2080 Entrance Questions

"Woeful" means full of woe or misery, which closely aligns with "deplorable" meaning very bad or in a state causing grief. "Punishable" means deserving punishment, "culpable" means deserving blame, and "shaky" means not stable, none of which are synonyms for "woeful".

Hence, the correct answer is option a. deplorable

"Rotund" means round or plump, typically describing a person's body shape. While "round" and "circular" describe shapes, "plump" specifically captures the connotation of a rounded body shape. "Healthy" is not related to the meaning of "rotund".

Hence, the correct answer is option b. plump

"Facetious" means treating serious issues with deliberately inappropriate humor, similar to being "flippant". "Sweet" and "charming" refer to pleasant traits, and "handsome" refers to physical attractiveness, none of which convey the same meaning as "facetious".

Hence, the correct answer is option c. flippant

"Coagulate" means to change from a fluid to a thickened mass, which is synonymous with "congeal". "Sweeten", "sharpen", and "mix up" have entirely different meanings.

Hence, the correct answer is option d. congeal

"Grotesque" means distorted and unnatural in shape or size, often ugly. The opposite would be "symmetrical", which means well-proportioned and balanced. "Proportionate" and "congruous" also oppose "grotesque" but "symmetrical" is the most directly opposite. "Ugly" is a synonym, not an antonym.

Hence, the correct answer is option b. symmetrical

"Erase" means to remove or delete. The opposite would be "engrave", which means to carve or etch into a surface permanently. "Drop", "delete", and "defend" do not serve as antonyms for "erase".

Hence, the correct answer is option c. engrave

"Tranquil" means calm and peaceful. The opposite would be "agitated," which means disturbed or anxious. "Peaceful" is a synonym, "angry" is not directly opposite, and "dull" is unrelated.

Hence, the correct answer is option b. agitated

"Spurious" means false or not genuine. The opposite is "genuine," which means real or authentic. "Duplicate" implies a copy, "valid" means logically sound, and "reliable" means dependable, none of which are direct antonyms.

Hence, the correct answer is option a. genuine

"Paleontology" is the study of fossils and early forms of life. "Pomology" is the study of fruits, "philology" is the study of language, and "teleology" is the study of purpose or design in natural phenomena.

Hence, the correct answer is option a. paleontology

"Ornithology" is the study of birds. "Embryology" is the study of embryos, "geology" is the study of the Earth, and "biology" is the study of living organisms, which is more general.

Hence, the correct answer is option a. ornithology

"Theology" is the study of God and religion. "Axiology" is the study of values, "metaphysics" is the study of the nature of reality, and "epistemology" is the study of knowledge.

Hence, the correct answer is option b. theology

"Imperious" means commanding, haughty, and arrogant. "Eccentric" means unconventional, "garrulous" means excessively talkative, and "amiable" means friendly and pleasant.

Hence, the correct answer is option b. imperious

"Fall out" means to have a disagreement or quarrel. The expression "the two friends fall out this afternoon" implies that the friends had a disagreement. "Fall on" and "fall upon" mean to attack or to come upon suddenly, and "fall in" typically means to align or collapse inward.

Hence, the correct answer is option c. fall out

"Put down" means to suppress or stop something forcibly, which fits with "rebellion". "Put on" means to dress or present, "put out" can mean to extinguish (like a fire), and "put up" means to accommodate or tolerate.

Hence, the correct answer is option c. put down

"Sit back" means to relax and do nothing while someone else is working. "Sit out" means to not participate, "sit in" means to attend as an observer or participant, and "sit on" means to delay action.

Hence, the correct answer is option d. sit back

"Work out" means to result in a good outcome or to be resolved. "Work up" means to develop or produce, "work off" means to get rid of by exercise or effort, and "work on" means to continue effort on something.

Hence, the correct answer is option d. work out

"A flash in the pan" refers to something that is initially exciting or successful but fails to be sustained. "Sudden fortune" and "successful life start" do not capture the temporary nature implied by the idiom, and "new day in life" is unrelated.

Hence, the correct answer is option a. a short lived success or enthusiasm

"Up and about" means to have recovered from an illness or injury and be active again. The other options do not capture this meaning.

