Model Questions-2079(New Syllabus)

Given,

set is {l,m,n,p} i.e n=4

For calculating subset we have formula 2^n= 2^4 = 16

Subsets are;Φ, {l},{m},{n},{p},{l,m},{l,n},...........

But in the questions we have to find the number of non-empty singleton subsets(i.e sets containing single set as we expands on subsets.)

So, singleton subsets are {l},{m},{n},{p}

Hence the correct answer is option a. 4

f: A->B (Invertible means inverse)

f is invertible if the given function is bijective function

For bijecive function(having both injective & Surjective)

injective means one to one

and Surjective means onto

Hence, the correct answer is option c. f is both one-one and onto

Given,

let, y= f(x)=3x-4, then f^-1(x)=?

We have to find the value of inverse of the given function

interchanging x& y

y+4=3x

x=(y+4)/3

f^-1(x)=(x+4)/3

hence, the correct answer is option a. (x+4)/3

Given,

f(x)=sinx.cosx

from option

a. -1/2= -0.5

f(-0.5)=sin(-0.5).cos(-0.5)= -0.0008

b. 1/2 = 0.5

f(0.5)=sin(0.5).cos(0.5)= 0.0008

c. 0

f(0)=sin(0).cos(0)= 0

d. 1

f(1)=sin(1).cos(1)= 0.017

From the questions we have to find the minimum value of given function so from above option the minimum value we get  from the option is -0.0008 i.e option a

Hence, the correct answer is option a. -1/2

Let, z= (1-x)^3 / (1-i^3)---------(i)

we know, i^2= -1 & i^3= i^2 x i

using (a-b)^3 = a^3 - 3a^2 b +3ab^2 - b^3

then equation(i) becomes

=(1^3 - 3 x 1^2 x i + 3 x 1 x i^2 - i^3 )/(1-i^3)

=(1^3 - 3 x 1^2 x i + 3 x 1 x i^2 - i^3 )/(1-i^3)

=(1^3 - 3 x 1^2 x i + 3 x 1 x i^2 - i^3 )/(1-i^3)

=(1^3 - 3 x 1^2 x i + 3 x 1 x i^2 - i^3 )/(1-i^3)

={1 - 3i + 3 x  (-1) - i^2 x i } /(1-i^2 x i)

={1 - 3i - 3  - (-1) x i } /{1-(-1) x i}

={1 - 3i - 3  + i } /{1+ i}

= (-2 -2i) / (1+i)

= -2(1+i) / (1+i)

= -2

=-2+i x 0  comparing with a+ib

a= -2, b=0

Modulus

√(a^2 + b^2)

= √{ (-2)^2 + 0^2 }

=√4

=2

hence, the correct answer is option d. 2

Given,

2x^2 - 3x+1 =0 comparing with ax^2 + bx+c=0

a=2, b= -3 c=1

then,

b^2- 4ac

(-3)^2 - 4 x 2 x 1

9-8

1>0 which is real, unequal, rational

Hence, the correct answer is option a. real, unequal, rational

The two lines are

6x-4y=10

2(3x-2y)=10

3x-2y=5--------(i)

3x-2y=5--------(ii)

equation (i) & (ii) are coincident line.By the definition of coincident line;Any two geometrical lines having infinite solutions are coincident lines.They are dependent and consistent

Intersecting Lines:Any two geometrical lines having unique solutions are intersecting lines.They are independent and consistent

Parallel Lines:Any two geometrical lines having no solutions are parallel lines.They are independent and inconsistent

Hence, the correct answer is option c. coincident

Given,

A.M=81

(a+b) / 2 =81

a+b=162

G.M= 18

√ab = 18

squaring on both sides

ab =324

then,

H.M= 2ab/a+b

=(2 x 324)/162

=648/162

=4

Hence, the correct answer is option d. 4

Let initial velocity of the bullet = u
After penetrating 3 cm its velocity becomes $\frac{\mathrm{u/}}{2}$

From ${\mathrm{v^}}^2={\mathrm{u^}}^2-2as$

(u/2)^2=u^2−2a(3)

⇒6a=(3u^2)/4 ⇒a=(u^2)/8

Let further it will penetrate through distance x and stops at point C.

