List of practice Questions

What should be added to the following expression so that the sum is 1? \[ \frac{9}{4} \times \frac{7}{18} \text{ of } \frac{72}{49} - \frac{7}{5} \text{ of } \frac{5}{28} \times \frac{2}{5} + \frac{3}{4} \times 2 \div \frac{31}{7} - \frac{2}{3} \times 7 \times \frac{3}{10} \]
For the nonempty sets \( A \) and \( B \), which of the following is NOT true? \( \overline{A} \) is the complement of A
If \( f(x) = \frac{x-1}{x+1} \), then which of the following will be true?
If U = { 1, 2, 3, 4, 5, 6, 7, 8 } is the universal set, A = { 2, 3, 6, 7 }, B = { 3, 4, 5, 6 }, and C = { 5, 6, 7, 8 }, then n[̅A ∩ (C - B)] + n[̅A ∩ (B ∨ C)] = k, where ̅A is the complement of set A. The value of k is:
Let \( A = \mathbb{R} - \{ 3 \} \) and \( B = \mathbb{R} - \{ 1 \} \). Let \( f : A \to B \) be defined by \( f(x) = \frac{x-2}{x-3} \). What is the value of \( f^{-1} \left( \frac{1}{2} \right) \)?
Let \( U \) be the universal set, and \( A \) and \( B \) be the subsets of \( U \). If \( n(U) = 450 \), \( n(A) = 200 \), \( n(B) = 205 \), and \( n(A \cap B) = 15 \), then \( n(\overline{A}\cap \overline{B}) \) is equal to:
The range of the function \( f(x) = \sqrt{16 - x^2} \) is:
Four figures have been given, out of which three are alike in some manner and one is different.
Select the figure that is different.
Select the figure that will come next in the following series.
Select the option that is related to the third figure in the same way as the second figure is related to the first figure.
option that is related to the third figure
‘A \# B’ means ‘A is not smaller than B.’
‘A @ B’ means ‘A is neither smaller than nor equal to B.’
‘A % B’ means ‘A is neither greater than nor equal to B.’
‘A \$ B’ means ‘A is neither smaller than nor greater than B.’
‘A \& B’ means ‘A is not greater than B.’ Read the following statements and conclusions and decide which of the conclusions is/are true.
Statements:
\( M @ N; S \& W; N \# S; W \$ Z \)
Conclusions:
I. \( N @ Z \)
II. \( S % M \)
III. \( Z @ S \)
‘A \# B’ means ‘A is not smaller than B.’
‘A @ B’ means ‘A is neither smaller than nor equal to B.’
‘A % B’ means ‘A is neither greater than nor equal to B.’
‘A \$ B’ means ‘A is neither smaller than nor greater than B.’
‘A \& B’ means ‘A is not greater than B.’ ‘A \& B’ means ‘A is not greater than B.’
Read the following statements and conclusions carefully and decide which of the conclusions is/are true.
Statements:
\( P % R; Q \$ S; R \# Q; S \& T \)
Conclusions:
I. \( S \& R \)
II. \( P @ S \)
III. \( T \# Q \)
A question is given, followed by two statements. Identify which of the statements is/are sufficient to answer the question.
Question:
What is the ratio of the cost price of an article to its printed price?
Statements:
I. The shopkeeper earns a profit of 8% on selling the article at a discount of 10% on the printed price.
II. The shopkeeper loses ₹15 on selling the article for ₹135 after giving a discount of 10% on the printed price.
Select the Venn diagram that best represents the relationship between the following classes.
Classes:
Relatives, Educated, Males
Which of the following equations would be correct if the signs ‘+’ and ‘\(\times\)’ are interchanged and so also the numbers ‘6’ and ‘12’?
A question is given, followed by two arguments. Decide which of the arguments is/are strong with respect to the question.
Question:
Should teachers of Indian universities be transferred from one state to another from time to time?
Arguments:
I. Yes. This would help in dissemination of knowledge beyond state boundaries.
II. No. It would be counter-productive as different states have different languages.
A question is given, followed by two statements. Identify which of the statements is/are sufficient to answer the question.
Question:
How is Virat related to Mayank’s son?
Statements:
I. Mayank’s wife is the sister of Virat’s father’s only son.
II. Mayank is the son-in-law of Rohit, whose only daughter Sheela is the sister of Virat.
A question is given, followed by two statements. Identify which of the statements is/are sufficient to answer the question.
Question:
Four girls, A, B, C and D, and four boys, E, F, G and H, are sitting around a circular table facing the centre such that no two boys are adjacent to each other. The distances between two neighbors are equal for all the persons. Who is sitting between C and D?
Statements:
I. D is facing B, who is third to the right of E. A is facing C, and F is facing E.
II. C is facing A, who is between E and H. D is second to the left of A, and G is second to the right of H.
A question is given, followed by two statements. Identify which of the statements is/are sufficient to answer the question.
Question:
Among five objects, V, W, X, Y and Z, V weighs as much as X. Which object is the second heaviest among all?
Statements:
I. Y is twice as heavy as W. W is 1.5 times as heavy as Z. W and Z together weigh as much as V and X together.
II. Y is twice as heavy as Z. Both Y and W together weigh as much as X and Z together.
A question is given, followed by two statements. Identify which of the statements is/are sufficient to answer the question.
Question:
Who is the tallest among A, B, C, D and E?
Statements:
I. E is taller than only C. B is taller than both A and C but shorter than D.
II. A is taller than both E and C. B is shorter than only D.
Consider the given statement and decide which of the given assumptions is/are implicit in the statement.
Statement:
Farmers are warned not to use chemical fertilizers just for the sake of increasing their crop yield.
Assumptions:
I. Crop yield would decrease as a result of using organic fertilizers.
II. Chemical fertilizers carry harmful effects.
Among five objects, M, N, P, Q and R, P is twice as heavy as M and N is thrice as heavy as R. Q is one and half times as heavy as M and twice as heavy as R. Which of the five objects is the heaviest?
B, D, F, G, and H are sitting in a row facing north. F is sitting to the immediate left of D. There are two persons sitting between D and G. B is sitting adjacent to G and to the immediate left of F. If G is not at any of the extreme ends, who is sitting exactly in the middle?
In a family of eight persons, A is the father of B, who is the brother of C. D is the daughter of E, who is married to B. F is the aunt of G, who is the brother of D. B’s nephew H is the son of C and the brother of J. How is E related to J?
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 snakes are reptiles.
2. Some reptiles are amphibians.
3. All amphibians are animals.
Conclusions:
I. Some snakes are amphibians.
II. Some animals are reptiles.