# Algebra : Linear Quadratic Equations

A collection of questions that typically appear from Linear (1st order equations - equation of straight lines) and Quadratic (parabolic functions) and cubic equations. These are core topics and will be a part of the quantitative reasoning / aptitude sections of TANCET, CAT, and GMAT. While you might occassionally get an easy question that provides the equation, many a times questions from these topics are what are called "word problems". Information is provided in sentence form and you are expected to convert the same into mathematical expressions and equations - some of which might be linear while others could be quadratic or in a few instances cubic.

1. If one of the roots of the quadratic equation x2 + mx + 24 = 0 is 1.5, then what is the value of m?

1. -22.5
2. 16
3. -10.5
4. -17.5

2. Find the remainder when the polynomial x4 - 3x2 + 7x - 10 is divided by (x - 2).

1. 8
2. -20
3. 18
4. 0

Concept: Polynomial Division

3. If one of the roots of the quadratic equation 2x2 - 7x + q = 0 is 3, find the other root.

1. -3
2. -$$frac{1}{2}\\$ 3. $\frac{1}{2}\\$ 4. $\frac{1}{4}\\$ Concept: Quadratic equations - roots 4. A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. What is the basic first class full fare and what is the reservation charge? 1. Rs. 105 and Rs. 6 2. Rs. 216 and Rs. 12 3. Rs. 210 and Rs. 12 4. Rs. 210 and Rs. 6 Concept: Word Prolems - Linear Equations 5. If p and q are the roots of the equation x2 - bx + c = 0, what is the equation if the roots are$pq + p + q) and (pq - p - q)?

1. x2 - 2cx + (c2 - b2) = 0
2. x2 - 2bx + (b2 + c2) = 0
3. bcx2 - 2(b + c)x + c2 = 0
4. x2 + 2bx - (c2 - b2) = 0

Concept: Quadratic - roots to equation

6. If (x + 2)2= 9 and (y + 3) 2 = 25, then the maximum value of $$frac{x}{y} \\$ is ____. 1. $\frac{1}{2}\\$ 2. $\frac{5}{2}\\$ 3. $\frac{5}{8}\\$ 4. $\frac{1}{8}\\$ Concept: Maximum - Minimum 7. For what values of 'm' is y = 0, if y = x2 +$2m + 1)x + m2 - 1? x is a real number.

1. m ≥ -2
2. m < 0
3. m = 0
4. m ≥ -1.25

Concept: Nature of roots

8. For what value of 'm' will the quadratic equation x2 + mx + 4 = 0 have real and equal roots?

1. 4
2. -4
3. 4 or -4
4. 16

Concept: Nature of roots - quadratic equation

9. Rajesh is 10 years younger to Baskar. 10 years back, Rajesh's age was two-thirds that of Baskar's. How old is Baskar now?

1. 30
2. 40
3. 20
4. 16
5. 28

Concept: Word Problems - Simultaneous Equations

10. An owner of a pizza stand sold small slices of pizza for Rs. 150 each and large slices for Rs. 250 each. One night he sold 5000 slices, for a total of Rs. 10.50 lakh. How many small slices were sold?

1. 3000
2. 2000
3. 4000
4. 2500
5. 3500

Concept: Word Problems - Linear Equation

11. Jack has three more cards than Bill. Together they have 47 cards. If x represents the number of cards Bill has, then an equation that can be used to determine the number of cards each one has is

1. x + 3 = 47
2. 2x + 3 = 47
3. x - 3 = 47
4. 2x - 3 = 47
5. 3x + 3 = 47

Concept: Framing Equation

12. There were P people in a room when a meeting started. Q people left the room during the first hour, while R people entered the room during the same time. What expression gives the number of people in the room after the first hour as a percentage of the number of people in the room who have been there since the meeting started?

1. $$frac{$P - Q$}{(P - Q + R)}$ 2. 100 x $\frac{$P - Q +R$}{(P - Q)}$ 3. $\frac{$P + R$}{(P - Q)}$ 4. 100 x $\frac{$P - Q$}{(P - Q + R)}$ 5. 100 x $\frac{$P + R$}{(P - Q)}$ Concept: Mathematical Expressions 13. It costs Rs. x each to make the first thousand copies of a compact disk and Rs. y to make each subsequent copy. If z is greater than 1,000, how many Rupees will it cost to make z copies of the compact disk? 1. 1000 x + yz 2. zx - zy 3. 1000$z - x) + xy
4. 1000 (z - y) + xz
5. 1000 (x- y) + yz

Concept: Framing Expressions

14. A clothing manufacturer has determined that she can sell 100 suits a week at a selling price of Rs. 200 each. For each rise of Rs. 4 in the selling price she will sell 2 less suits a week. If she sells the suits for Rs. x each, how many rupees a week will she receive from the sales of the suits?

1. $$frac{x^2}{2}\\$ 2. $200 - \frac{x}{2}\\$ 3. $50x - \frac{x^2}{4}\\$ 4. $150x - \frac{x^2}{4}\\$ 5. $200x - \frac{x^2}{2}\\$ Concept: Equations, Expressions 15. A charity solicited P persons over the phone who agreed to an average pledge of Rs.R each. Q of these people who had pledged an average of Rs. S each never sent in the pledged amount. Which of the following expressions represents the percentage of pledged money that the charity received? 1. 100 x $\frac{PR}{QS}\\$ 2. 100 x $\frac{QS}{PR}\\$ 3. 100$PR - QS)
4. 100 (1 - $$frac{QS}{PR}\\$) 5. 100$PR - $\frac{QS}{PR}\\$)

Concept: Word Problems - Equations

16. Find the equation of the graph shown below. 1. y = 3x - 4
2. y = 2x2 - 40
3. x = 2y2 - 40
4. y = 2x2 + 3x - 19
5. x = 2y2 + 3y - 19

Concept: Fitting the curve

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