CAT Practice Test: Month (April) - CAT MCQ

If A is point on the x – axis whose abscissa is 5 and B is the point (1, – 3), then the distance AB is

The point where the perpendicular bisector of the line segment joining the points A(2, 5) and B(4, 7) cuts is:

Ajesh saves Rs 50,000 every year and deposits the money in a bank at compound interest of 10%(compunded annually).What would be his total saving at the end of the 5th year?

Define the following functions:
(a) (a M b) = a – b (b) (a D b) = a + b
(c) (a H b) = (ab) (d) (a P b) = a/b

Q.

Which of the following functions will represent a² – b²?

Define the following functions:
(a) (a M b) = a – b (b) (a D b) = a + b
(c) (a H b) = (ab) (d) (a P b) = a/b

Q.

What is the value of (3M4H2D4P8M2)?

Define the following functions:
(a) (a M b) = a – b (b) (a D b) = a + b
(c) (a H b) = (ab) (d) (a P b) = a/b

Q.

Which of the four functions defined has the minimum value?

If 0 < a <1 and 0 < b < 1 and if a < b, which of the following expressions will have the highestvalue?

What values of 'x' satisfy the inequality x^2/3 + x^1/3 - 2 ≤ 0?

If f(x) = x³ - 4x + p and f(0) and f(1) have opposite signs, then which of the following is necessarily true?

a² + b² is always

If xyz = 8, then what is the minimum value of 2^x + 2^y + 2^z?  

How many pairs of natural numbers at (x, y) satisfy the inequality 3x + 5y < 20?  

For what values o f c in the equation 2x² - (c³ + 8c - l)x + c² - 4c = 0 the roots of the equation would be opposite in signs?

The expression x² + kx + 9 becomes positive for what values of k (given that x is real)?

In the Maths Olympiad of 2020 at Animal Planet, two representatives from the donkey’s side, while solving a quadratic equation, committed the following mistakes: (i) One of them made a mistake in the constant term and got the roots as 5 and 9. (ii) Another one committed an error in the coefficient of x and he got the roots as 12 and 4.But in the meantime, they realised that they are wrong and they managed to get it right jointly. Find the quadratic equation.

For what value of b and c would the equation x² + bx + c = 0 have roots equal to b and c.

A journey between Mumbai and Pune (192 km apart) takes two hours less by a car than by a truck. Determine the average speed of the car if the average speed of the truck is 16 km/h less than the car.

Direction: The question consists of three statements followed by two conclusions labelled I and II. Consider the statements to be true even if they are at variance from the commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow(s) from the given statements.

Statements:
All Punjabi is Nigerian.
Some German is Punjabi.
Some European is German.
All American is Nigerian.
Conclusions:
I. All German is Nigerian.
II. Some European is American.
III. Some Punjabi is European.

Directions: In the question below are given three statements followed by three conclusions numbered I, II and III. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the statements and then decide which of the given conclusions logically follow(s) from the given statements, disregarding commonly known facts.

Statements:
Some messages are important.
Some important are urgent.
No important is required.
Conclusions:
I. All required may be messages.
II. Some urgent are not important.
III. Some required is urgent.

Directions: In the question below, four statements are followed by conclusions numbered I, II, III and IV. You have to take the given statements to be true, even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow(s) from the given statements, disregarding commonly known facts.

Statements:
Some pencils are kites.
Some kites are desks.
All desks are jungles.
All jungles are mountains.
 

Conclusions:
I. Some mountains are pencils.
II. Some jungles are pencils.
III. Some mountains are desks.
IV. Some jungles are kites.

Directions: In the question below, four statements are followed by four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow(s) from the given statements, disregarding commonly known facts.

Statements:
All birds are horses.
All horses are tigers.
Some tigers are lions.
Some lions are monkeys.
Conclusions:
I. Some tigers are horses.
II. Some monkeys are birds.
III. Some tigers are birds.
IV. Some monkeys are horses.

Direction: In the question below, three statements are given followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the statements and then decide which of the two conclusions logically follow(s) from the given statements, disregarding commonly known facts.

Statements:
Some buildings are sofas.
Some sofas are benches.
Some benches are tables.
 

Conclusions:
I. Some tables are sofas.
II. No table is a sofa.

Pointing to Varman, Madhav said, "I am the only son of one of the sons of his father." How is Varman related to Madhav?

If A + B means A is the brother of B; A % B means A is the father of B and A x B means A is the sister of B. Which of the following means M is the uncle of P?

Introducing a woman, Shashank said, "She is the mother of the only daughter of my son." How that woman is related to Shashank?

If A + B means B is the brother of A; A x B means B is the husband of A; A - B means A is the mother of B and A % B means A is the father of B, which of the following relations shows that Q is the grandmother of T?

1. A3P means A is the mother of P
2. A4P means A is the brother of P
3. A9P means A is the husband of P
4. A5P means A is the daughter of P

Which of the following means that K is the mother-in-law of M?