List of practice Questions

Magnetic field at a distance $r$ from z axis is $ B = B_0 r \, \text{kt} $ present in the region. $ B_0 $ is constant and $t$ is time. The magnitude of induced electric field at a distance $r$ from z-axis is.

Select a figure from the given four alternatives which when placed in the blank space of the given figure would complete the pattern.

The slope of a line L passing through the point $(-2, -3)$ is not defined. If the angle between the lines L and $ ax - 2y + 3 = 0 $ (where $ a>0 $) is 45Â°, then the angle made by the line $ x + ay - 4 = 0 $ with positive X-axis in the anticlockwise direction is:

Which of the following hormones is responsible for preparing the uterus for implantation of a fertilized egg?

If $ (a, b) $ is the stationary point of the curve $ y = 2x - x^2 $, then the area bounded by the curves $ y = 2x - x^2 $, $ y = x^2 - 2x $, and $ x = a $ is:

A boy gave a bundle of RS.100 notes to a guy. The serial number of notes are from CJJ103440 to CJJ103490. What is the total amount given to the guy

Evaluate $ \int_{1}^{2} \frac{x^4 - 1}{x^6 - 1} dx $:

Identify the major product $(P)$ in the following reaction sequence: \[ (\text{CH}_3)_3\text{CBr} \xrightarrow[\Delta]{\text{Alcoholic KOH}} X \xrightarrow{\text{HBr}} P \]

A body falling freely under gravity from rest from a certain height reaches the ground in $5$ seconds. The distance travelled by the body in the last two seconds of its motion is:

Identify the final product formed when Toluene undergoes a series of reactions with reagents given in the order:
(i) $ \text{Cl}_2 / \text{Sunlight} $
(ii) $ \text{H}_2\text{O}/373 \, \text{K} $
(iii) Acetophenone / $ \text{OH}^- $ at 293 K

100 mL of 0.1 M HA (weak acid) and 100 mL of 0.2 M NaA are mixed. What is the pH of the resultant solution? $(K_a \text{ of HA is } 10^{-5}, \log 2 = 0.3)$

The real values of $ x $ that satisfy the equation \[ \tan^{-1}x + \tan^{-1}2x = \frac{\pi}{4} \] is:

4 statements are given below. Identify the incorrect statement:

(A) Phenol has lower $ pK_a $ value than $ \text{p} $-cresol.
(B) 2-Chlorophenol is more acidic than phenol.
(C) Ortho and para nitrophenols can be separated by steam distillation since $ \text{p} $-Nitrophenol is more steam volatile than $ o $-Nitrophenol.
(D) Phenol on reaction with $ \text{Cr}_2\text{O}_7^{2-} / \text{H}^+ $ yields a conjugated diketone.

If two positive numbers are in the ratio $ 3 + 2\sqrt{2} : 3 - 2\sqrt{2} $, then the ratio between their A.M (arithmetic mean) and G.M (geometric mean) is:

In Young's double slit experiment light of wavelength 500 nm is used to form interference pattern. A uniform glass plate of refractive index 1.5 and thickness 0.1 mm is introduced in the path of one of the interfering beams. The number of fringes that will shift due to this is

If the matrix $ A $ is such that $ A \begin{pmatrix} -1 & 2 \\ 3 & 1 \end{pmatrix} = \begin{pmatrix} -4 & 1 \\ 7 & 7 \end{pmatrix} \text{ then } A \text{ is equal to} $

Evaluate: $ \cot^{-1} \left( -\frac{3}{\sqrt{3}} \right) - \sec^{-1} \left( -\frac{2}{\sqrt{2}} \right) - \csc^{-1}(-1) - \tan^{-1}(1) $

Choose the incorrect statement related to life cycles:
I. Sporophyte generation is represented by a single-celled zygote.
II. Gametophyte is multicellular in Pteridophytes and Gymnosperms.
III. Life cycle is diphlaplontic in Bryophytes.
IV. Life cycle is haplodiplontic in Pteridophytes.

Concave mirrors can produce

A coil of inductance 1H and resistance 100Ω is connected to an alternating current source of frequency $ \frac{50}{\pi} $ Hz. What will be the phase difference between the current and voltage?

If a committee of 10 members is to be formed from 8 men and 6 women, then the number of different possible committees in which the men are in majority is:

One card is selected from a well-shuffled deck of 52 cards, the probability of getting the queen of diamonds is:

भारत की राजभाषा है:

'गोदान' के लेखक हैं:

The equation of the circle which touches the x-axis, passes through the point (1, 1) and whose centre lies on the line $ x + y = 3 $ in the first quadrant is