If $ \theta = \tan^{-1}\dfrac{1}{1+2} + \tan^{-1}\dfrac{1}{1+2\cdot3} + \tan^{-1}\dfrac{1}{1+3\cdot4} + \ldots + \tan^{-1}\dfrac{1}{1+n(n+1)} $, then $\tan\theta$ is equal to:

If $(1 + x - 2x^2)^6 = 1 + a_1 x + a_2 x^2 + \ldots + a_{12} x^{12}$, then the value of $a_2 + a_4 + a_6 + \ldots + a_{12}$ is:

A square with side $a$ is revolved about its centre through $45^\circ$. What is the area common to both the squares?

A and B throw a die in succession to win a bet with A starting first. Whoever throws ‘1’ first wins Rs. 110. What are the respective expectations of A and B?

How many different paths in the $xy$-plane are there from $(1,3)$ to $(5,6)$, if a path proceeds one step at a time either right (R) or upward (U)?

If the distance of $(x,y)$ from the origin is defined as $d(x,y) = \max(|x|,|y|)$, then the locus of points where $d(x,y)=1$ is:

If $\sin^{-1}x + \cos^{-1}(1-x) = \sin^{-1}(1-x)$ then $x$ satisfies the equation:

A and B are independent witnesses. Probability A speaks the truth = $x$, Probability B speaks the truth = $y$. If both agree on a statement, the probability that the statement is true is:

If $A$ is a $3\times 3$ matrix with $\det(A)=3$, then $\det(\operatorname{adj}A)$ is:

A set contains $(2n+1)$ elements. If the number of subsets that contain at most $n$ elements is $4096$, then the value of $n$ is:

The total number of relations that exist from a set $A$ with $m$ elements into the set $A \times A$ is:

Water runs into a conical tank of radius $5$ ft and height $10$ ft at a constant rate of $2\text{ ft}^3/\text{min}$. How fast is the water level rising when the water is $6$ ft deep?

The probability that a man who is 85 yrs old will die before attaining the age of 90 is $1/3$. $A_1, A_2, A_3, A_4$ are four persons aged 85 yrs. The probability that $A_1$ will die before attaining 90 and will be the first to die is:

A box open at the top is made by cutting squares from the four corners of a $6 \times 6$ m sheet. The height of the box for maximum volume is:

If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors, then $|\vec{a}-\vec{b}|^2 + |\vec{b}-\vec{c}|^2 + |\vec{c}-\vec{a}|^2$ does not exceed:

Let $f(x) = \lfloor x^2 - 3 \rfloor$ where $\lfloor \cdot \rfloor$ is the greatest integer function. Number of points in $(1,2)$ where $f$ is discontinuous:

If $a + b + c \neq 0$, the system of equations: $(b+c)(y+z) - ax = b - c$ $(c+a)(z+x) - by = c - a$ $(a+b)(x+y) - cz = a - b$ has:

If $y = f(x)$ is odd and differentiable on $(-\infty,\infty)$ such that $f'(3) = -2$, then $f'(-3)$ equals:

The value of $\displaystyle \int_{0}^{\pi} \frac{x \sin x}{1+\cos^2 x},dx$ is:

If $\tan^{-1}(2x) + \tan^{-1}(3x) = \dfrac{\pi}{4}$, then $x$ is:

The equation $\sin^4 x + \cos^4 x + \sin 2x + \alpha = 0$ is solvable for:

If $x < -1$ and $2^{|x+1|} - 2^x = |2x - 1| + 1$ then the value of $x$ is:

The vector $\vec{B} = 3\vec{i} + 4\vec{k}$ is to be written as the sum of a vector $\vec{B_1}$ parallel to $\vec{A} = \vec{i} + \vec{j}$ and a vector $\vec{B_2}$ perpendicular to $\vec{A}$. Then $\vec{B_1}$ is:

Find $k$ in the equation $x^3 - 6x^2 + kx + 64 = 0$ if roots are in geometric progression.

If $P = {(4n - 3n - 1) : n \in N}$ and $Q = {(9n - 9) : n \in N}$, then $P \cup Q$ equals to:

If $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$, then $I + A + A^2 + A^3 + \cdots \infty$ equals:

$A_1, A_2, A_3, A_4$ are subsets of $U$ (75 elements). Each $A_i$ has 28 elements. Any two intersect in 12 elements. Any three intersect in 5 elements. All four intersect in 1 element. Find the number of elements belonging to none of the four subsets.

