Equation `1+x^2+2x"sin"(cos^(-1)y)=0` is satisfied by (a) exactly one value of `x` (b) exactly two value of `x` (c) exactly one value of `y` (d) exactly two value of `y`

If p and q are distinct reals,then 2{(x-p)(x-q)+(p-x)(p-q)+(q-x)(q-p)}=(p-q)^(2)+(x-p)^(2)+(x-q)^(2) is satisfied by no value of x(B) exactly one value of x(C) exactly two value of x(D) infinite values of x

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 .

If 0lt=xlt=2pi, then 2^(cosec^2(x)) sqrt(1/2y^2-y+1)lt=sqrt(2) (a) is satisfied by exactly one value of y (b) is satisfied by exactly two value of x (c) is satisfied by x for which cosx=0 (d) is satisfied by x for which sinx=0

The function f(x) : (x-1)/(x( x^(2) -1)) is discontinuous at (a) exactly one point (b) exactly two points (c) exactly three points (d) no point

If P and Q are the points of intersection of the circles x^2+""y^2+""3x""+""7y""+""2p""""5""=""0 and x^2+""y^2+""2x""+""2y""""p^2=""0 , then there is a circle passing through P, Q and (1,""1) for (1) all values of p (2) all except one value of p (3) all except two values of p (4) exactly one value of p

The function f(x)=|x|-2| is not derivable at( (1) exactly one point (2) exactly two point (3) exactly three point (4) exactly four point

For the equation 1-2x-x^(2)=tan^(2)(x+y)+cot^(2)(x+y) (a)exactly one value of x exists (b)exactly two values of x exists (c)y=-1+n pi+(pi)/(4),n in Z(d)y=1+n pi+(pi)/(4),n in Z

The equation e^(sin x)-e^(-sin x)-4=0 has (A) infinite number of real roots (B) no real roots (C) exactly one real root (D) exactly four real roots

If the lines (x-2)/1=(y-3)/1=(z-4)/(-k) and (x-1)/k=(y-4)/2=(z-5)/1 are coplanar then k can have (A) exactly two values (B) exactly thre values (C) any value (D) exactly one value

If the lines (x-2)/(1)=(y-3)/(1)=(x-4)/(-k) and (x-1)/(k)=(y-4)/(2)=(x-5)/(1) are coplanar,then k can have (1) exactly one value (2) exactly two values (3) exactly three values (4) any value