The probability distribution function of a random variable $X$ is given by $f(x) = \dfrac{x}{18}, ; 0 \le x \le 6$ $= 0, \text{ otherwise}$ Then the value of $P(X > 2)$ is

Find the probability of guessing correctly at least six of 10 answers in a True or False objective test.

If, for a binomial distribution, the number of trials is $9$, the variance is $2$ and the probability of success is greater than that of failure, find the probability of both success.

Two customers, Rachana and Bhakti, are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on consecutive days?

A pendulum swings through an angle of $30^\circ$ and describes an arc of $17.6\ \text{cm}$ in length. Find the length of the pendulum.

Two cubes each of volume $64\ \text{cm}^3$ are joined end to end. Find the surface area of the resulting cuboid.

The incomes of $A$, $B$ and $C$ are in the ratio $7 : 9 : 12$ and their spending are in the ratio $8 : 9 : 15$. If $A$ saves $\dfrac{1}{4}$ of his income, then the savings of $A$, $B$ and $C$ are in the ratio of

Two trains, A and B, start simultaneously from two stations $300\ \text{km}$ apart. Train A travels at $60\ \text{km/h}$, and Train B travels at $90\ \text{km/h}$. If a bird starts flying from Train A towards Train B at $120\ \text{km/h}$ and immediately turns back upon reaching Train B, continuing this until the trains meet, what total distance does the bird cover?

Find the distance from the eye at which a coin of $2\ \text{cm}$ diameter should be held so as to conceal the full moon whose angular diameter is $31'$.

A circular wire of radius $7.5\ \text{cm}$ is cut and bent to lie along the circumference of a hoop of radius $120\ \text{cm}$. Find (in degrees) the angle subtended at the hoop’s centre.

The population of a town grows at $10%$ per year. How long will it take for the population to triple?

A company models the rate of change of concentration by $(y^2+3xy),dx+(x^2+xy),dy=0$, with $y=1$ when $x=1$. Find $y$ as a function of $x$ (choose the correct option).

A family of parabolas $y=ax^{2}$ $(a>0)$ has vertices on the $x$–axis and axis parallel to $y$–axis. The differential equation of this family is:

The coefficient of $x^{n}$ in the expansion of $(1+x)^{2n}$ and $(1+x)^{2n-1}$ are in the ratio

The equation of a parabola is $y^2=4x$. Which of the following points lies on the parabola?

In $\triangle ABC$, sides are $a=9$, $b=7$, $c=12$. Find angle $C$ (opposite side $c$) using the Law of Cosines.

The number of real solutions of $\sqrt{1+\cos 2x}=\sqrt{2},\cos^{-1}(\cos x)$ in $\left[\frac{\pi}{2},\pi\right]$ is

Given $,\dfrac{dy}{dx}+y=1,$ with $y(0)=2$, find $y(1)$.

The valid range of $x$ for which $\cos^{-1}(2x-3)$ is defined is

The perpendicular distance of the point $P(1,2,3)$ from the line $\dfrac{x-6}{3}=\dfrac{y-7}{2}=\dfrac{z-7}{-2}$ is

The projections of a line segment on the $X,Y,Z$ axes are $12,4,3$ respectively. The length and direction cosines are

If $\tan^{-1}\left(\dfrac{1-x}{1+x}\right)=\dfrac{1}{2}\tan^{-1}x$, then $x$ is

Find the total number of ways to put $20$ balls into $5$ boxes so that the first box contains only one ball.

The number of parallelograms formed by a set of $4$ parallel lines intersecting another set of $3$ parallel lines is

A study finds that employees working fewer hours per week are more productive during their working hours and concludes that reducing working hours can increase productivity and job satisfaction. Which assumption underpins the conclusion?

A study found that employees who worked fewer hours per week were more productive. Which of the following, if true, weakens the study’s conclusion?

In a certain code “SAND” is written as “UCPF”. How is “STONE” written in that code?

Three of the following four words are alike in a certain way and one is different. Select the odd one.

Look at this series: $53,53,40,40,27,27,\ldots$ What number should come next?

In a certain language, “BOOK” is written as $4300$, “MATE” as $3900$. Then $1600$ represents which word?

If CLAUSE is coded as ECSLUA, then the code of UMPIRE will be

Birds on trees $A$ and $B$ say: if $2$ from $B$ move to $A$, numbers are equal; if $2$ from $A$ move to $B$, then $B$ becomes double of $A$. Find numbers on $A,B$.

How many pairs of letters are there in “CAMBRIDGE” that have as many letters between them in the word as in the English alphabet?

Five friends $A,B,C,D,E$ travel from Goa to five cities: Chennai, Kolkata, Delhi, Varanasi, Bangalore using bus, train, airplane, car, boat (all distinct). Given: $C\to$ Bangalore by car; $D\to$ by boat; $B\to$ Kolkata by airplane; $E\to$ by train; the Delhi traveler did not use boat; Goa has no bus to Delhi or Chennai. Who traveled to Delhi?

