List of practice Questions

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') = ?
Let \( A = \{ 1, 2, 5 \} \), \( B = \{ 1, 2, 3, 4 \} \), and \( C = \{ 2, 5, 6 \} \) be the three sets. If \( D = [A \times (B \cap C)] \cap [(A - B) \times C] \), then which of the following is true?
If \( f(x) = \frac{x-1}{x+1} \), then for \( k>0 \), \( f^{-1} \left( \frac{1}{2k+3} \right) = ?
Which of the following functions satisfies these two criteria: \( f(0) = 0 \) and \( f(x+1) = 2f(x) + 1 \)?
If \( f(x) = \frac{1}{x^2 + 1} \), \( 0<x<1 \), then \( f^{-1} \left( \frac{1}{4} \right) + f^{-1} \left( \frac{3}{4} \right) \)= : ?
Consider the given statement and decide which of the given assumptions is/are implicit in the statement.
Statement:
This year the state will not import onions from other states.
Assumptions:
I. The onion production in the state would meet the consumer needs.
II. The quality of onions grown in other states is poor.
Select the figure that will come next in the following series.
figure that will come next in the following series.
Four cubes have been given, three of which are rotated versions of the same cube and one is different. Select the cube that is different.
Select the option that is related to the third figure in the same way as the second figure is related to the first figure.
related to the third figure
Select the figure that will come next in the following series.
figure that will come next in the following series
A team is to be formed from among four girls A, B, C and D and four boys P, Q, R and S with the following conditions.
i. B and S have to be together.
ii. Q and C cannot go together.
iii. A cannot be teamed with R.
iv. P has to go with D.
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.
Among five friends, Naresh is taller than Virat and Prakash. Hiten is shorter than Prakash but taller than Arun. If Arun is taller than Virat, then who will be in the middle if all of them stand in the ascending order of their heights?
Question :
Five friends A, B, C, D and E are standing in a line according to height from the shortest to the tallest. If A is the shortest, then who is the tallest of them all? Statements:
I. B is between E and C and D is between A and E.
II. There are two persons between A and B and C is taller than B.
Question :
In a class of 60 students, the ratio of boys to girls is 2 : 3. What is the rank of Neha, a girl student in the class? Statements:
I. 15 boys have scored more than Neha and 15 girls have scored less than her.
II. Neha’s rank is 10th among girls and the number of boys scoring less than Neha is twice the number of boys scoring more than her.
Question :
a, b and c are three numbers. Which is the largest number? Statements:
I. The sum of the squares of a, b and c is 371 and the difference between the largest and the smallest number is 10.
II. The square of the largest number exceeds the sum of the squares of the other two numbers by 79.
Select the Venn diagram that best represents the relationship between the following classes.
Wolves, Goats, Mammals
Study the given symbols.
A@ B means A is not smaller than B.
A # B means A is not greater 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.
Based on the symbols, read the given statements and conclusions carefully and decide which of the conclusions are true. % Statements Statements:
A) S & W
B) T % S
C) W @ T % Conclusions Conclusions:
I. Z # W
II. T $ S
III. S & Z
Study the given symbols.
A @ B means A is not smaller than B.
A # B means A is not greater 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.
Based on the symbols, read the given statements and conclusions carefully and decide which of the conclusions is/are true. % Statements Statements:
A) K & F
B) B @ G
C) B $ K % Conclusions Conclusions:
I. B & F
II. G # K
III. G % F
If the signs ‘+’ and ‘-’ are interchanged in each of the given equations, then which one equation would be correct?
Question :
Four boys A, B, C and D and four girls M, N, P and Q are sitting around a round table facing the centre such that no two girls are adjacent to one another. Who is sitting between P and Q? Statements:
I. A is sitting between M and P, who is facing N sitting to the immediate left of C.
II. M is third to the left of C, who is to the immediate left of Q.
If ‘P + Q’ means ‘P is the son of Q’; ‘P \(\times\) Q’ means ‘P is the brother of Q’; and ‘P - Q’ means ‘P is the sister of Q’, then which of the following means ‘A is the nephew of D’?
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.
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 leaves are vegetables.
2. Some vegetables are costly products.
Conclusions : I. Some leaves are costly products.
II. All costly products are vegetables.
III. All vegetables that are not costly products are leaves.
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. No mansion is a hut.
2. Some houses are buildings.
3. Some buildings are mansions.
Conclusions :
I. Some houses are mansions.
II. No house is a hut.
III. Some buildings are not huts.