Hence, the correct answer is option b. recovered and in good health

"Thrills and spills" refers to the excitement and risks, including both successes and failures, typically in a situation or activity. The other options do not correctly capture this dual nature.

Hence, the correct answer is option c. success and failures

"Be out like a light" means to fall asleep very quickly. The other options do not match this meaning.

Hence, the correct answer is option d. fall quickly into a deep sleep

"Mind over matter" means using mental strength to overcome physical challenges or limitations. The other options do not accurately reflect this concept.

Hence, the correct answer is option a. overcome physical weakness by means of will power

The correct prepositions are "for" and "in". "She was fined for parking her car in a no parking area." "For" indicates the reason for the fine, and "in" indicates the location.

Hence, the correct answer is option b. for, in

"Died of cancer" is the correct expression to use because "of" indicates the cause of death. "Died from the loss of blood" is also correct because "from" is used to indicate the cause or origin of something.

Hence, the correct answer is option c. of, from

"Throwing the rubbish at the fire" is correct because "at" indicates the target of the action. "He heard voices from the hedge" would be more accurate, but if we consider the closest correct preposition from the given options, "on" could be used, though "from" would be ideal.

Hence, the correct answer is option a. at, on

"Guard family members against any danger" is correct because "against" is used to indicate protection from harm. "Live by honest labour" is correct because "by" indicates the means or method of living.

Hence, the correct answer is option a. against, by

"In dire need of money" is correct because "of" is used to specify what is needed. "For the treatment of my sick wife" is correct because "for" indicates the purpose or use of the money.

Hence, the correct answer is option b. of, for

The correct stress pattern is: plu-TO-ni-um.

Hence, the correct answer is option b. 3rd syllable

In the phrase "cyber squatting," the primary stress falls on the first syllable of "squatting."

Here’s the breakdown:

"cyber" is stressed on the first syllable: CY-ber.

"squatting" is stressed on the first syllable: SQUAT-ting.

The overall stress pattern for the phrase is primarily on "squatting," with the stress on its first syllable.

Hence, the correct answer is option d. 1st syllable

The stress is on "ac" in re-TRAC-ta-ble.

Hence, the correct answer is option d.4th syllable

"Insolvency" means the state of being unable to pay one's debts, which is similar to bankruptcy.

Hence, the correct answer is option a. insolvency

The idiom "a baptism of fire" refers to a difficult or challenging introduction to a new job or activity, especially when faced with tough situations right at the start.

Hence, the correct answer is option b. a difficult introduction to a new job or activity

To "face the music" means to accept the criticism or punishment for one's own actions or mistakes.

Hence, the correct answer is option d. accept the criticism or punishment for one's own work

The conjunction "although" is used to introduce a subordinate clause that contrasts with the main clause. In this case, it indicates a contrast between getting the job and having no suitable qualifications.

So the complete sentence would be: "He got the job although he had no suitable qualification."

Hence, the correct answer is option a. although

The conjunction "because" explains the reason for breaking the window, and "but" introduces a contrasting idea that he later realized his mistake.

Hence, the correct answer is option b. because, but

The phrase "neither... nor" is used to indicate that two negative statements are true. Here, it means that Kanu is illiterate and cannot read or write even a single word.

Hence, the correct answer is option c. neither, nor

The sentence is in passive voice, indicating that the action was done by someone. "Taken" is the correct past participle form to use in this context.

Hence, the correct answer is option d. taken

The possessive adjective "our" correctly indicates that the trip belongs to the speaker and others they are referring to.

Hence, the correct answer is option a. our

The preposition "over" indicates that the lorry passed on top of the dog, which is consistent with the context of being killed by a vehicle.

Hence, the correct answer is option b. over

The word "so" is used to indicate the extent of the heaviness of the statue, followed by a result (a crane was brought to lift it).

Hence, the correct answer is option c. so

The phrase "catch cold" is a common idiom meaning to become ill with a cold. "Catch" is the correct verb to use here.

Hence, the correct answer is option a. catch

A "jaunt" is a short journey taken for pleasure, making it the correct answer.

Hence, the correct answer is option a. jaunt

"Celibacy" refers to the state of abstaining from marriage and sexual relations, while "bachelor" and "spinster" refer to individuals who are unmarried but do not specifically denote the state of choosing not to marry.

