Algebra — practice questions, page 6
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The expression 6ax − 4ay − 3bx + 2by factorises as:The polynomial x⁵ − a²x³ + 2x + a + 3 has (x − a) among its factors. Then a equals:The polynomial x³ − 3x² + ax + b is divisible by (x − 1)². Then a + b equals:The remainder when 2x³ + 3x² − 5x + 7 is divided by (2x − 1) is:A polynomial p(x) leaves the remainder 3 when divided by (x − 1) and the remainder 5 when divided…When 3x⁴ + 2x³ − x² + 5 is divided by (x² + 1), the remainder is:If a + b + c = 15 and a² + b² + c² = 83, then ab + bc + ca equals:If a + b + c = 9 and ab + bc + ca = 26, then a³ + b³ + c³ − 3abc equals:If x² + 1/x² = 7 and x is positive, then x³ + 1/x³ equals:For positive real numbers a and b, the least value of (a + b)(1/a + 1/b) is:If (√(a + x) + √(a − x))/(√(a + x) − √(a − x)) = 2, then x : a equals:If (x³ + 3x)/(3x² + 1) = 341/91, then x equals:The value of x satisfying √(x + 5) + √x = 5 is:If √x + √y = 7 and √x − √y = 1, then xy equals:If 2x + 3y = 46 and 3x + 5y = 74, then the value of 5x + 8y is:Solved by the cross-multiplication method, the pair 3x − 5y − 4 = 0 and 9x = 2y + 7 gives:A prize fund of ₹840 was to be shared equally among the winners of a quiz. Four more students won…Two natural numbers differ by 5 and their reciprocals differ by 5/14. The larger number is:Three arithmetic means are inserted between 5 and 29. The second of those means is:In a geometric progression of positive terms the 2nd term is 6 and the 6th term is 96. Its 5th…The sum of all three-digit numbers that leave the remainder 2 when divided by 5 is:Three numbers in geometric progression add up to 39 and their product is 729. The smallest of them…For a positive real number x, the least value of x + 4/x is:If f(x) = x² − 3x + 2, then f(x + 1) − f(x) equals:A function satisfies f(x) + 2f(1/x) = 3x for every non-zero x. The value of f(2) is:
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