The weight of $X$, in kg, is denoted by $X$. The weights of $A$, $B$, $C$, $D$, $P$, $Q$, $R$ and $S$ are measured. Given : $A + B + C + D = 17$ $A + C = 6$ $P + Q + S + D = 15$ $P + Q + R + B = 17$ $P = R \text{ and } Q = S$

Which one of the following statements is correct?

How many words can one form by shuffling the letters of the word QUEUE, if Q is always followed by U? The words thus formed need not necessarily have any meaning.

$X$, $Y$ and $Z$ jump forward $4'$, $6'$ and $5'$, respectively. At 8 AM, they all land on mark $199'$. How many times will they all land on the same mark (need not be at the same moment) between mark $195'$ and $1000'$, if all of them cross mark $1000'$ by 9 AM?

If $10^m \times 1000 \times n = 75^{25} \times 25^{32} \times 32^{75}$, where $n$ is not divisible by $10$, then the value of $m$ is

Three variables $x$, $y$ and $z$ take values $2, 3, 4$ or $5$ such that their values are always distinct. If $M$ and $N$ denote the largest possible value and the smallest possible value, respectively, for the expression $\{(x \times y) + z\}$; then $M - N$ is

The speed of a train $T$ is $100$ km per hour and the speed of a person $P$ is $4$ km per hour. $T$ crosses $P$ in $15$ seconds, if $P$ travels along the direction of motion of $T$. If $P$ travels along the opposite direction of $T$, then in how much time does $T$ cross $P$, in seconds, approximately?

$X$ receives three coins of different denominations : $1$, $2$, $5$, $10$ and $20$. If the total amount received by $X$ is $m$, does $X$ receive a coin of denomination $5$? Statement I : $m$ is not a prime number. Statement II : The sum of the digits of $m$ is greater than $5$.

If $x$, $y$ and $z$ are integers, each greater than $1$, then is $x$ a prime number? Statement I : $xy^2 = 116$ Statement II : $xz = 261$

Consider the following three statements, namely S1, S2 and S3 :

S1. Protecting the environment is an existential exigency for humans, given the impact of environmental degradation on climate change.

S2. Scientific consensus has not been achieved with regard to the extent of the contribution of human intervention to climate change.

S3. Environmental activism includes climate alarmism and other extremist points of view that often become the focus of climate change deniers.

Which of the following relationships based on the statements given above is/are correct?

1. S3 is a counterpoint to S1
2. S3 is unconnected to S1 and S2
3. S2 could be the reason for S3

Select the answer using the code given below.

A toy $T$ jumps forward or backward. In each forward jump, it moves $5'$ forward whereas in each backward jump, it moves $2'$ backward. If in $31$ jumps, $T$ moves exactly $15'$ forward, then what is the difference of the number of forward and backward jumps?

In a recruitment process, the selection of candidates is based on their performance in three components. The weightages of the components 1, 2 and 3 are $0.2$, $0.3$ and $0.5$, respectively. Use the data given below and find the cutoff score if exactly three candidates are to be selected :

For two distinct real numbers $x$ and $y$, which of them is bigger? Statement I : $x^2 < y < 1$ Statement II : $y < \sqrt{x} < 1$

The top of a table is rectangular and its dimensions are $6' \times 10'$. Two rectangular portions of the table top are painted in blue colour; both these portions have dimensions $2.5' \times 8'$ and each of them has exactly two sides common with two edges of the table top. If the table is fixed to the ground and the remaining portion of the table top is painted in white, how many different patterns are possible when observed from above?

Three partners $A$, $B$ and $C$ entered into a business. $A$ invested one-third of the capital for one-third duration. $B$ invested one-fourth of the capital for one-fourth duration. $C$ invested the remaining capital for the whole duration. Out of a profit of ₹ $17,000$, how much profit will $C$ get?

There are two chemicals which do not react with each other. A container contains $10$ litres of the chemical $A$. One litre of this chemical is removed from it and one litre of the chemical $B$ is poured. Then one litre of the mixture is removed from the container and one litre of $B$ is poured. If this process of replacing one litre of the mixture by one litre of $B$ is performed once more, then what is the volume of $B$ that is present in the container approximately (in percentage)?

If $x$ and $y$ are integers, then is $x$ even? Statement I : $x^2 y^2$ is even. Statement II : $1 + x^2 + y^2$ is odd.

A shopkeeper employs a delivery boy and gives him a motorcycle for home delivery. For every delivery, the boy is given ₹ $5$. At the end of the day, he also gets ₹ $2$ for every kilometre of the distance covered in the day. The boy wants to earn more than ₹ $500$ a day, but does not want to travel more than $100$ km. Which of the following numbers of deliveries would definitely meet his target?

If the product of the HCF and LCM of two distinct numbers is the cube of one of the numbers, then which of the following statements is/are correct?

I. The difference of the numbers is an even number. II. One of the numbers is a perfect square.

Select the answer using the code given below.

If $x$ and $y$ are two digits and the number $4x5y790$ is divisible by $11$, then what is the remainder, if $x+y$ is divided by $11$?

The class average $x$ in a test increases by $4$ when the score of a student is rectified, whose corrected score is $100$ instead of $0$. Later, the score of another student was found to have been recorded as $81$ in place of $56$. If there are no other corrections and the final corrected average is $y$, then $y - x$ is

For $\frac{1}{3} < x < y < 2$, which of the following statements is/are always correct? I. $x + \frac{1}{x} < y + \frac{1}{y}$ II. $\frac{\sqrt{1 + y^2}}{y} < \frac{\sqrt{1 + x^2}}{x}$ Select the answer using the code given below.

