A sum of money was divided into 2 parts in the ratio 2:5. First part was invested for 2 years at the annual interest rate of 20% compounded annually. At what rate of simple interest per annum the second part must be invested for 2 years, so that the interest earned in both cases is the same?

A group of 630 children is arranged in rows for a group photograph. Each row contains three fewer children than the row in front of it. What number of rows is not possible?

How many triangles are there in the figure given below?

A number which, when increased by 15% becomes 161. What is the original number?

The length of the projection of $\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k}$ on $\vec{b} = -2\hat{i} + \hat{j} + 2\hat{k}$, is equal to:

If $8^{x-1}=(1/4)^{x}$, then the value of $\frac{1}{log_{x+1}4-log_{x+1}5}+\frac{1}{log_{1-x}4-log_{1-x}5}$ is

Consider the matrix $$B=\begin{pmatrix}{-1} & {-1} & {2} \\ {0} & {-1} & {-1} \\ {0} & {0} & {-1}\end{pmatrix}$$ . The sum of all the entries of the matrix $B^{19}$ is

The curve $y=\frac{x}{1+x\tan x}$ attains maxima

The scores of students in a national level examination are normally distributed with a mean of 500 and a standard deviation of 100. If the value of the cumulative distribution of the standard normal random variable at 0.5 is 0.691, then the probability that a randomly selected student scored between 450 and 500 is

Number of permutations of the letters of the word BANGLORE such that the string ANGLE appears together in all permutations, is

Let A and B be two square matrices of same order satisfying $A^2+5A+5I =0$ and $B^2+3B+I=0$ repectively. Where I is the identity matrix. Then the inverse of the matrix $C= BA+2B+2A+4I$ is

The captains of five cricket teams, including India and Australia, are lined up randomly next to one other for a group photo. What is the probability that the captains of India and Australia will stand next to each other?

The value of $\frac{d}{dx}\int ^{2\sin x}_{\sin {x}^2}{e}^{{t}^2}dt$ at $x=\pi$

There are two coins, say blue and red. For blue coin, probability of getting head is 0.99 and for red coin, it is 0.01. One coin is chosen randomly and is tossed. The probability of getting head is

The number of all even integers between 99 and 999 which are not multiple of 3 and 5 is

Let A = {1,2,3, ... , 20}. Let $R\subseteq A\times A$ such that R = {(x,y): y = 2x - 7}. Then the number of elements in R, is equal to

If x, y and z are three cube roots of 27, then  the determinant of the matrix $\begin{bmatrix}{x} & {y} & {z} \\ {y} & {z} & {x} \\ {z} & {x} & {y}\end{bmatrix}$ is 

Let $A=\{{5}^n-4n-1\colon n\in N\}$ and $B=\{{}16(n-1)\colon n\in N\}$ be sets. Then

Let $\vec{a}$, $\vec{b}$ and $\vec{c}$ be unit vectors such that the angle between them is ${\cos }^{-1}\Bigg{\{}\frac{1}{4}\Bigg{\}}$. If $\vec{b}=2\vec{c}+\lambda \vec{a}$, where $\lambda$ > 0 and $\vec{b}=4$, then $\lambda$ is equal to

Consider the sample space $\Omega={\{(x,y):x,y\in{\{1,2,3,4\}\}}}$ where each outcome is equally likely. Let A = {x ≥ 2} and B = {y > x} be two events. Then which of the following is NOT true?

Let the line $\frac{x}{4}+\frac{y}{2}=1$ meets the x-axis and y-axis at A and B, respectively. M is the midpoint of side AB, and M' is the image of the point M across the line x + y = 1. Let the point P lie on the line x + y = 1 such that the $\Delta$ABP is an isosceles triangle with AP = BP. Then the distance between M' and P is

Which one of the following is NOT a correct statement?

An equilateral triangle is inscribed in the parabola $y^2 = x$. One vertex of the triangle is at the vertex of the parabola. The centroid of triangle is

The angles of depression of the top and bottom of an 8m tall building from the top of a multi storied building are 30° and 45°, respectively. What is the height of the multistoried building and the distance between the two buildings?