For distance BC, v=0, u=u/2, s=x, a=(u^2)/8

From ${\mathrm{v^}}^2={\mathrm{u^}}^2-2as$

⇒0=(u/2)^2 - 2 .  (u^2)/8 . x  

⇒x=1cm.

∴x=1cm

Hence, the correct  answer is option d. 1cm

Given,

Horizontal range(R) is 4√3 times the maximum height(H) i.e R=4√3 H -------(i)

We know,

Horizontal range R=(u^2sin⁡2θ)/g

Maximum height H=(u^2 sin⁡^2 θ)/2g

Then, equation(i) becomes,

R=4√3 H

​or, (u^2sin⁡2θ)/g =  4√3  (u^2 sin⁡^2 θ)/2g

or, 2sinθ cosθ = 2√3  sin⁡^2 θ

or, sinθcosθ =1/√3

or, tanθ = 1/√3

θ =30°

hence, the correct answer is option c. 30°

If the net force is zero, the acceleration must be zero (Newton's First Law).

Hence, the correct answer is option b. acceleration is not zero

Young's modulus is a material property and does not depend on the dimensions of the sample. It will remain the same.

Hence, the correct answer is option c. remain same

Work done W to blow a soap bubble is proportional to the surface area, which is proportional to r^2.

The work done to increase the radius from $R$ to 3R would be proportional to (3R)^2−R^2=9R^2−R^2=8R^2

Hence, it would require 8W to increase from $R$ to $R$.

Hence, the correct answer is option b. 8 W

When a metallic ball is immersed in alcohol and the system is heated, the volume of both the metal ball and the alcohol will increase due to thermal expansion. However, since the coefficient of cubical expansion of metal is less than that of alcohol, the alcohol will expand more than the metal ball.

As a result, the metal ball will experience a buoyant force that is greater than before because the volume of alcohol displaced by the ball will increase more than the volume of the ball itself. This will cause the metal ball to float higher in the alcohol.

However, the weight of the ball itself does not change with temperature. The weight of an object is the force exerted on it by gravity, and it is determined by the mass of the object and the acceleration due to gravity. Neither the mass of the ball nor the acceleration due to gravity changes with temperature.

Therefore, the weight of the ball remains the same when the system is heated.

Hence, the correct answer is option b. remains unchanged

At the critical temperature, the distinction between liquid and gas phases disappears, so latent heat is zero.

Hence, the correct answer is option b. critical temperature

According to the equipartition theorem, each degree of freedom contributes 1/2kBT to the average kinetic energy, where kB​ is the Boltzmann constant and $T$ is the temperature.

Hence, the correct answer is option c. 1/2 KT

The heat radiated by a sphere (Stefan-Boltzmann law) is proportional to the surface area A=4πr^2

If the radii are in the ratio 3:2, the surface areas are in the ratio (3^2):(2^2)=9:4

Hence, the correct answer is option c. 9:4

For a single slit, the condition for minima is asin⁡θ=nλ, where a is the slit width, λ is the wavelength, and $n$ is the order of the minima.

For the second minima (n=2)

22×10^−7sin⁡θ=2×550×10^−9

on solving

θ=30°

Hence, the correct answer is option b. 30°

When two adjacent mirrors are at 90 degrees to each other, the number of images formed is given by:

n=360°/θ ​− 1

where θ is the angle between the mirrors.

For θ=90°:

n=360°/90° ​− 1

n=4-1

n=3

Hence, the correct answer is option b. 3

The wavelength λ of the sound wave is λ=v/f=(360 m/s) / 500 Hz=0.72 m

For a phase difference of 60° (which is 1/6 of a full cycle), the distance is 1/6×0.72 m=0.12 m

Converting to cm, 0.12 m=12 cm

Hence, the correct answer is option d. 12 cm

For equilibrium, the forces due to $q$ and $4q$ on the third charge must be equal.