Seven persons $A$, $B$, $C$, $D$, $E$, $F$ and $G$ travel by three cars $X$, $Y$, $Z$. $A$ and another two of them travel by $X$. Only $E$ travels with $G$. $C$ travels by $Z$, but $B$ does not travel by $Y$. Besides, $A$ and $B$ do not travel by the same car. Then which of the following are correct? I. No one travels alone. II. Only $D$ travels with $F$. III. Only $C$ travels with $B$. Select the answer using the code given below.

Suppose $x$, $y$ and $z$ are variables taking positive real numbers as their possible values. It is given that $y$ is directly proportional to $x^2$ and $x$ is inversely proportional to $z$. For $z = \frac{7}{25}$, the values of $x$ and $y$ are $5$ and $50$, respectively. If $y = 98$, what is $z$ equal to?

An explosion takes place at a certain distance from an army camp. As soon as the sensor in the camp receives the sound of the explosion, a drone starts flying towards the spot of explosion. The drone clicks a picture from the spot and the camp receives it at the same time. Immediately another drone starts flying to the spot and it also sends a picture as soon as it reaches the spot. The two pictures were received at 5:02 PM and 5:05 PM, respectively. If the speed of the drones is 30 m/s, at what time did the explosion take place? Assume that the speed of sound is 300 m/s.

How many three-digit numbers can be expressed as an integral power of $2$?

$X$ and $Y$ are two runners who run for the same duration of time on the same circular track. They started running at the same time in the same direction with uniform speeds. When $X$ completed $7$ rounds, $Y$ did exactly $5$. After completing $5$ rounds, $Y$ changed his direction and started running in the opposite direction with speed which is double of his earlier speed. On the other hand, $X$ continued to run with the same speed. They stopped running when $X$ completed exactly $21$ rounds. How many times did $X$ and $Y$ meet after they had started and before they finally stopped?

In an objective type question paper, $5$ marks are awarded for a correct answer and $2$ marks are deducted for a wrong answer. A student attempted all the questions and got a score of $69$. Had he been awarded $4$ marks for a correct answer and $1$ mark deducted for a wrong answer, he would have scored $84$. How many questions were there in the question paper?

What is the minimum number of times one needs to measure to get $298$ litres of water from a tank, if the measuring cylinders have capacities $1$ litre, $6$ litres, $25$ litres and $100$ litres?

The digit in the unit place of the number $6^{129} \times 7^{307}$ is

A person saves 10% of his salary every month. If his salary increases by 12% and the expenditure increases by 10%, then what will be the change in his saving per month?

How many times does $5$ appear in all two-digit positive integers?

There are four types of weights, namely $1$ kg, $2$ kg, $5$ kg and $10$ kg. What is the maximum number of different ways one can measure $20$ kg, if at least eight but not more than eleven weights of $1$ kg are to be used while measuring?

$X$ travels $6$ km on a bicycle with average speeds of $5$ km per hour, $10$ km per hour and $4$ km per hour during the first $1$ km, the next $2$ km and the remaining $3$ km, respectively. $Y$ travels the same distances with average speeds of $4$ km per hour, $10$ km per hour and $5$ km per hour, respectively. How many minutes early will $Y$ complete the journey if both $X$ and $Y$ start at the same time?

In a sequence of numbers, each number other than the first two is the sum of the two immediately preceding numbers from it. If the first two numbers in the sequence are $4$ and $7$, then the sixth number is

The ratio of male to female workers in two companies $A$ and $B$ is $13 : 10$ and $7 : 5$, respectively. If both the companies have the same number of female workers, then what is the ratio of the total number of workers in $A$ to those in $B$?

A cut on a solid object divides the object into two parts where the new surfaces thus produced are plane. On the other hand, one single cut can be used to cut more than one object at a time. In an experiment, the total number of pieces produced by applying $n$ cuts is denoted by $x_n$. The experiment is performed on a solid cube where pieces remain unmoved after each cut. In this experiment, if after the third cut, the pieces are identical, then which of the following is not a possible value for $x_4$?

An alloy $P$ contains $20\%$ copper and $80\%$ zinc by weight. Another alloy $Q$ contains $60\%$ copper and $40\%$ zinc by weight. A third alloy $R$ is to be prepared from $P$ and $Q$ so that it contains equal amount of copper and zinc. In what ratio, amounts of $P$ and $Q$ be mixed in order to get $R$?

$A$ is a 2-digit number with different digits. $B$ is also a 2-digit number and is obtained by reversing the digits of $A$. If $A - B$ is a multiple of $27$, where $A > B$, how many such different $A$'s are possible?

There are three types of rectangular tiles : $3' \times 3'$, $3' \times 7'$ and $3' \times 11'$. An area of rectangular shape of dimensions $3' \times 100'$ is to be covered using these tiles without breaking them. If $x$ and $y$ are the maximum and minimum numbers of tiles of various sizes, respectively, that can be used to cover the area exactly, then $x - y$ is

A train has to complete a journey of $800$ km. If it meets a minor accident, its speed becomes half of the existing speed. If there is a mechanical defect, the speed becomes one-fourth of the existing speed. On its way, the train meets with a minor accident after $200$ km; and $400$ km thereafter, it develops a mechanical defect. Had the train developed the mechanical defect after $200$ km and met the minor accident $400$ km thereafter, it would have taken $4$ more hours to reach its destination. What was the original speed of the train in km per hour?