### These CAT Algebra questions/problems with solutions provide you vital practice for the topic. The purpose of these posts is very simple: to help you learn through practice.

Question 1: If one root of *x ^{2} + px + *12 = 0 is 4, while the equation

*x*= 0 has equal roots, then the value of

^{2}+ px + q*q*is

**(a)**49/4

**(b)**4/49

**(c)**4

**(d)**1/4

### Answers and Explanations

**Answer : (a)**

The given equation is x^{2} + px +12 = 0. Since x = 4 is a root of this equation, so it will satisfy it.

Hence, we have 16 + 4p + 12 = 0 => 4p = – 28 => p = -7.

Hence the second equation becomes x^{2} – 7x + q = 0.

Now the roots of this equation are equal, so its discriminant = (b^{2} – 4ac) will be 0.

We get:

( -7)^{2} – 4q = 0 => 4q = 49 => q = 49/4.

**Question 2:** For the given pair (*x, y*) of positive integers, such that 4*x* – 17*y* = 1 and *x *__<__ 1,000, how man*y* integer values of *y *satisf*y* the given conditions?

**(a)** 55

**(b)** 56

**(c)** 57

**(d)** 58

### Answers and Explanations

**Directions for questions 3 – 5: **A young girl Roopa leaves home with x flowers, goes to the bank of a nearby river. On the bank of the river, there are four places of worship, standing in a row. She dips all the x flowers into the river, the number of flowers doubles. Then, she enters the first place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the second place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the third place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the fourth place of worship, offers y flowers to the deity. Now she is left with no flowers in hand.

**Question 3:** If Roopa leaves home with 30 flowers, the number of flowers she offers to each deity is:

**(a)** 30

**(b)** 31

**(c)** 32

**(d)** 33

### Answers and Explanations

**Question 4:** The minimum number of flowers that could be offered to each deity is:

**(a)** 10

**(b)** 15

**(c)** 16

**(d)** Cannot be determined

### Answers and Explanations

**Question 5:** The minimum number of flowers with which Roopa leaves home is :

**(a)** 16

**(b)** 15

**(c)** 10

**(d)** Cannot be determined