Algebra : Linear Quadratic Equations - Practice Questions

A collection of questions that typically appear on Linear (1st order equations - equation of straight lines) and Quadratic (parabolic functions) and cubic equations.

1. Question 1: If one of the roots of the quadratic equation x² + mx + 24 = 0 is 1.5, then what is the value of m? 
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2. Question 2:  Find the remainder when the polynomial x⁴ - 3x² + 7x - 10 is divided by x - 2.
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3. Question 3:  If one of the roots of the quadratic equation 2x² - 7x + q = 0 is 3, then find the other root.
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4. Question 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?
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5. Question 5:  If p and q are the roots of the equation x² - bx + c = 0, then what is the equation if the roots are (pq + p + q) and (pq - p - q)?
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6. Question 6:  If (x + 2) ² = 9 and (y + 3) ² = 25, then the maximum value of x / y is.
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7. Question 7:  For what values of 'm' is y = 0, if y = x² + (2m + 1)x + m² - 1? X is a real number.
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8. Question 8:  For what value of m will the roots of the quadratic equation x² + mx + 4 = 0 have real and equal roots?
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9. Question 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?
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10. Question 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?
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11. Question 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
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12. Question 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?
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13. Question 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?
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14. Question 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?
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15. Question 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?
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CAT, XAT, TANCET Practice Questions and Answers : Listed Topicwise

Number Theory		Permutation Combination		Probability		Inequalities
Geometry		Mensuration		Trigonometry		Data sufficiency
Percentages		Profit Loss		Ratio Proportion		Mixtures Alligation
Speed Time Distance		Pipes Cisterns		Interest		Races
Average, Mean		AP, GP, HP		Set Theory		Clocks Calendars
Algebra		Function		English Grammar		General Awareness