# CAT Model Paper 1 Questions and Answers with Detailed Explanations (Official Sample Questions-Most Important for 2022-2023) 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)

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 Rectangle with Perimeter 88 M is Partitioned into 5 Congru …

(A) 80

(B) 40

(C) 120

(D) None of these

Solution: A Rectangle with Perimeter 88 M is Partitioned into 5 Congru …

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

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

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

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

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