# CAT Model Paper 1 Questions and Answers with Detailed Explanations (Official Sample Questions-Most Important for 2020-2021) Part 2

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5. Set N consists of all natural. Number from 1 to 10. There numbers are selected at random from this set. Find the probability that the product of two of the number is equal to the third.

(A)

(B)

(C)

(D)

Answer: D

Solution:

The only set of number possible = (2,3,6) (2,4,8) and (2,5,10) thus required probability

7. A rectangle with perimeter 88 m is partitioned into 5 congruent rectangles as shown in the diagram. The Perimeter of each of the congruent rectangle is

(A) 80

(B) 40

(C) 120

(D) None of these

Solution:

Here AD = BC , 3a = 2b, a=2y, b=3y

The Perimeter of rectangle

The Perimeter of each of the congruent rectangle is

8. The integers 34041 and 32506, when divided by a three digit integer n, leave the same remainder. What is the value of n?

(A) 289

(B) 367

(C) 453

(D) 307

Answer: D

Solution:

If 34041 and 32506 are the only two terms in an AP, they will have common difference of 32506-34041 = 1535. Thus, all numbers which are factors of this common difference will divide the integers such that they will leave a constant remainder.

Now go from answer option. We are looking for factors of 1535. Of the answer options, only 307 is a factor of 1535.

9. A square field has length of 4 meter. On the one corner of the square, a cow is tied with the rope length of 5 meter. What is the maximum area cow can graze? (Approximate)

(A) 17

(B) 12

(C) 15

(D) 18

Answer: (C)

Solution:

Area of square – area of triangle

Area grazed by cow should lie around 15.

10. what is the value of S?

(A) 2020

(B) 5050

(C) 5024

(D) 5000

Answer: B

Even simple ways of calculation would be.

= sum of first 100 natural numbers

11. The function f(x) satisfies the equation , for all x not equal to Zero. The value of (99) is

(A) 0

(B)

(C)

(D) 1

Answer: C

Substituting gives and substituting

98 times of first equation plus 99 times of the second equation simplify to 9703 f(99) = 197.

12. In the given diagram ABCD, what is the value of ?

(A)

(B)

(C)

(D) None of these

Answer: A

Soluction:

Given figure, we can divide into 4 kites. Where and and .

From the given figure ;

So,