The number of accidents per week in a town follows Poisson distribution with mean 2. If the probability that there are three accidents in two weeks time is $ke^{-6}$, then the value of k is

If $B=sin^2 y+cos^4 y$, then for all real y

Let $F_1, F_2$ be foci of hyperbola $\frac{{x}^2}{{a}^2}-\frac{{y}^2}{{b}^2}=1$, a>0, b>0, and let O be the origin. Let M be an arbitrary point on curve C and above X-axis and H be a point on $MF_1$ such that $MF_2\perp{{F}}_1{{F}}_2$, $MF_1\perp{{O}}{{H}}$, $|OH|=\lambda |OF_2|$ with $\lambda \in(2/5, 3/5)$, then the range of the eccentricity $e$ is

A circle with its center in the first quadrant touches both the coordinate axes and the line x -y - 2 = 0. Then the area of the circle is

If $\alpha$ and $\beta$ are the two roots of the quadratic equation $x^2 + ax + b = 0, (ab \ne 0)$ then the quadratic roots whose roots $\frac{1}{\alpha^3+\alpha}$ and $\frac{1}{\beta^3+\beta}$ is

The maximum value of $sinx+sin(x+1)$ is $k cos \frac{1}{2}$. Then the value of k is 

Let $\mathbb{R}\rightarrow\mathbb{R}$ be any function defined as $f(x)=\begin{cases}{{x}^{\alpha}\sin \frac{1}{{x}^{\beta}}} & {,x\ne0} \\ {0} & {,x=0}\end{cases}$, $\alpha , \beta \in \mathbb{R}$. Which of the following is true? ($\mathbb{R}$ denotes the set of all real numbers)

The number of 3-digit integers that are multiple of 6 which can be formed by using the digits 1,2,3,4,5,6 without repetition is

The circle $x^2 + y^2+ \alpha x+ \beta y+ \gamma=0$ is the image of the circle $x^2 + y^2- 6x- 10y+ 30=0$ across the line 3x + y = 2. The value of $[\alpha+ \beta+ \gamma]$ is (where [.] represents the floor function.)

Let $\vec{a}=2\hat{i}-3\hat{j}+4\hat{k}$, $\vec{b}=\hat{i}+2\hat{j}-\hat{k}$ and $\vec{c}=3\hat{i}+\hat{j}+\lambda \hat{k}$ be the co-terminal edges

The area enclosed between the curve y = sin x, y = cosx, $0\leq x\leq\frac{\pi}{2}$ is

Given the equation $x+y =1$, $x^2+y^2 =2$, $x^5 +y^5 =A$. Let N be the number of solution pairs (x,y) to this system of equations. Then AN is equal to

Number of three digit numbers that can be formed using 0, 1, 2, 3 and 5 where these digits are allowed to repeat any number of times, is equal to

Let $g:\mathbb{R}\rightarrow \mathbb{R}$ and $h:\mathbb{R}\rightarrow \mathbb{R}$, be two functions such that $h(x) = sgn(g(x))$. Then select which of the following is not true?( $\mathbb{R}$ denotes the set of all real numbers, sgn stands for signum function)

An airplane, when 4000m high from the ground, passes vertically above another airplane at an instant when the angles of elevation of the two airplanes from the same point on the ground are 60° and 30°, respectively. Find the vertical distance between the two airplanes.

Suppose $t_1, t_2, ...t_55$ are in AP such that $\sum ^{18}_{l=0}{{t}}_{3l+1}=1197$ and ${{t}}_7+{{3}}t_{22}=174$. If $\sum ^9_{l=1}{{{t}}_l}^2=947b$, then the value of $b$ is

Let E and F be two events such that P(E) > 0 and P(F) > 0. Which one of the following is NOT equivalent to the condition that $P(E) =P(E|F)$?

What is the general solution of the equation $tan \theta + cot \theta = 2$ ?

If $cos^2(10°)cos(20°)cos(40°)cos(50°) cos(70°) = \alpha+\frac{\sqrt{3}}{16} cos(10°)$, then $3\alpha^{-1}$ is equal to

The slope of the normal line to the curve $x = t^2 + 3t - 8$ and $y = 2t^2 - 2t - 5$ at the point (2,-1) is

A tower subtends an angle of 30° at a point on the same level as the foot of the tower. At a second point h meters above the first, the depression of the foot of the tower is 60°. What is the horizontal distance of the tower from the point?

