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`

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

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+npi+pi/4,n in Z (d) y=1+npi+pi/4, n in Z

The lines x+y-1=0,(m-1)x+(m^2-7)y-5=0, and (m-2)x+(2m-5)y=0 are a.) concurrent for three values of m b.) concurrent for no value of m c.) parallel for one value of m d.) parallel for two value of m

sintheta+sqrt(3)costheta=6x-x^2-11 ,0lt=thetalt=4pi,x in R , (a) hold for no values of x and theta (b) one value of x and two values of theta (c) two values of x and two values of theta (d) two point of values of (x ,theta)

2x +(y-1)/3=0 in this equation replace y by x and find value of x and y.

If the equation x^(log_(a)x^(2))=(x^(k-2))/a^(k),a ne 0 has exactly one solution for x, then the value of k is/are

Find the possible values of p such that the equation p x^2=(log)_e x has exactly one solution.

If 2tan^2x-5secx=1 is satisfied by exactly seven distinct values of x in [0,((2n+1)pi)/2],n in N , then the greatest value of n is________.