Three of the following four are alike in a certain way and hence form a group. Which one does not belong to the group?

The question is based on the six numbers: $283, 347, 518, 829, 748, 827$. If the first and third digits of each number are interchanged, which number will be the third lowest?

Teacher’ is related to ‘school’ in the same way as ‘cook’ is related to …….

If the digits of $5734629$ are arranged in ascending order from left to right, how many digits remain in the same position?

A man travels $2,\text{km}$ to the north and turns east and travels $10,\text{km}$, and again he turns north and travels $3,\text{km}$ and again turns to the east and travels $2,\text{km}$. How far is he from the starting point?

Ten years ago, the average age of $A$ and $B$ was $20$ years. The average age of $A,B,C$ is $30$ years today. How old will $C$ be after $5$ years?

Find the odd one out:

Complete the analogy: Book : Reading :: Knife : ?

If “APPLES” is coded as “BQQMFT”, how is “ORANGE” coded?

What is the next number in the sequence: $1,4,9,16,25,\ ?$

Which word does not belong to the group?

Complete the analogy: Pineapple : Fruit :: Carrot : ?

If “BEAN” is coded as “CFBO,” how is “CORN” coded?

What is the opposite of “Transparent”?

All roses are flowers. Some flowers are yellow. Which of the following is true?

Find the missing number in the series: $3,9,27,81,?$

What type of verb is “will” in the sentence, “I will go to the cinema.”?

Which sentence uses a conjunction correctly?

Choose the correct synonym for the word “abundant”:

Imagine a short story titled “The Mysterious Garden,” which narrates the adventures of two children, Alice and Theo, who discover a hidden garden behind their home. The garden is magical, with plants that talk and animals that walk on two legs. One day, they meet a wise old tree that gives them a series of riddles to solve, promising a treasure if they succeed. What is the main conflict in the story?

Which word best describes something extremely ordinary and commonplace?

Which of the following sentences demonstrates irony?

The ancient art of storytelling has been a cornerstone of human communication for millennia. Stories are not just entertainment; they serve as a means to convey values, traditions, and knowledge. In many cultures, oral storytelling was a primary method for passing down history before the advent of written language. Today, storytelling has taken on new forms, from novels to movies, but its core purpose remains the same: to connect people and make sense of the world. What is the main purpose of the passage?

The ancient art of storytelling has been a cornerstone of human communication for millennia. Stories are not just entertainment; they serve as a means to convey values, traditions, and knowledge. In many cultures, oral storytelling was a primary method for passing down history before the advent of written language. Today, storytelling has taken on new forms, from novels to movies, but its core purpose remains the same: to connect people and make sense of the world.
What can be inferred from the passage about oral storytelling?

What can be inferred from the statement: "The new policy has left many employees disgruntled"?

Choose the correct option to complete the sentence: "Neither the manager nor the employees _____ responsible for the mistake."

Choose the correct word to fill the blank: "The new policy aims to _______ equality among all citizens."

The area of the equilateral triangle is 49√3 cm^². Taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle. Find the area of triangle not included in the circles. (Take √3 =1.73)

Identify the correct sentence:

The invention of the printing press was a turning point in human history. It enabled mass production of books, leading to the widespread dissemination of knowledge and ideas. This innovation also laid the foundation for the Reformation and the Enlightenment.” What was the primary effect of the printing press?

Calculate the area other than the area common between two quadrants of circles of radius 16 cm each, which is shown as the shaded region in the figure given.

Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.

Choose the sentence with correct punctuation:

If X denotes the number obtained on the uppermost face of cubit die when it is tossed, then E(X) is

Find the part with an error: "The committee have decided to postpone their meeting until next week."

Global warming is causing unprecedented climate changes worldwide. Rising temperatures are leading to melting ice caps, rising sea levels, and extreme weather events." What is one major consequence of global warming mentioned in the passage?

Identify the sentence with correct subject-verb agreement.

Which of the following is not a type of computer architecture?

What is the binary equivalent of the decimal number 13?

What is the result of the binary subtraction 1100 − 1010 using 2's complement?

Which of the following is a correct way to declare a variable in C?

What is the main difference between a process and a thread?

Which data structure uses the FIFO (First In, First Out) principle?

Which register in a CPU holds the address of the next instruction to be executed?

Interval between the time of submission and completion of the job is called...

________ is a technique of improving the priority of process waiting in Queue for CPU.

What traversal method is used to traverse a binary tree in the order: left subtree, root, right subtree?

What does the term RISC stand for in computer architecture?

The first generation of computers used which of the following components?

Convert the decimal number $45$ into binary.

How many bits are used to represent a character in ASCII encoding?

Which statement is true about compilers?

Which of the following scheduling algorithms is non-preemptive?

What is the hexadecimal representation of the binary number 10110111₂?

Simplify the Boolean expression A·(B + C).

In a Venn diagram, what does the overlapping region of two sets A and B represent?

Select a figure from among the answer figures which will continue the same series as given in the Problem Figures.

How many parallelograms are there in the following figure?