# CAT Model Paper 2 Questions and Answers with Explanation Part 2

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Q: 7. The equation has 666 positive integral solutions. Find the maximum possible value of N?

(A)

(B)

(C)

(D) No such N exists

Ans: C

Sol:

The equation is of the form , where where Y assumes the minimum value 2 as we are considering only positive integral solutions.

For has only one solution namely .

For , we get 2 solutions.

For , we get solutions.

Hence, the total number of solutions for Y is given by ; where p is the maximum possible value p can take. Whenever we assign a value to Y, x takes the residual value.

By the given directions, . Solving, we get

Thus, the possible values of N are given by the equation,

, where x is a member of the set .

Hence, the maximum value of N is .

Q: 8. Find the value of

(A)

(B)

(C)

(D)

Ans: D

Sol:

Consider the expression , which can be rewritten as

Hence, the value is .

Q: 9. The sum of three positive numbers x, y and z is 1. Find the minimum value of

(A)

(B)

(C)

(D)

Ans: A

Sol:

For two positive numbers, Arithmetic mean Geometric mean

Consider and

Similarly

Adding the three expressions, Equation (1)

We know that

Substituting the above value in Equation (1)

But

Q: 10. find the value of

(A)

(B)

(C)

(D) Cannot be determined

Ans: D

Sol:

Hence,

By trial and error,

′ can take two values: 2 and 4.

Hence, cannot be determined.

Q: 11. Rehan borrows from a money lender at interest compounded annually. He repays the loan in two equal installments, one at the end of half year and the other a year later. What is the value of each installment?

(A)

(B)

(C)

(D)

Ans: C

Sol:

Let the value of each installment be x.

After half year, principal will become

He pays x remaining principal

After 1 year it will become

Other a year later it will become

Hence, the value of each installment is **₹ 1100**.

Q: 12. In the quadratic equation, one root of the equation is twice the other root and the roots are positive. What is the value of “b” ?

(A)

(B)

(C)

(D)

Ans: A

Sol:

For the quadratic equation, .

Since the root are positive, let the roots be .

Product of roots

Hence. . But a can take only positive values. Sum of roots,

.

The correct choice (A)