Let the distance from $q$ be $x$, then the distance from 4q is r−x

Equating the forces:

(kqQ) / (x^2) = (k4qQ) / (r−x)^2

on solving x=2r/3

Hence, the correct answer is option a. 2r/3 from 4q

Maximum capacitance is when capacitors are in parallel: Cparallel=nC

Minimum capacitance is when capacitors are in series: Cseries=C/n

ratio of maximum to minimum capacitance is

Cparallel /  Cseries = (nC) / (C/n) = n^2

Hence, the correct answer is option a. n^2

Resistance R of the heater coil is proportional to its length. Cutting it in half reduces the resistance to half.

Power $R$

Hence, the correct answer is option b. Doubled

Given,

Voltage(V)=50 V

Resistor(R)=10 Ohm

Current(I)=4.5 Amperes

Using Ohm's Law

V=IR

or, 50 = 4.5 ×(10+r)

or, 50=45+4.5r

or, 4.5r=5

r= 1.1 Ohm

Hence, the correct answer is option d. 1.1 Ohm

In a non-uniform magnetic field, a magnetic needle experiences both a force and a torque due to the gradient of the field.

Hence, the correct answer is option b. a force and a torque

Given,

Resistance (R) = 5 Ohm

Resonance frequency(ωL=XL)​= 100 Hz

We know that,

The quality factor Q=ωL / R = 100/ 5= 20 

Hence, the correct answer is option c. 50

Given,

Capacitor(C)= 420 pF = 420×10^−12 F

Frequency(f)=1020 kHz = 1020×10^3 Hz

Inductance(L)=?

The resonant frequency for an LC circuit is given by f=1/(2π√LC )

L= 1/(2πf)^2 C

L=1/{ (​2π x 1020×10^3)^2 x 420×10^−12}

L≈5.8×10^−5 H

Hence, the correct answer is option c. 5.8×10^−5 H

Given,

Potential difference(V)=100 volts

Charge of an electron(e)=1.6×10^−19 C,

Mass of an electron (m)=9.1×10^−31 kg

We know from Kinetic energy gained by the electron:

eV=1 x mv^2 / 2

or, 1.6×10^−19 C x 100 volts = 1 x 9.1×10^−31 kg v^2 / 2

or, v^2 = (2x 1.6×10^−17 ) / ( 9.1×10^−31 )

v≈5.9×10^6 m/s

Hence, the correct answer is option d. 5.9×10^6 m/s

When a proton collides with an electron, the system typically exchanges energy, and the proton's kinetic energy can increase due to the transfer of energy.

Hence, the correct answer is option a. Energy

Given,

Half-life of a radioactive sample(t1/2​)=10 years

For mean life

we know,

τ={t1/2)/{ln⁡(2)}

τ=10/0.693 ≈14.43 years​

​Hence, the correct answer is option c. 14.43 years​

NPN transistors are preferred because electrons, which are the majority carriers in NPN transistors, have higher mobility than holes, the majority carriers in PNP transistors. This higher mobility translates to better performance in terms of switching speed and efficiency.

Hence, the correct answer is option d. high mobility of electrons than holes

The azimuthal quantum number defines the shape of the electron orbital (s, p, d, f). For instance, l=0 corresponds to s-orbitals (spherical shape), l=1corresponds to p-orbitals (dumbbell shape), and so on.

Hence, the correct answer is option c. orbital shape

Gamma rays are highly penetrating electromagnetic waves and can pass through most materials, making them more penetrating than alpha and beta particles.

Hence, the correct answer is option c. γ rays

Magnesium chloride (MgCl2) is formed by the transfer of electrons from magnesium (Mg) to chlorine (Cl), resulting in the formation of Mg^2+ and Cl^- ions, making it an ionic compound.

Hence, the correct answer is option a. MgCl2

Fluorine has the highest electronegativity value (3.98 on the Pauling scale) among all elements due to its high effective nuclear charge and small atomic radius.

