If one of the roots of `x^2-|a-3|x+5=0` lies in (1, 5) then number of integral values of `(a-3)^2` is
a.`5` b. `10` c. `15` d. infinite

If one root of 10 x^3 -x^2 - 278 x + 165=0 is 5 then product of the remaining two roots is

The value m for which one of the roots of x^2-3x+2m=0 is double of one of the roots of x^2-x+m=0 is a. -2 b. 1 c. 2 d. none of these

If the equation |2 - x| - |x + 1|= k has exactly one solution, then number of integral values of k is (A) 7 (B) 5 (C) 4 (D) 3

If one root of the equation x^2+a x+3=0 is 1, then the other root is (a) 3 (b) -3 (c) 2 (d) -2

Number of real solutions of sqrt(2x-4)-sqrt(x+5)=1 is (a) 0 (b) 1 (c) 2 (d) infinite

If cos(x+pi/3)+cos x=a has real solutions, then (a) number of integral values of a are 3 (b) sum of number of integral values of a is 0 (c) when a=1 , number of solutions for x in [0,2pi] are 3 (d) when a=1, number of solutions for x in [0,2pi] are 2

Let real and distinct roots of equation x^2-mx+4=0 lies in [1,5] then range of m is (a) (3,4) (b) (4,5) (c) (-5,-4) (d) (-3,4)

The number of integral solutions of (x+2)/(x^2+1)>1/2 is (A) 4 (B) 5 (C) 3 (D) 2 (E) 6

If one root of the polynomial f(x)=5x^2+13 x+k is reciprocal of the other, then the value of k is (a) 0 (b) 5 (c) 1/6 (d) 6

Consider the quadratic equation (c - 5)x^(2) - 2cx + (c - 4) = 0, c ne 5 . Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is a. 11 b. 18 c. 10 d. 12