$ABC$ is isosceles with $AB = AC$. $BC$ is parallel to x-axis. $m_1, m_2$ are slopes of the medians from $B$ and $C$. Then:

The smaller area bounded by $y = 2 - x$ and $x^2 + y^2 = 4$ is:

There are 10 points, out of which 6 are collinear. Number of triangles formed:

Number of distinct integer values of $a$ satisfying $2^{2a} - 3(2^{a+2}) + 25 = 0$ is:

A man has 5 coins: 2 double-headed 1 double-tailed 2 normal He randomly picks a coin and tosses it. Probability that the lower face is a head is:

If $A = \cos^2\theta + \sin^4\theta$, then for all values of $\theta$:

From 50 students: 37 passed Math, 24 Physics, 43 Chemistry. At most 19 passed Math & Physics, at most 29 passed Math & Chemistry, at most 20 passed Physics & Chemistry. Intersection of all 3 is $x$. Find maximum possible value of $x$.

Number of solutions for $\tan^{-1}\sqrt{x(x+1)} + \sin^{-1}\sqrt{x^2 + x + 1} = \dfrac{\pi}{2}$ is:

If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar unit vectors and $\vec{a} \times (\vec{b} \times \vec{c}) = \dfrac{\vec{b} + \vec{c}}{\sqrt{2}}$, then the angle between $\vec{a}$ and $\vec{b}$ is:

The straight lines $\dfrac{x}{a} + \dfrac{y}{b} = k$ and $\dfrac{x}{a} + \dfrac{y}{b} = \dfrac{1}{k}$ (with $k\neq0$) meet on:

Events $A$ and $B$ satisfy: $P(A \cup B) = \dfrac{1}{6}$, $P(A \cap B) = \dfrac{1}{4}$, $P(A) = \dfrac{1}{4}$ Then events $A$ and $B$ are:

An anti-aircraft gun fires a maximum of four shots. Probabilities of hitting in the 1st, 2nd, 3rd, and 4th shot are 0.4, 0.3, 0.2 and 0.1 respectively. Find the probability that the gun hits the plane.

If $2x^4 + x^3 - 11x^2 + x + 2 = 0$ then the values of $x + \dfrac{1}{x}$ are:

If all digits 6 in the numbers from 1 to 100 are replaced by 9, by how much does the algebraic sum change?

Pick 1st, 2nd, 4th, 5th, 6th letters from REASONING, form another word, then write the first and last letters of the new word.

The sum of the numbers from 1 to 100 which are not divisible by 3 and 5 is:

A train travels 60 km, then due to an accident runs at $\dfrac{3}{4}$ of its former speed and reaches 40 minutes late. If the accident had occurred 25 km later, it would be 10 minutes earlier. Find the original speed and distance.

Find the remainder when $X = 1! + 2! + 3! + \cdots + 100!$ is divided by $240$.

Find the unit digit of $(13647)^{3265}$.

Find the value of $x$, if: $\left( 2^{\frac{1}{\log_x 4}} \right) \left( 2^{\frac{1}{\log_x 16}} \right) \left( 2^{\frac{1}{\log_x 256}} \right) \cdots = 2$

How many 5s are there in the number series each of which is immediately followed by 4 but not immediately preceded by 6? Series: 456 656 455 455 654 456 456 5454

You are in the land of logic where there are 3 types of rabbits. Blue rabbits always tell the truth, green rabbits sometimes tell the truth and red rabbits never tell the truth. A rabbit says to you: “I always lie.” What colour is the rabbit?

How many pairs of letters are there in the word PRISON such that the number of letters between them in the word is the same as in the English alphabet?

If A1 = {3}, A2 = {5, 7, 9}, A3 = {11, 13, 15, 17, 19}, A4 = {21, 23, 25, 27, 29, 31, 33} and so on, what is the average of the numbers of the set A20?

Identify the number of triangles in the given figure.

Reena met Natasha’s children. Rahul said, “The square of my age plus the cube of my sister’s age is 7148.” Preeti said, “The square of my age plus the cube of his age is 5274.”

Cars are safer than planes. Fifty percent of plane accidents result in death, while only one percent of car accidents result in death. Which of the following, if true, would most seriously weaken the argument above?

Bala had three sons. He had some chocolates which he distributed among them. To his eldest son, he gave 3 chocolates more than half the number of chocolates with him. To his second eldest son he gave 4 chocolates more than one third of the remaining number of chocolates with him. To his youngest son he gave 4 chocolates more than one fourth of the remaining number of chocolates with him. He was left with 11 chocolates. How many chocolates did he initially have?

Twelve villages in a district are divided into 3 zones with 4 villages per zone. The telephone department intends to connect villages so that every two villages in the same zone are connected with three direct lines and every two villages belonging to different zones are connected with two direct lines. How many direct lines are required?

A teacher gave a student the task of adding ‘N’ natural numbers starting from 1. After a while, the student reported his result as 700. The teacher replied that the result was wrong. The student realized he had added one number twice. Find the sum of digits of the number which the student had added twice.

