CAT 2020 Slot 3 | Past Year Question Paper

Question 1.

If $x_{1}$ = -1 and $x_{m}$ = $x_{m + 1}$ + (m + 1) for every positive integer m, then $x_{100}$ equals

A

-5050

B

-5051

C

-5150

D

-5151

Question 2.

Let N, x and y be positive integers such that N = x + y, 2 < x < 10 and 14 < y < 23. If N > 25, then how many distinct values are possible for N?

Question 3.

Let $log_{a}$ 30 = A, $log_{a}\frac{5}{3}$ = -B and $log_{2}$ a = $\frac{1}{3}$ , then $log_{3}$ a equals

A

\frac{2}{A+B-3}

B

\frac{A+B-3}{2}

C

\frac{A+B}{2}

- 3

D

\frac{2}{A+B}

- 3

Question 4.

A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only 1.5 km road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?

Question 5.

The area, in sq. units, enclosed by the lines x = 2, y = |x - 2| + 4, the X-axis and the Y-axis is equal to

A

12

B

8

C

6

D

10

Question 6.

Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is 1 year less than the average age of all three, then Harry's age, in years, is

Question 7.

How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

A

41

B

42

C

40

D

43

Question 8.

In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, is

A

399

B

439

C

357

D

417

Question 9.

If f(x+y) = f(x)f(y) and f(5) = 4, then f(10) - f(-10) is equal to

A

3

B

0

C

14.0625

D

15.9375

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cat 2020 Complete Paper Solution | Slot 3

Question 1.

If $x_{1}$ = -1 and $x_{m}$ = $x_{m + 1}$ + (m + 1) for every positive integer m, then $x_{100}$ equals

Question 2.

Let N, x and y be positive integers such that N = x + y, 2 < x < 10 and 14 < y < 23. If N > 25, then how many distinct values are possible for N?

Question 3.

Let $log_{a}$ 30 = A, $log_{a}\frac{5}{3}$ = -B and $log_{2}$ a = $\frac{1}{3}$ , then $log_{3}$ a equals

Question 4.

A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only 1.5 km road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?

Question 5.

The area, in sq. units, enclosed by the lines x = 2, y = |x - 2| + 4, the X-axis and the Y-axis is equal to

Question 6.

Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is 1 year less than the average age of all three, then Harry's age, in years, is

Question 7.

How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

Question 8.

In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, is

Question 9.

If f(x+y) = f(x)f(y) and f(5) = 4, then f(10) - f(-10) is equal to

Question 10.

$\frac{2×4×8×16}{(log_{2}4)^{2}(log_{4}8)^{3}(log_{8}16)^{4}}$ equals

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cat 2020 Complete Paper Solution | Slot 3

Question 1.

If x1x_{1}x1​ = -1 and xmx_{m}xm​ = xm+1x_{m + 1}xm+1​ + (m + 1) for every positive integer m, then x100x_{100}x100​ equals

Question 2.

Let N, x and y be positive integers such that N = x + y, 2 < x < 10 and 14 < y < 23. If N > 25, then how many distinct values are possible for N?

Question 3.

Let logalog_{a}loga​30 = A, loga53log_{a}\frac{5}{3}loga​35​ = -B and log2log_{2}log2​a = 13\frac{1}{3}31​ , then log3log_{3}log3​a equals

Question 4.

A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only 1.5 km road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?

Question 5.

The area, in sq. units, enclosed by the lines x = 2, y = |x - 2| + 4, the X-axis and the Y-axis is equal to

Question 6.

Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is 1 year less than the average age of all three, then Harry's age, in years, is

Question 7.

How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

Question 8.

In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, is

Question 9.

If f(x+y) = f(x)f(y) and f(5) = 4, then f(10) - f(-10) is equal to

Question 10.

2×4×8×16(log24)2(log48)3(log816)4\frac{2×4×8×16}{(log_{2}4)^{2}(log_{4}8)^{3}(log_{8}16)^{4}}(log2​4)2(log4​8)3(log8​16)42×4×8×16​ equals

If $x_{1}$ = -1 and $x_{m}$ = $x_{m + 1}$ + (m + 1) for every positive integer m, then $x_{100}$ equals

Let $log_{a}$ 30 = A, $log_{a}\frac{5}{3}$ = -B and $log_{2}$ a = $\frac{1}{3}$ , then $log_{3}$ a equals

$\frac{2×4×8×16}{(log_{2}4)^{2}(log_{4}8)^{3}(log_{8}16)^{4}}$ equals