CAT 2020 Slot 2 | Past Year Question Paper

Question 1.

In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. The distance (in km) over which the race has been conducted is

A

550

B

475

C

500

D

450

Question 2.

From the interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the perpendiculars is 's'. Then the area of the triangle is

A

\frac{s^{2}}{2√3}

B

\frac{2s^{2}}{√3}

C

\frac{s^{2}}{√3}

D

\frac{√3s^{2}}{2}

Question 3.

In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by

A

5

B

3

C

4

D

6

Question 4.

The number of pairs of integers(x,y) satisfying x ≥ y ≥ -20 and 2x + 5y = 99 is

Question 5.

The value of $log_{a}\frac{a}{b}$ + $log_{b}\frac{b}{a}$ , for 1 < a ≤ b cannot be equal to

A

-0.5

B

1

C

0

D

-1

Question 6.

Let teh m-th and n-thterms of a Geometric progression be $\frac{3}{4}$ and 12, respectively, when m < n. If the common ratio of the progression is an integer r, then the smallest possible value of r + n - m is

A

-4

B

-2

C

6

D

2

Question 7.

If x and y are positive real numbers satisfying x + y = 102, then the minimum possible value of 2601(1 + $\frac{1}{x}$ )(1 + $\frac{1}{y}$ ) is

Question 8.

For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125. Then the principal amount in rupees is

Question 9.

Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to

A

6.6

B

7.2

C

8.8

D

7.8

Question 10.

For real x, the maximum possible value of $\frac{x}{√(1 + x^{4})}$ is

A

1

B

\frac{1}{2}

C

\frac{1}{√2}

D

\frac{1}{√3}

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cat 2020 Complete Paper Solution | Slot 2

Question 1.

In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. The distance (in km) over which the race has been conducted is

Question 2.

From the interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the perpendiculars is 's'. Then the area of the triangle is

Question 3.

In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by

Question 4.

The number of pairs of integers(x,y) satisfying x ≥ y ≥ -20 and 2x + 5y = 99 is

Question 5.

The value of $log_{a}\frac{a}{b}$ + $log_{b}\frac{b}{a}$ , for 1 < a ≤ b cannot be equal to

Question 6.

Let teh m-th and n-thterms of a Geometric progression be $\frac{3}{4}$ and 12, respectively, when m < n. If the common ratio of the progression is an integer r, then the smallest possible value of r + n - m is

Question 7.

If x and y are positive real numbers satisfying x + y = 102, then the minimum possible value of 2601(1 + $\frac{1}{x}$ )(1 + $\frac{1}{y}$ ) is

Question 8.

For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125. Then the principal amount in rupees is

Question 9.

Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to

Question 10.

For real x, the maximum possible value of $\frac{x}{√(1 + x^{4})}$ is

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cat 2020 Complete Paper Solution | Slot 2

Question 1.

In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. The distance (in km) over which the race has been conducted is

Question 2.

From the interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the perpendiculars is 's'. Then the area of the triangle is

Question 3.

In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by

Question 4.

The number of pairs of integers(x,y) satisfying x ≥ y ≥ -20 and 2x + 5y = 99 is

Question 5.

The value of logaablog_{a}\frac{a}{b}loga​ba​ + logbbalog_{b}\frac{b}{a}logb​ab​ , for 1 < a ≤ b cannot be equal to

Question 6.

Let teh m-th and n-thterms of a Geometric progression be 34\frac{3}{4}43​ and 12, respectively, when m < n. If the common ratio of the progression is an integer r, then the smallest possible value of r + n - m is

Question 7.

If x and y are positive real numbers satisfying x + y = 102, then the minimum possible value of 2601(1 + 1x\frac{1}{x}x1​ )(1 + 1y\frac{1}{y}y1​ ) is

Question 8.

For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125. Then the principal amount in rupees is

Question 9.

Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to

Question 10.

For real x, the maximum possible value of x√(1+x4)\frac{x}{√(1 + x^{4})}√(1+x4)x​ is

The value of $log_{a}\frac{a}{b}$ + $log_{b}\frac{b}{a}$ , for 1 < a ≤ b cannot be equal to

Let teh m-th and n-thterms of a Geometric progression be $\frac{3}{4}$ and 12, respectively, when m < n. If the common ratio of the progression is an integer r, then the smallest possible value of r + n - m is

If x and y are positive real numbers satisfying x + y = 102, then the minimum possible value of 2601(1 + $\frac{1}{x}$ )(1 + $\frac{1}{y}$ ) is

For real x, the maximum possible value of $\frac{x}{√(1 + x^{4})}$ is