Hence, the correct answer is option c. celibacy

"Convalescence" refers to the gradual recovery of health and strength after illness, which fits the context of the question.

Hence, the correct answer is option c. convalescence

The phrase "run into debt" means to incur debt, which is the correct usage here. The phrase indicates how easily one can accumulate debt.

Hence, the correct answer is option d. into

"Rumbling" is the appropriate term to describe the sound of thunder. Other options do not fit the typical description of thunder sounds.

Hence, the correct answer is option d. rumbling

"Tyro" is not a prefix; it refers to a beginner or novice. The other options ("anti-", "post-", and "pre-") are commonly used prefixes.

Hence, the correct answer is option a. tyro-

The correct form is "underhearted," which means having little courage. The other options do not form a correct word when combined with "hearted."

Hence, the correct answer is option d. under

This sentence contains an independent clause ("John is my best friend") and a dependent clause ("who is wearing a white shirt"), making it a complex sentence.

Hence, the correct answer is option c. complex

Declarative sentences like "I saw a blackbird" typically end with a falling intonation, indicating the completion of a statement.

Hence, the correct answer is option a. falling

Deism is the belief in the existence of a supreme being, specifically a creator who does not intervene in the universe. It emphasizes reason and rejects religious dogma. The other terms (Pantheism, Theism, and Henotheism) do not fit this specific description.

Hence, the correct answer is option b. Deism

The data bus is bidirectional because it allows data to be transferred in both directions between the CPU and other components.

Hence, the correct answer is option a. Data bus

EEPROM (Electrically Erasable Programmable Read-Only Memory) is a type of flash memory that can be erased and reprogrammed multiple times.

Hence, the correct answer is option d. EEPROM

The Harvard architecture has separate storage and signal pathways for instructions and data, allowing simultaneous access to both.

Hence, the correct answer is option c. Harvard

Given, we have to subtract into given binary numbers

1000

-100

100

OR,

binary 100 (which is 4 in decimal) from binary 1000 (which is 8 in decimal) results in binary 100 (which is 4 in decimal).

Hence, the correct answer is option c. 100

"Blackberry" typically refers to the Blackberry operating system or software, which is application software.

Hence, the correct answer is option b. Application

Fortran is a high-level procedural programming language used primarily for scientific and engineering applications.

Hence, the correct answer is option d. Fortran

The "&&" operator is a logical AND operator used in programming to combine two boolean expressions.

Hence, the correct answer is option c. &&

PAN (Personal Area Network) covers the smallest area, typically a few meters around a person.

Hence, the correct answer is option c. PAN

Bluetooth is a full duplex communication system, allowing simultaneous two-way communication between devices.

Hence, the correct answer is option b. Bluetooth

The full form of MAC is the Media Access Control Address. The MAC address is known as the hardware id number. In particular, each computer’s NIC (network interface card), including a Bluetooth, Wi-Fi card or Ethernet card, has an unchanged MAC address inserted by the manufacturer at the time of production. A few well-recognized NIC manufacturing companies include Nortel, Dell, Nortel and Cisco. By substituting the NIC cards, one might alter the given default address of the system.

Hence, the correct answer is option d. Media Access Control

RSA (Rivest-Shamir-Adleman) is an encryption algorithm used in cyber security for secure data transmission. The other options (AI, Internet of Things, and Data warehouse) are related to technology but not specifically components of cyber security.

Hence, the correct answer is option d. RSA

The term "biased hat hacker" is not a recognized category of hackers. Ethical hackers are generally categorized as white hat hackers (ethical) and gray hat hackers (sometimes ethical), while black hat hackers are unethical. "Biased hat hacker" does not exist in the commonly accepted terminology.

Hence, the correct answer is option c. Biased hat hacker

Digital systems are primarily used for automatic computations because they use discrete signals to represent data, allowing for precise and reliable computation. While hybrid and analog systems exist, digital systems are the standard for automatic computation in modern computing.

Hence, the correct answer is option c. Digital

Among the listed options, the hard disk is the slowest in terms of access speed and data transfer rates. RAM, cache, and registers are all much faster.

