Number of integral values of `lambda` for which `(lim)_(xvec1)sec^(-1)((lambda^2)/((log)_e x)-(lambda^2)/(x-1))` does not exist is a. 1 b. 2 c. `3` d. 4

Evaluate : ("lim")_(xvec1)(x^2+x(log)_e x-(log)_e x-1)/((x^2-1)

Evaluate: ("lim")_(xvec2)(x-2)/((log)_a(x-1))

The number of integral values of lambda for which the equation x^2+y^2+lambdax+(1-lambda)y+5=0 is the equation fo a circle whose radius cannot exceed 5, is 14 (b) 18 (c) 16 (d) none of these

Evaluate : ("lim")_(xvec1)(2/(1-x^2)+1/(x-1))

If lambda_(1) and lambda_(2) be two values of lambda for which the expression x^(2)+(2-lambda) x+lambda-(3)/(4) becomes a perfect square, then calculate the value of (lambda_(1)^(2)+lambda_(2)^(2)) .

Find all values of lambda for which the (lambda-1)x+(3lambda+1)y+2lambdaz=0(lambda-1)x+(4lambda-2)y+(lambda+3)z=0 2x+(3lambda+1)y+3(lambda-1)z=0 possess non-trivial solution and find the ratios x:y:z, where lambda has the smallest of these value.

the value of lambda for which the line 2x-8/3lambday=-3 is a normal to the conic x^2+y^2/4=1 is:

If lambda = -2, determine the value of |(0,2lambda,1),(lambda^(2),0,3lambda^(2)+1),(-1,6lambda-1,0)| .

Find the range of values of lambda for which the point (lambda,-1) is exterior to both the parabolas y^2=|x|dot

("lim")_(xvec0)1/xcos^(-1)((1-x^2)/(1+x^2)) is equal to (a)1 (b) 0 (c) 2 (d) none of these