Algebra — practice questions, page 9
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QuestionFind the sum of the first 15 terms of the arithmetic progression: 2, 5, 8, ...QuestionThe cost of 3 pens and 4 pencils is ₹52, and the cost of 5 pens and 2 pencils is ₹54. Find the…QuestionThe 5th term of an arithmetic progression is 17 and the 9th term is 33. Find its first term.QuestionFor what positive value of k does x² − kx + 9 = 0 have equal roots?QuestionThe sum of the first 20 terms of the AP 5, 9, 13, 17, ... is ?QuestionThe sum of a positive number greater than 1 and its reciprocal is 26/5. The number is ?QuestionA fraction becomes 1/2 when 1 is subtracted from its numerator, and becomes 1/3 when 8 is added to…QuestionFor what positive value of p does the equation 2x² + px + 8 = 0 have two equal real roots?QuestionIf α and β are the roots of 2x² − 5x + 1 = 0, find the value of 1/α + 1/β.QuestionIn an arithmetic progression, the 10th term is 25 and the 20th term is 55. Find the first term.QuestionFind the sum of the first 15 terms of the arithmetic progression 2, 5, 8, 11, ...QuestionThe pair of linear equations 2x + 3y = 12 and 4x + 6y = 24 has:QuestionIf (x − 2) is a factor of the polynomial x³ − 3x² + kx − 8, find the value of k.QuestionThe roots of the equation x² − px + 12 = 0 are in the ratio 1 : 3. Find the value of p (p > 0).QuestionFind the sum of the first 20 terms of the arithmetic progression: 3, 7, 11, 15, ...QuestionThe polynomial 2x³ + kx² − 5x − 6 is exactly divisible by (x + 1). What is the value of k?QuestionFor which positive value of k does 4x² + kx + 49 = 0 have two equal real roots?QuestionThe present age of a father is 3 times that of his son. After 12 years, the father's age will be…QuestionFind the sum of the first 20 terms of the arithmetic progression 5, 8, 11, ...QuestionIf (x − 2) is a factor of x³ − 3x² + kx − 6, then the value of k is:QuestionRiya has only ₹10 and ₹5 coins in her piggy bank: 23 coins worth ₹165 in all. How many ₹10 coins…QuestionThe cost of 2 pens and 3 pencils is ₹22, and 3 pens and 2 pencils cost ₹23. The cost of one pen…QuestionThe sum of a number and its reciprocal is 10/3. The number greater than 1 is:QuestionIn an arithmetic progression, the 10th term is 25 and the 20th term is 55. The first term is:QuestionHow many terms of the arithmetic progression 3, 7, 11, ... are needed to give a sum of 210?
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