Rajita has unique way of attempting the question paper having 50 questions. She starts from question 1 and attempts all questions which are in A.P. with a common difference of 3 in the forward direction and 3 in reverse direction. If she reaches a stage when she cannot attempt any more question, she starts in the reverse direction with the first unanswered question. She repeats the same process and when she reaches a stage when she can not process any further, she reverses her direction again starting with the first unanswered question.

Rajita has unique way of attempting the question paper having 50 questions. She starts from question 1 and attempts all questions which are in A.P. with a common difference of 3 in the forward direction and 3 in reverse direction. If she reaches a stage when she cannot attempt any more question, she starts in the reverse direction with the first unanswered question. She repeats the same process and when she reaches a stage when she can not process any further, she reverses her direction again starting with the first unanswered question.

All the letters of the word 'INDIA' are permuted… the 58th word in dictionary order is?

13 identical balls, one odd (heavier or lighter not known). Minimum weighings?

Sum of all 3-digit numbers (digits non-zero) where all digits are perfect squares.

Which number will be there in the place of question mark (?) in the following figure?

Divide Rs. 1074 (in whole Rs., having incremental amounts) into a number of bags so that any amount between Rs. 1 and Rs. 1074 can be given by selecting some bags without opening them. What is the minimum number of bags required?

After months of talent searching for an administrative assistant to the president of the college the field of applicants had been narrowed down to five (A, B, C, D and E). It was announced that the finalist would be chosen after a series of all day group personal interviews. The examining committee agreed upon the following procedure. 1. The interviews will be held once a week. 2. Three candidates will appear at any all day interview session. 3. Each candidate will appear at least once. 4. If it becomes necessary to call applicants for additional interviews, no more than one such applicant should be asked to appear the next week. 5. Because of a detail given in the written applications, it was agreed that whenever candidate B appears, A should also be present. 6. Because of travel difficulties, it was agreed that C will appear for only one interview.
 
At the first interview, the following candidates appear: A, B, and D. Which of the following combinations can be called for the interview to be held the next week?

After months of talent searching for an administrative assistant to the president of the college the field of applicants had been narrowed down to five (A, B, C, D and E). It was announced that the finalist would be chosen after a series of all day group personal interviews. The examining committee agreed upon the following procedure. 1. The interviews will be held once a week. 2. Three candidates will appear at any all day interview session. 3. Each candidate will appear at least once. 4. If it becomes necessary to call applicants for additional interviews, no more than one such applicant should be asked to appear the next week. 5. Because of a detail given in the written applications, it was agreed that whenever candidate B appears, A should also be present. 6. Because of travel difficulties, it was agreed that C will appear for only one interview.
 

When you reverse the digits of the number 13, the number increases by 18. How many other two digit numbers increase by 18 when their digits are reversed?

In the virtual memory system, the address space specified by address lines of the CPU must be ______ than the physical memory size and ______ than the secondary storage size.

To change upper case to the lower case letter in ASCII, correct mask and operation should be:

The switching expression corresponding to $f(A,B,C,D) = \Sigma(1,4,5,9,11,12)$ is:

Assuming all numbers are in 2’s complement representation, which of the following numbers is divisible by $11111011$?

Why is the width of a data bus so important to the processing speed of a computer?

A computer with a 32 bit word size uses 2’s complement to represent numbers. The range of integers that can be represented by this computer is:

On receiving an interrupt from an I/O device, the CPU:

A switching circuit that produces one in a set of input bits as an output based on the control value of control bits is termed as:

Index register in a digital computer is used for:

Micro programmed control unit is:

If someone is “gung ho” then he/she is:

The pleasures of the table are never of consequence to one naturally abstemious. The word abstemious can be replaced by:

A sentence has been given in active (or passive) voice. Out of the four alternatives select the one which best expresses the same sentence in passive (or active) voice. I know him.

Which of the underlined parts in the sentence given below is a mistake which may need to be deleted or modified? He can $\underline{\text{be able}}$ to pass the test in $\underline{\text{flying colours}}$ without any $\underline{\text{difficulties}}$ $\underline{\text{whatsoever}}$.

Identify the correct sentence.

Fill in the blank: I could not __________ him to attend the meeting.

For the word “QUIBBLE” find the most appropriate meaning from the alternatives given below:

The idiom “I will be a monkey’s uncle” means:

Find the antonym of the word “DISPARAGE”.

Choose the pair of words which exhibits the same relationship between each other as the given pair of words. WRITING : PLAGIARISM

Choose the word which can be used to replace the underlined word, in both the sentences. 1.It is certainly a thing which tempts people. 2.I take exception to what he has just said.