form "4n+1" of the number $(10)^{10} \cdot (11)^{11} \cdot (13)^{13}$ is equal to ________.

The distance of the point P(3, 4, 4) from the point of intersection of the line joining the points Q(3, -4, -5) and R(2, -3, 1) and the plane $2x+y+z=7$, is equal to ________.