Hence, the correct answer is option a. Hard disk

The CPU performs both arithmetic and logic operations as per the given instructions and stores the results back in memory.

Hence, the correct answer is option c. Arithmetic and Logic operations

Pressing F5 in most presentation software, such as Microsoft PowerPoint, starts the slide show from the beginning.

Hence, the correct answer is option c. F5

1 petabyte (PB) is equivalent to 1000 terabytes (TB).

Hence, the correct answer is option d. 1000 TB

The standard ASCII code uses 7 bits to represent characters, allowing for 128 different characters.

Hence, the correct answer is option b. 7 bits

The ASCII code for the character "a" is 97 in decimal.

Hence, the correct answer is option b. 97

Dividend       Remainder
24/2 = 12        0
12/2 = 6          0
6/2 = 3            0
3/2 = 1            1
1/2 = 0            1

Write the remainder from bottom to top
Therefore, the binary equivalent of decimal number 24 is 11000.

Hence, the correct answer is option c. 11000

The octal number system uses the digits 0 to 7.

Hence, the correct answer is option b. 0 to 7

A command interpreter is also known as a shell. It interprets and executes the commands entered by the user.

Hence, the correct answer is option c. shell

Booting refers to the process of starting or restarting a computer system, including loading the operating system into memory.

Hence, the correct answer is option a. Restarting computer

Bootstrapping, or booting, typically refers to a cold boot, which is the process of starting a computer from a powered-down state.

Hence, the correct answer is option a. Cold boot

Real-time operating systems (RTOS) are designed for process control applications, where timely processing and response to input are critical. Examples include operating systems used in embedded systems and industrial control systems.

Hence, the correct answer is option d. Process Control

After booting and loading the GUI, the desktop manager is typically the first program to run. It manages the desktop environment and provides the graphical interface for user interaction.

Hence, the correct answer is option a. Desktop Manager

The code swaps the values of a and b. Initially, a = 3 and b = 5. After swapping, a becomes 5 and b becomes 3. Thus, the output is "5 3".

Hence, the correct answer is option d. 53

A web browser is a software application used to access and display web pages written in HTML.

Hence, the correct answer is option c. Web Browser

SNMP (Simple Network Management Protocol) uses port 161 for sending and receiving management messages.

Hence, the correct answer is option a. 161

The rel attribute specifies the relationship between the current document and the linked document/resource.

Hence, the correct answer is option c. REL

HTML provides six levels of headers, <h1> through <h6>, with <h1> being the largest and <h6> the smallest.

Hence, the correct answer is option d. 6

Multimedia is often used in corporate communications and presentations to convey information effectively through various media forms like text, audio, and video.

Hence, the correct answer is option a. Corporate

Poor bandwidth can cause slow loading times or failure to load large files such as heavy videos in web-based training (WBT). Bandwidth is the capacity of the internet connection.

Hence, the correct answer is option d. Bandwidth

Stalking involves the persistent and unwanted following or harassment of an individual by another person or group.

Hence, the correct answer is option c. Stalking

Cyber ethics refers to the study and practice of appropriate and ethical behavior in the online environment and on digital media platforms.

Hence, the correct answer is option b. Cyber Ethics

Code Red is a well-known computer virus that affected Windows operating systems in 2001.

Hence, the correct answer is option c. A computer virus

A firewall is a network security device that monitors and controls incoming and outgoing network traffic based on predetermined security rules, protecting against unauthorized access.

Hence, the correct answer is option b. It is a device installed at the boundary of incorporation to protect it against unauthorized access.

A worm is a type of malware that replicates itself and spreads to other computers without needing a host program.

Hence, the correct answer is option b. Worm

To realize the expression Y=CD+EF+G, we need three AND gates for the terms CD and EF (G does not need an AND gate because it is a single variable).

Hence, the correct answer is option c. 3

To realize the expression Y=BD+CE+AB, we need three two-input AND gates to generate BD, CE, and AB, and two two-input OR gates to combine these terms into the final output.

Hence, the correct answer is option a. 3, 2

In HTML, the hexadecimal color code for blue is #0000ff, where the first two digits (00) represent the red component, the second two digits (00) represent the green component, and the last two digits (ff) represent the blue component.

