List of practice Questions

If \( f\left(1 - \frac{1}{x} \right) = \frac{5x + 1}{x}, \, x \neq 0 \), then \( f(x) = k - x \). What is the value of \( k \)?
Let \( x \) be the median of the data: 23, 17, 19, 11, 7, 3, 13, 2, 5, 29. Let \( y \) be the median of the same data set obtained by replacing 2 by 21 and 13 by 31. What is the value of \( |x - y| \)?
The heights (in cm) of 8 students are recorded as 162, 163, 160, 164, 160, 170, 161, 164. The standard deviation of the data is closest to:
A team of four with at least two females is to be selected from among five male players P, Q, R, S and T and three female players K, L and M under the following conditions.
i. R cannot be put with K.
ii. P and M have to be together.
iii. K will always be with T.
iv. S cannot go with N.
A shopkeeper has two varieties of rice A and B. By selling A at ₹75 per kg, he loses 20%; and by selling B at ₹90 per kg, he gains 25%. If he mixes A and B in the ratio 4 : 5 and sells the mixture at ₹110.25 per kg, then his profit percentage is:
In a class of 100 students, 55 students passed in Mathematics and 65 passed in English. Five students failed in both the subjects. Let \( m \) be the number of students who passed in exactly one of the two subjects and \( n \) be the number of students who failed in at least one subject, then what is the value of \( (m - n) \)?
If \( 3\sin^2 x + 10\cos x - 6 = 0 \), \( 0^\circ<x<90^\circ \), then the value of \( \sec x + \cosec x + \cot x \) is:
The four sentences (labelled 1, 2, 3, 4) below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:
1.Man has used poisons for assassination purposes ever since the dawn of civilization, against individual enemies but also occasionally against armies.
2. These dangers were soon recognized, and resulted in two international declarations—in 1874 in Brussels and in 1899 in The Hague—that prohibited the use of poisoned weapons.
3. The foundation of microbiology by Louis Pasteur and Robert Koch offered new prospects for those interested in biological weapons because it allowed agents to be chosen and designed on a rational basis.
4. Though treaties were all made in good faith, they contained no means of control, and so failed to prevent interested parties from developing and using biological weapons.
Convert the sentence into indirect speech.:
He said, "I would buy a new house, if I were rich".
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements :
1. All cars are vehicles.
2. Some four-wheelers are cars.
Conclusions : I. Some four-wheelers are vehicles.
II. Some four-wheelers are not vehicles.
A and B are two sets such that \( n(A) = 12 \), \( n(B) = 15 \) and \( n(A \cup B) = 20 \). Then, \( n(B \cap A') - n(A \cap B') = ?
Given \( f(x) = \frac{-4x + 1}{4} \) and \( g(x) = \sqrt[3]{x} \), then \( (g \circ f^{-1})\left(\frac{3}{8}\right) = \)
Five jumbled up sentences, related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd one out and key in the number of the sentence as your answer:
Identify the word from options that has same meaning of given word
TACITURNITY
In an arithmetic progression, the 4th term equals three times the first term and the 7th term exceeds two times the third term by one. The sum of its first ten terms is:
X and Y are two points that are 135 m apart on the ground on either side of a pole and in the same line. The angles of elevation of a bird sitting on the top of the pole from X and Y are \( 30^\circ \) and \( 60^\circ \) respectively. The distance of Y from the foot of the pole (in m) is:
Find the missing term in the series: A15, B10, ______, D3.
The following passage consists of six sentences. The first and the sixth sentence (as S1 and S6) are given in the beginning. The middle four sentences in each have been removed and jumbled up. These are labelled as P, Q, R and S. You are required to find out the proper sequence of the four sentences
S1: I decided to take a chance.
S6: I wanted to travel and visit several places.
P: I wanted a new experience.
Q: The cooking and washing clothes everyday had taken away my happiness.
R: I was fed up of leading a monotonous life.
S: Going out and seeing the world was important for me.
Statement :
The doctor is of the opinion that the patient’s condition would become normal after this operation.
Conclusions: I. The patient’s condition is such that he can be operated upon.
II. Certain costly medicines can be administered to the patient and the operation may not be necessary.
Two persons A and B start moving at the same time towards each other from points x and y, respectively. After crossing each other, A and B now take \( \frac{4}{6} \) hours and 6 hours, respectively, to reach their respective destinations. If the speed of A is 72 km/h, then the speed (in km/h) of B is:

You are given a question and two statements. Identify which of the statements is/are sufficient to answer the question.
 If the breadth of a rectangle is 10 cm, then what is its length?
Statements:
I. If the length of the rectangle is increased by 25% and its breadth by 20%, its area increases by 70 cm\textsuperscript{2}.
II. The length remaining the same, if its breadth is increased by 20%, the ratio of the new area to the original area becomes 6:5.
In a year, out of 160 games to be played, a cricket team wants to win 80% of them. Out of 90 games already played, the success rate is \( 66\frac{2}{3} %\). What should be the success rate for the remaining games in order to reach the target?
Select the Venn diagram that best represents the relationship between the following classes.
Wolves, Goats, Mammals
The sum of the first 10 terms of the series \[ \frac{7}{3} + \frac{7}{15} + \frac{1}{5} + \frac{1}{9} + \dots \quad \text{where} \quad \text{HCF}(a,b) = 1. \] What is the value of \( |a - b| \)?
Question :
How is Q exactly related to P? Statements:
I. P’s father is the son of Q’s mother.
II. P’s sister R is the daughter of Q’s husband.