Hence, the correct answer is option b. fluorine

In Cr2O7^2-, oxygen has an oxidation number of -2. Let the oxidation number of chromium be x.

2x+7(−2)=−2

or, 2x−14=−2

or,2x=12

x=+6

Thus, the oxidation number of chromium in Cr2O7^2- is +6.

Hence, the correct answer is option a. +6

Zinc oxide (ZnO) is an amphoteric oxide because it can react with both acids and bases. For example, ZnO reacts with hydrochloric acid to form zinc chloride and with sodium hydroxide to form sodium zincate.

Hence, the correct answer is option d. ZnO

The structure of Buckminsterfullerene, also known as a "buckyball," consists of 60 carbon atoms arranged in a spherical shape with 20 hexagons and 12 pentagons.

Hence, the correct answer is option a. 20 six-member rings and 12 five-member rings

Down's process involves the electrolysis of molten sodium chloride to produce sodium metal and chlorine gas.

Hence, the correct answer is option c. sodium

Iso-butane has the structure where a methane group is attached to the second carbon of propane, making its IUPAC name 2-methylpropane.

Hence, the correct answer is option a. 2-methylpropane

Baeyer's reagent is an alkaline solution of potassium permanganate used for the qualitative analysis of unsaturation (double and triple bonds) in organic compounds.

Hence, the correct answer is option b. Baeyer's reagent

The Wurtz reaction involves the coupling of two alkyl halides using sodium metal in dry ether to form a higher alkane.

Hence, the correct answer is option a. Wurtz reaction

Alkanes follow the general formula CnH(2n+2), indicating they are saturated hydrocarbons with single bonds between carbon atoms.

Hence, the correct answer is option b. CnH(2n+2)

Lassaigne's test involves the fusion of the organic compound with sodium metal, converting nitrogen, sulfur, and halogens into soluble sodium salts, which can then be detected.

Hence, the correct answer is option a. Lassaigne's test

Methane has a tetrahedral structure, with carbon at the center and four hydrogen atoms at the corners of a tetrahedron.

Hence, the correct answer is option c. tetrahedral

In an acidic medium, the oxidation state change for chromium in potassium dichromate (K2Cr2O7) involves a total of 6 electrons per formula unit, so the equivalent weight is the molecular weight divided by 6.

Hence, the correct answer is option a. (mol. wt.)/6

Ammonia (NH3) is a Lewis base because it has a lone pair of electrons on the nitrogen atom that can be donated to a Lewis acid.

Hence, the correct answer is option d. NH3

An electrochemical cell, galvanic cell, and voltaic cell all refer to a device that generates electricity through redox reactions. They are essentially different names for the same concept.

Hence, the correct answer is option d. all of the above

1 calorie is defined as exactly 4.184 joules, which is the amount of energy needed to raise the temperature of 1 gram of water by 1 degree Celsius.

Hence, the correct answer is option a. 4.184 joules

The rate of a reaction depends on the concentration of reacting species, temperature, and surface area of the reactants. Each of these factors can affect the frequency and energy of collisions between reactant molecules.

Hence, the correct answer is option d. all of the above

In benzene (C6H6), each carbon atom is sp^2 hybridized, forming a planar hexagonal ring with delocalized π electrons above and below the ring.

Hence, the correct answer is option b. sp^2 hybridized

Tertiary alcohols react with Lucas reagent (ZnCl2 in concentrated HCl) to form an alkyl chloride, which is insoluble in water, causing immediate turbidity.

Hence, the correct answer is option c. turbidity appears immediately

Fats are a type of lipid, which are biomolecules that are insoluble in water but soluble in nonpolar solvents. They are important for energy storage, insulation, and cell membrane structure.

Hence, the correct answer is option a. lipid

Bakelite is a thermosetting plastic formed by the condensation reaction of phenol with formaldehyde, resulting in a hard, heat-resistant polymer.

Hence, the correct answer is option a. phenol and formaldehyde

Mercuric chloride (HgCl2) is known as corrosive sublimate due to its ability to sublime and its highly toxic and corrosive nature.