Hence, the correct answer is option c. #0000ff

The tag which is not valid in HTML5 among the given option is <<l> tag because the tag is incorrect it should be <l>

Hence, the correct answer is option a. <<l> tag

Phishing is a technique where attackers try to trick individuals into providing sensitive information, such as passwords, by pretending to be a trustworthy entity in electronic communications.

Hence, the correct answer is option c. phishing

The distributive law in Boolean algebra states that the product of a variable and the sum of two other variables is equal to the sum of the product of the variable and each of the two variables. Mathematically, this is expressed as A.(B+C)=A.B+A.C This law is analogous to the distributive property in arithmetic where a⋅(b+c)=a⋅b+a⋅c

Hence, the correct answer is option d. A.(B+C)=A.B+A.C

The absorption law in Boolean algebra states that A+(A.B)=A and A.(A+B)=A

Hence, the correct answer is option A+ (A.B)=A

The identity law in Boolean algebra states that any variable ORed with 0 is equal to the variable itself (a+0=a) and any variable ANDed with 1 is equal to the variable itself (a.1=a).

Hence, the correct answer is option a. a +0=0+ a = a

An IPv4 address consists of four decimal numbers, each ranging from 0 to 255, separated by dots. Option (d) is the only one that fits this format.

Hence, the correct answer is option d. 128.64.0.0

A cyber attack is an attempt to steal, spy, damage, or destroy computer systems, networks, or their associated information.

Hence, the correct answer is option a. Cyber attack

The term "hacker" originated at the Massachusetts Institute of Technology (MIT) in the 1960s, referring to individuals who enjoy exploring the details of programmable systems and stretching their capabilities.

Hence, the correct answer is option a. MIT

Linux is an open-source operating system, meaning its source code is available for anyone to view, modify, and distribute. Unix, while similar, is not necessarily open source, and Windows and MS Word are proprietary software.

Hence, the correct answer is option b. Linux

Let's see from the option

a. Give me a book: This is a command, not a statement that can be judged as true or false.

b. x-2=10: This is an equation, not a factual statement. It can be solved to find $x$, but it’s not a statement that is inherently true or false without context.

c. Rara lake is in Pokhara: This statement is factually incorrect. Rara Lake is actually in the Mugu District of Nepal, not in Pokhara.

d. y>0: This is an inequality and can be true or false depending on the value of $y$, but it is not a factual statement.

Hence, the correct answer is option c. Rara lake is in Pokhara

Given,

x^2+4=0

or, x^2 = -4

taking the square root of both sides

or, √(x^2) = √(-4)

Since √(-4) involves the imaginary unit $i$,

we know i^2 = -1

then,

or, √(x^2) = √(4 i ^2)

x= ±2i

However, since $i$ and $-2i$ are not real numbers (they are complex numbers),there are no real solutions to the equation x^2+4=0.

S=∅

Hence, the correct answer is option d. S=∅

Let's see from the option

a. Long rivers of Nepal: This option refers to a collection of several long rivers found in Nepal. It is a broad category encompassing multiple entities.

b. Longest river of Nepal: This option refers to a single specific river, the one that holds the record for being the longest in Nepal.

c. Tall plants in a garden: This option refers to a collection of several tall plants found within a garden. Similar to option (a), it is a broad category covering multiple entities.

d. Nice books: This option refers to a collection of several books that are considered nice. Like options (a) and (c), it is a broad category covering multiple entities

Hence, the correct answer is option b. longest river of Nepal

Given,

S= {x:x≥ -2,x ∈ R}, which means $S$ contains all real numbers $x$ that are greater than or equal to -2.

Let's see from the option

a. [-2, ∞): This notation means the set includes all real numbers from -2 to infinity, including -2. This is correct because the set $S$ starts from -2 and includes all numbers greater than or equal to -2.

b. (-2, ∞): This notation means the set includes all real numbers greater than -2 but does not include -2 itself. This is not correct because the set S includes -2.

c. (∞, -2]: This notation is incorrect because it represents a set that includes all real numbers less than or equal to -2, which is the opposite of what is given.

d. [-2, ∞]: This notation means the set includes all real numbers from -2 to positive infinity, including both -2 and positive infinity. This is almost correct, but it should be ∞, not a closed interval.

