[Download PDF] CAT 2000 Question Paper Paper with Solutions

Instructions

For the following questions answer them individually

Question 161

Triangle PQR has angle PRQ equal to 90 degrees. What is the value of PR + RQ?

A. Diameter of the inscribed circle of the triangle PQR is equal to 10 cm.
B. Diameter of the circumscribed circle of the triangle PQR is equal to 18 cm

Video Solution

Solution

Let a,b and c be length of PR, QR and PQ.

By 2nd statement we know that c=18 and also area = (a*b*c)/9 and by using statement A we have area = inradius*(a+b+c)/c.

Using both the equations we can find out value of PR + RQ . Hence option C.

Question 162

Harshad bought shares of a company on a certain day, and sold them the next day. While buying and selling he had to pay to the broker one percent of the transaction value of the shares as brokerage. What was the profit earned by him per rupee spent on buying the shares?

A.The sales price per share was 1.05 times that of its purchase price.
B. The number of shares purchased was 100.

Video Solution

Solution

Let the purchase price be P and sale price be S. So total brokerage = 0.01P + 0.01S.

If we consider statement A we have S = 1.05*P.

Hence we can find brokerage value in terms of P.

then total profit = S - brokerage = Constant * P.

Then profit per rupee would be dividing last equation by P

Hence statement A is sufficient.

Using statement B we cant make out the profit percentage.

Hence , option A.

Question 163

For any two real numbers:

a + b = 1 if both a and b are positive or both a and b are negative.
a + b = -1 if one of the two numbers a and b is positive and the other negative.

What is (2 + 0) + (-5 + -6)?
A. a + b is zero if a is zero
B. a + b = b + a

Video Solution

Solution

We have (2 + 0) + (-5 + -6)

Now using statement B it can be written as (0 + 2) + (-5 + -6).

Using trhe statement A we can get the answer to the required question.

Hence,the question can be answered by using both the statements together, but cannot be answered by using either statement alone.

Question 164

There are two straight lines in the x-y plane with equations:

ax + by = c

dx + ey = f

Do the two straight lines intersect?

A. a, b, c, d, e and f are distinct real numbers.

B. c and f are non-zero.

Video Solution

Solution

Using option B we know that since the constant terms are non-zero and unique , the lines do not intersect at the origin. Also since other coefficients are not equal , the lines can be parallel or intersecting . Hence, the question cannot be answered even by using both statements together.

Question 165

O is the centre of two concentric circles. AE is a chord of the outer circle and it intersects the inner circle at points B and D. C is a point on the chord in between B and D. What is the value of AC/CE?

A. BC/CD=1
B. A third circle intersects the inner circle at B and D and the point C is on the line joining the centres of the third circle and the inner circle.

Video Solution

Solution

Using statement A we know that C is midpoint of both BD and AE . Also using statement B we know that C is midpoint of BD and AE. Hence , the question can be answered by using either statement alone.

CAT Content

CAT 2000 Question Paper

Triangle PQR has angle PRQ equal to 90 degrees. What is the value of PR + RQ?

A. Diameter of the inscribed circle of the triangle PQR is equal to 10 cm.
B. Diameter of the circumscribed circle of the triangle PQR is equal to 18 cm

For any two real numbers:

a + b = 1 if both a and b are positive or both a and b are negative.
a + b = -1 if one of the two numbers a and b is positive and the other negative.

What is (2 + 0) + (-5 + -6)?
A. a + b is zero if a is zero
B. a + b = b + a

There are two straight lines in the x-y plane with equations:

ax + by = c

dx + ey = f

Do the two straight lines intersect?

A. a, b, c, d, e and f are distinct real numbers.

B. c and f are non-zero.

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CAT Content

CAT 2000 Question Paper

Triangle PQR has angle PRQ equal to 90 degrees. What is the value of PR + RQ? A. Diameter of the inscribed circle of the triangle PQR is equal to 10 cm. B. Diameter of the circumscribed circle of the triangle PQR is equal to 18 cm

For any two real numbers: a + b = 1 if both a and b are positive or both a and b are negative. a + b = -1 if one of the two numbers a and b is positive and the other negative. What is (2 + 0) + (-5 + -6)? A. a + b is zero if a is zero B. a + b = b + a

There are two straight lines in the x-y plane with equations: ax + by = c dx + ey = f Do the two straight lines intersect? A. a, b, c, d, e and f are distinct real numbers. B. c and f are non-zero.

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CAT Quant Questions | CAT Quantitative Ability

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CAT Verbal Ability Questions | VARC Questions For CAT

Triangle PQR has angle PRQ equal to 90 degrees. What is the value of PR + RQ?

A. Diameter of the inscribed circle of the triangle PQR is equal to 10 cm.
B. Diameter of the circumscribed circle of the triangle PQR is equal to 18 cm

For any two real numbers:

a + b = 1 if both a and b are positive or both a and b are negative.
a + b = -1 if one of the two numbers a and b is positive and the other negative.

What is (2 + 0) + (-5 + -6)?
A. a + b is zero if a is zero
B. a + b = b + a

There are two straight lines in the x-y plane with equations:

ax + by = c

dx + ey = f

Do the two straight lines intersect?

A. a, b, c, d, e and f are distinct real numbers.

B. c and f are non-zero.