How many linear equations are satisfied by `x=2\ a n d\ y=-3?` (a) only one (b) Two (c) three (d) infinitely many

How many linear equations in x and y can be satisfied by x=1 and y=2 ?

Number of triplets of a, b & c for which the system of equations, ax - by = 2a - b and (c +1)x+cy = 10-a + 3 b has infinitely many solutions and x = 1. y = 3 is one of the solutions, is: (A) exactly one (B) exactly two (C) exactly three (D) infinitely many

If a m!=b l , then the system of equations a x+b y=c ,\ \ \ \ l x+m y=n (a) has a unique solution (b) has no solution (c) has infinitely many solutions (d) may or may not have a solution

How many diagonals does a triangle have? a) 0 b) 1 c) 2 d) 3

The number of values of k for which the equation x^3-3x+k=0 has two distinct roots lying in the interval (0,1) is (a) three (b) two (c) infinitely many (d) zero

The no. of solutions of the equation a^(f(x)) + g(x)=0 where a>0 , and g(x) has minimum value of 1/2 is :- (a) One (b) Two (c) Infinitely many (d) Zero

The system of linear equations x+lambday-z=0 , lambdax-y-z=0 , x+y-lambdaz=0 has a non-trivial solution for : (1) infinitely many values of lambda . (2) exactly one value of lambda . (3) exactly two values of lambda . (4) exactly three values of lambda .

The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-lambdaz=0 has a non-trivial solution for : (1) infinitely many values of lambda . (2) exactly one value of lambda . (3) exactly two values of lambda . (4) exactly three values of lambda .

The number of vectors of unit length perpendicular to vectors vec a=(1,1,0)a n d vec b=(0,1,1) is a. one b. two c. three d. infinite

The number of vectors of unit length perpendicular to vectors vec a=(1,1,0)a n d vec b=(0,1,1) is a. one b. two c. three d. infinite