Hence, the correct answer is option a. [-2, ∞)

Given,

| x-5| ≤ 3

From the definition of absolute value

−3≤x−5≤3

-3+5 ≤ x−5+5≤ 3+5

2≤ x≤ 8

the solution to ∣x−5∣≤3 is x∈[2,8]

Hence, the correct answer is option b. [2,8]

Given,

(2a-1,-3)=(1,b+3)

from the definition of equal ordered pair

2a-1 =1                   -3 = b+3

or 2a=1+1                   -3-3 = b

or, 2a = 2                       b=-6

a=1

(a,b)=(1,-6)

Hence, the correct answer is option a. (1,-6)

Given,

f(x)=2x+5-------(i)

and pre-image f(x)=7-----(ii) then x=?

from equation(i) and (ii)

7=2x+5

or, 7-5 = 2x

or, 2= 2x

x=1

Hence, the correct answer is option c. 1

Given,

f(x)=√(1-x^2)

we need to ensure that the expression under the square root is non-negative because the square root function is only defined for non-negative numbers.

so,  1−x^2≥0

On solving

1≥x^2

or equivalently

x^2≤1

Taking the square root of both sides, we get:

−1≤x≤1

the domain is: [−1,1]

Hence, he correct answer is option d. [-1,1]

Given,

y=a^x passing through (2,4)

or, 4=a^2

or, 2^2 = a^2

a=2

Hence, the correct answer is option b. 2

Given,

f(x)= x^2 -2-----------(i)

for even function, f(-x)=f(x)

then equation(i) becomes

f(-x)=(-x)^2 -2 = x^2-2 = f(x)

f(-x)= f(x) which is satisfied

for odd function; f(-x)= -f(x)

f(-x)=(-x)^2 -2 = x^2-2 ≠ - f(x)

Hence, the correct answer is option a. an even function

Let's see from the option

a. a ration number is expressed as p/q and q≠0

b. integer number:  It doesn't necessary to express in the form of p/q it include positive whole number, negative whole number, zero but they are a subset of a rational number

i.e{............. -4, -3, -2, -1, 0, 1, 2, 3, 4,..........}

c. Irrational number: √2, Π, √3, e

Hence, the correct answer is option a. a rational number

Given,

geometric sequence a, ak, a k^2, ..........

general form of sum of geometric sequence is

S= a + ar+ a r^2+ ..........

where a= first term, r=common ratio

using formula,

S base ∞ = (a)/(1-r) such that | r | <1

from given questions, first term is a and common ratio is k then,

S base ∞ = (a)/(1-k) such that | k | <1

| k | <1

-1<k<1

Hence, the correct answer is option d. -1<k<1

Given,

2k + 1, 3K+ 2 and 5k+ 1 are in A.P.,

From using A.P formula

3k+2 = {(2k+1) + (5K+1) } / 2

or 6k+4 = 7K + 2

or 4-2 = 7k - 6k

K=2

Hence, the correct answer is option a. 2

Singular Matrix: A matrix A is said to be singular matrix if |A|=0 these matrices have no inverse

Hence, the correct answer is option d. |A|=0

Let denote the root of the equation by α and -α(i.e equal in magnitude but opposite in sign)

Sum of roots; α+(-α) = 0

According to the quadratic equation formula

sum of roots= -q/p (i.e α+β = -b/a)

-q/p = 0

q=0

Product of roots; α.β = α.(-α) = α^2

Quadratic equation formula,

Product of roots = r/p (i.e α.β = c/a)

-α^2 = r/p

since α is a real number α^2 is non-negative and thus r/p must be non-positive

Hence, the correct answer is option b. q=0

Given,

x^2 +kx+4=0 comparing with ax^2 +bx+c=0

then, a=1, b=k, c=4

the discriminant(Δ) of the quadratic equation is given by;