There are 40 female and 20 male students in a class. If the average heights of female and male students are 5.15 feet and 5.66 feet, respectively, then the average height (in feet) of all the students in the class equals

Let $x$ be a positive real number such that $x^{(8log_5(x)-24)}=5^{-4}$. Then the product of all possible values of x is =

The obtuse angle between lines 2y = x + 1 and y = 3x + 2 is

What is the value of $\lim _{{x}\rightarrow\infty}-(x+1)\Bigg{(}{e}^{\frac{1}{x+1}}-1\Bigg{)}$?

The value of $\int ^{\frac{\pi}{2}}_0\frac{(1+2\cos x)}{({2+\cos x)}^2}dx$

Read definition and all four choices carefully, and find the answer that provides the best example of the given definition. Answer the question solely on the basis of the definition given.
Definition: An informal gathering occurs when a group of people get together in a casual, relaxed manner.

Which situation below is the best example of an informal gathering?

In a certain code language, the word "REASON" is encoded as TDDQSK. Using the same rule, how is the word PRAYER coded?

Four people (P,Q,R & S) are standing in a queue. Q is ahead of P. R is between P and S. If S is at the end of the queue, who is at the front of the queue?

Statements:
I. The meteorological department predicts deficient rainfall during monsoon season.

II. The GDP growth estimates have been revised downwards by the government.

Choose the correct option:

A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips back 20 feet before he again starts climbing in the beginning of the next hour. If he begins his ascent at 8.00 am., at what time will he first touch a flag at 120 feet from the ground?

In a remote research outpost, five scientists (Dr. Anand, Dr. Beena, Dr. Chirag, Dr. Dinesh, and Dr. Elango) are studying a rare phenomenon. They communicate through a secure, text-based system. Over the course of an hour, the following exchanges occur: At the end of this hour, who has received the most messages directly from other scientists within the group? (Consider only messages sent within the described hour and only between the five scientists mentioned).

The percentage change in area of a rectangle by decreasing its length and increasing its breadth by 5% is

In a certain code language, 'SUN' is written as 'RWK' and 'MOON' is written as 'LQLR'. Following the same pattern, how will 'STAR' be written?

If a number is increased by 30% and then decreased by 20%, what is the net change?

A two digit number is such that the product of its digits is 12. If 36 is added to the number, the digits interchange their places. What is the number?

At an IIM entrepreneurship summit, two young founders - Karan and Deepak - introduced their startup. In their quirky opening, they said: "The product of our ages is 240. And just like in our startup strategy, twice Deepak's age is 4 years more than Karan's age." How old was Deepak two years ago?

Average Cost (AC) is defined as the sum of Average Fixed Cost (AFC) and Average Variable Cost (AVC), and dumping is defined as selling a product at a price less than AC but more than AVC. A company in India, suddenly, found that the demand for its product "ZOOM" has fallen to 60% of the output produced in that financial year. As a result, the company must sell 40% of the produced output in a foreign market. If it decides to "dump" 40% of its output in a neighbouring country (by reducing the price by 20%), what would be the objective of its 'dumping strategy', among the following? (The company has set a profit margin of 10% of AC while fixing the price of its product for sale in India).
(a) To minimize losses,
(b) to maximize profits,
(c) to contribute to the recovery of fixed costs,
(d) to contribute to the recovery of variable costs

What is the next number in each of the following 3 sequences?

Ten years ago, Ram was twice as old as Shyam. Ten years from now, the ratio of their ages will be 3:2. What is Ram's present age?

Consider the following statements followed by two conclusions. Statements: 1. Some men are great. 2. Some men are wise 

A, B, C, D, E, F and G are travelling in three different vehicles: Swift, Creta, and Nexon. There are at least two passengers in each vehicle. Among them, only two are male. There are two engineers, two doctors and three teachers.What is the profession of F?

If 1st January 2022 was a Saturday, what day of the week will 1st January 2023 be?

Statements: 

Which word in the following is the "odd man" out?

If John's mother's father's granddaughter is Maria, what is Maria's relation to John?

A person walks 8 km north, turns right, walks 4 km, turns right again and walks 6 km. Finally, he turns left and walks 3 km. How far is he from the starting point?

Consider a sequence formed by concatenating the positive integers in increasing order: 12345678910111213 ... Which among the following is the closest to the 2028th digit in this infinite sequence?

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° degree and 45° repectively. If the lighthouse is 100 m high, the distance between the two ships is

A research team is studying the effects of three different fertilizers (X, Y, and Z) on the growth of a specific plant species. They have four experimental plots with different fertilizer combinations:After a period of observation, they note the following:Based on these observations, which of the following conclusions is best supported?