List of practice Questions

Let C be the circle in the complex plane with centre z₀ = $\frac{1}{2}$ (1+3i) and radius r = 1. Let z₁ = 1+ i and the complex number z2 be outside the circle C such that |z₁ – z₀| |z₂ – z₀| = 1. If z₀, z₁ and z₂ are collinear, then the smaller value of |z₂|² is equal to

For which of the following aqueous ion, spin only magnetic moment is 3.87 BM?

During the qualitative analysis of $SO _3^2$ using dilute $H _2 SO _4, SO _2$ gas is evolved which turns $K _2 Cr _2 O _7$ solution (acidified with dilute $H _2 SO _4$ ) :

The minimum number of elements that must be added to the relation $R=\{(a, b),(b, c),(b, d)\}$ on the set $\{a, b, c, d\}$ so that it is an equivalence relation, is _______

The dissociation constant of acetic acid is $x \times 10^{-5}$ When $25 \,mL$ of $0.2 \,M \,CH _3 COONa$ solution is mixed with $25 \,mL$ of $0.02\, M \,CH _3 COOH$ solution, the $pH$ of the resultant solution is found to be equal to 5. The value of $x$ is ___

If $a_1,a_2,.......a_n$ are in arithmetic progression with common difference $d>n$, then find limit $\lim_{n \to \infty}\sqrt{\frac{d}{n}}(\frac{1}{\sqrt{a_1}+\sqrt{a_2}})+\frac{1}{\sqrt{a_2}+\sqrt{a_3}}+.......+\frac{1}{\sqrt{a_n}+\sqrt{a_{n-1}}})$ is____.

Element not present in Nessler’s reagent is

The solubility product of BaSO₄ is $1 \times 10^{-10}$ at 298 K. The solubility of BaSO₄ in 0.1 M K₂SO₄(aq) is $x \times 10^{-9}$ g L⁻¹. Calculate the value of $x$.

A radioactive element ${}^{242}_{92}X$ emits two $\alpha$-particles, one electron, and two positrons. The product nucleus is represented by ${}^{234}_{P}Y.$ The value of $P$ is _______.

Let $A = \{x \in \mathbb{R}: |x+3| + |x+4| \le 3\}$,} \[ B = \left\{ x \in \mathbb{R} : 3 \cdot \sum_{r=1}^{\infty} \frac{3^{x-3}}{10^r} < 3^{-3x} \right\}, \] where $[x]$ denotes the greatest integer function. Then,

A person has been using spectacles of power $-1.0$ dioptre for distant vision and a separate reading glass of power $2.0$ dioptres What is the least distance of distinct vision for this person :

An object of mass $8 kg$ is hanging from one end of a uniform rod CD of mass $2 kg$ and length $1 m$ pivoted at its end $C$ on a vertical wall as shown in figure It is supported by a cable $AB$ such that the system is in equilibrium The tension in the cable is : (Take $g =10 m / s ^2$ )

The frequency ($ \nu $) of an oscillating liquid drop may depend upon the radius ($ r $) of the drop, density ($ \rho $) of the liquid, and the surface tension ($ s $) of the liquid as: \[ \nu = k r^a \rho^b s^c \]
The values of $ a $, $ b $, and $ c $ respectively are:

Let $\alpha x+\beta y+y z=1$ be the equation of a plane passing through the point$(3,-2,5)$and perpendicular to the line joining the points $(1,2,3)$ and $(-2,3,5)$ Then the value of $\alpha \beta y$is equal to ____

The density of a monobasic strong acid (Molar mass $242 \,g$ mol) is $121 \,kg \,L$ The volume of its solution required for the complete neutralization of $25 \,mL$ of $024\, M\, NaOH$ is ___$\times 10^{-2} mL$ (Nearest integer)

The ratio of silica to alumina in cement is:

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R
Assertion (A):- fan spins even after switch is off
Reason (R):- Fan in rotation has rotational inertia.
In the light of the above statements, choose the correct answer from the options given belows

The value of the integral $∫_{\frac 12}^2 \frac{tan^{-1}x}{x}dx$ is equal to

Equivalent resistance of the following circuit (in ohms) is equal to $\frac{x}{7}$. Value of x is equal to _____.

(S1): (p⇒q)∧(p∧((~q)) is a contradiction and
(S2): (p∧q)v((~q)v((~p)∧ q)v (p∧(~q))v((~p)∧ (~q)) is a tautology

Shown in the image above is an example of a bus stop during the busy hours. Draw and annotate FIVE distinct design problems in this context.
Use only one visual for each problem.
Answer in the given space only.

Evaluation Criteria:
Severity of the identified problem
Ability to make distinct observations
Ability to communicate through visuals

An abstract three-dimensional form is shown below. Visualize the form of a cutlery set (fork, bowl, and glass) for 3-6 years old children based on the image of the given form. It should match the design language with relevant details. Sketch and render the form of the cutlery set.

Evaluation Criteria:
Consistency with the visual language of the form
Form should complement function
Relevant details of the product
Surface shading
Quality of lines/strokes

Create a new visual identity for Indian Women’s Hockey Association. The identity has to be original and should have the abbreviations ‘IWHA’ as part of the visual design. DO NOT draw from any existing designs. Evaluation Criteria:
Creative visual representation
Effective communication of the concept
Visual Aesthetics
Composition

Each of the boxes in the answer script shows some visual elements and the FIRST word for a title of the image. Draw recognizable images by interpreting the visual elements and give a title to the images using the given first word. Use only BLACK pencil/pen. Draw only within the boundaries of the boxes.

Evaluation Criteria:
Uniqueness: Ability to create unusual images
Diversity: Variation between the created images
Clarity: Effective use of the visual elements and title
Fun: Ability to use humor and surprise in the images and title

Mr. Singh (5 Feet, 11 inches tall) is smiling and capturing a selfie of his entire family with his mobile phone held vertically. He is with his wife (5 feet tall), standing towards his left with her two mischievous kids. Pinky (girl) and Bablu (boy) are making funny expressions looking into the mobile. They all are standing facing a digital camera installed in the top corner of the room. The size of the room is 12 x 12 x 12 feet. Draw the picture of the above description from the point of view of a digital camera capturing this moment. Additional Instructions:
Use only pencils.
Do not illustrate the surroundings. Only draw the family.
Evaluation Criteria:
Imagination
Overall composition of the picture
Quality of lines
Attention to details
Anatomy and perspective