Hence, the correct answer is option b. HgCl2

Haematite (Fe2O3) is a primary ore of iron and is used extensively in the extraction and production of iron and steel.

Hence, the correct answer is option a. iron

The word "permissible" is stressed on the second syllable: per-MIS-si-ble.

Hence, the correct answer is option b. 2^nd

The word "perish" is stressed on the first syllable: PER-ish. The other words are stressed on later syllables

Hence, the correct answer is option a. perish

The correct idiomatic expression is "glad of your help."

Hence, the correct answer is option c. of

The correct phrase is "slave to his drug habit."

Hence, the correct answer is option a.to

"Vendetta" means a prolonged bitter quarrel with or campaign against someone.

Hence, the correct answer is option d. feud

"Acerbity" means sharpness or bitterness of speech or temper, similar to "acrimony."

Hence, the correct answer is option b. acrimony

Replete" means full or well-supplied; the opposite is "empty."

Hence, the correct answer is option a. empty

"Quell" means to suppress or put an end to; the opposite is to "encourage."

Hence, the correct answer is option a. encourage

"Contagious" specifically refers to diseases that can be spread by direct or indirect contact.

Hence, the correct answer is option d. contagious

Pork comes from pigs, while lamb, mutton, and venison come from different types of animals (sheep and deer, respectively).

Hence, the correct answer is option b. pork

"Ad nauseam" means to a sickening or excessive degree.

Hence, the correct answer is option a. to a disgusting degree

The correct tag question for a positive statement like "I think she will succeed" is "won't she?"

Hence, the correct answer is option b. won't she?

Let's see from the option

"Width" is a noun that refers to the measurement of something from side to side.

"Autumnal" is an adjective that describes something related to autumn.

"Advantages" is a plural noun that refers to favorable conditions or circumstances.

"Beauty" is a noun that refers to the quality of being physically attractive or the qualities in a person or thing that give pleasure to the senses or the mind.

Hence, the correct answer is option b. autumnal

The idiom "don't stand on ceremony" means not to be overly formal or not to insist on strict adherence to etiquette. It suggests that one should behave naturally and not worry about formalities.

Hence, the correct answer is option c. pay too much attention to correct rules of behavior or be too formal

The phrase "double Dutch" is an idiom meaning something that is very difficult to understand or incomprehensible. When someone says a legal document is "double Dutch," they mean it is confusing or written in a way that is hard to understand.

Hence, the correct answer is option d. difficult to understand

Analog computers work with continuous data, which is typically represented by continuous electrical signals.

Hence, the correct answer is option d. continuous electrical pulses.

Wildcard characters ? and * are used in Windows Explorer for searching files. ? represents a single character, while * represents any sequence of characters.

Hence, the correct answer is option c. ?,*

The order of memory measurements from smallest to largest is Byte, Megabyte, Gigabyte, Terabyte. Therefore, Gigabyte is the second largest.

Hence, the correct answer is option b. Gigabyte

Cache memory is a small-sized type of volatile computer memory that provides high-speed data access to the CPU and stores frequently used computer programs, applications, and data.

Hence, the correct answer is option c. CPU and RAM.

A nanosecond is one billionth of a second (10^-9 seconds).

Hence, the correct answer is option b. Nanosecond

Binary Coded Decimal (BCD) typically uses 4 bits to represent each decimal digit. However, in practice, BCD can be stored using 8 bits (1 byte) per digit for convenience and standardization.

Hence, the correct answer is option b. 8 bits

RAM (Random Access Memory) is called volatile memory because it loses its content when the power is turned off.

Hence, the correct answer is option b. Volatile memory.

The CPU (Central Processing Unit) is the primary component of a computer that performs most of the processing inside a computer.

Hence, the correct answer is option d. Central Processing Unit.

To copy text, the shortcut used is Control (Ctrl) + C on most operating systems.

Hence, the correct answer is option a. Control & C

LaTeX is a document preparation system, not an operating system. Windows, Linux, and Unix are all operating systems.

Hence, the correct answer is option d. LaTex