Δ = b^2  - 4ac

b^2  - 4ac = 0

or, k^2 - 4x1x4=0

or, k^2 -16=0

k=±4

Hence, the correct answer is option a. ±4

Given, line is px+qy+c=0

For slope= - coefficient  of x/coefficient of y = -p/q

Hence, the correct answer is option d. -p/q

The homogeneous equation is 𝑎𝑥^2 + 2ℎ𝑥𝑦 + 𝑏𝑦^2 = 0

Hence, the correct answer is option b. 𝑎𝑥^2 + 2ℎ𝑥𝑦 + 𝑏𝑦^2 = 0

Given lines is 𝑘𝑥^2 + 𝑥𝑦 − 𝑦^2 = 0, is comparing with 𝑎𝑥^2 + 2ℎ𝑥𝑦 + 𝑏𝑦^2 = 0

then, a=k, 2h=1, b= -1

h=1/2

for perpendicular

a+b=0

or, k+(-1)=0

k=1

Hence, the correct answer is option a. 1

Given,

point p(1,2,3) and origin O(0,0,0)

using distance of a point from the origin formula

OP=√{ (x-0)^2 + (y-0)^2 + (z-0)^2 }

OP=√{(1-0)^2 + (2-0)^2 + (3-0)^2 }

OP=√{ 1^2 + 2^2 +3^2 }

OP=√1+4+9

OP=√14

Hence, the correct answer is option c. √14

Given,

two points are A(4,5,0) and B(2,3,4)

two points AB are joined then it's direction ratio are

=(x2-x1,y2-y1,z2-z1)

=(2-4,3-5,4-0)

=(-2,-3,4)

Hence, the correct answer is option d. (-2,-3,4)

Given,

vector is ai+bj

direction of the vector is

θ=tan^−1 ( b/ a )

Hence, the correct answer is option b. tan^−1 ( b/ a )

Given,

Total cards(n)=52

No. of ace of clubs=1

No. of king of spades=1

since, these are distinct cards, there are 1+1=2 favorable outcomes

probability=(Numbers of favorable outcomes)/(Total numbers of cards)

= 2/52

=1/26

Hence, the correct answer is option a. 1/26

Given,

y= 𝑥^3 − 𝑥^2---------(i)

differentiate equation(i) with respect to 'x'

dy/dx = 3x^2-2x

from questions

dy/dx=0

or, 3x^2-2x=0

or, x(3x-2)=0

either,                                  or,

x=0                                     3x-2=0

x=2/3

Hence, the correct answer is option d. 0,2/3

Given,

f(x)=2x+5-----------(i)

for increasing; f'(x)>0

for decreasing; f'(x)<0

differentiate equation(i) with respect to x

f'(x)=2>0 i.e the function is increasing

Hence, the correct answer is option c. increasing

Hence, the correct answer is option b.

For three forces to be in equilibrium, their vector sum must be zero. When three forces of equal magnitude act at a point and are in equilibrium, they must form an equilateral triangle when placed head to tail.

In an equilateral triangle, all internal angles are equal to 60°. However, because the forces act from a common point and not along the sides of the triangle, the angle between any two forces is the external angle of the triangle formed by the forces.

The external angle at each vertex of an equilateral triangle is 180°−60°=120°. Thus, the angle between any two of the three equal forces in equilibrium is 120°.

Hence, the correct answer is option a. 120°.

Given:

Initial velocity (u)=0

Acceleration (a)=5 m/s^2

Time (t)=3 s

Using the equation of motion:

v=u+atv = u + at

=0+5×3

=15 m/s

Hence, the correct answer is option b. 15m/sec

Given:

Vertical component: 4N

Horizontal component: 3N

The magnitude of the resultant force $F$ is given by the Pythagorean theorem:

F=√{ (4N)^2+(3N)^2 }

F=√(16+9)

F=√25

F=5N

hence, the correct answer is option d. 5N​

Given:

Initial velocity (u)=30 m/s

Time (t)=10 s

Acceleration due to gravity (g)=9.8 m/s^2

First, calculate the displacement $s$ of the stone after 10 seconds using the second equation of motion:

s=ut−​gt^2 x 1/ 2

s=30×10−9.8×10^2 x 1/2

s=300−4.9×100

s=300−490

s=−190m

The negative sign indicates that the displacement is downwards, meaning the stone is 190 meters below the initial point after 10 seconds. Thus, the height of the tower is 190 meters.

Hence, the correct answers is option c. 200 m