Find the values of 'a' which `4^t-(a-4)2^t+9/4alt0,foralltin(1,2)`

Using determinant : Find the value of t for which the area of the triangle having vertices at (-1,t),(t-2,1) and (t-2,t) is 121/2 square unit .

If t is a real number satisfying the equation 2t^3-9t^2+30-a=0, then find the values of the parameter a for which the equation x+1/x=t gives six real and distinct values of x .

(a) Find the value of t if the point (4,t^2-4t+4) lie on the x-axis.

Find the value of |[1, 2, 4],[-1,3, 0],[4 ,1, 0]|

Find the value of x, y, z and t for which 3{:[(x,y),(z,t)]={:[(x,6),(-1,2t)]+{:[(4,x+y),(z+t,3)]:}

Find the value of each of the following polynomials for the indicated value of variables: (i) p(x) = 4x ^(2) - 3x + 7 at x =1 (ii) q (y) = 2y ^(3) - 4y + sqrt11 at y =1 (iii) r (t) = 4t ^(4) + 3t ^(3) -t ^(2) + 6 at t =p, t in R (iv) s (z) = z ^(3) -1 at z =1 (v) p (x) = 3x ^(2) + 5x -7 at x =1 (vi) q (z) = 5z ^(3) - 4z + sqrt2 at z =2

Find the derivatives w.r.t. x : (e^(2x))^(4)

(ii) Find the value of t if the point (-t,t^2+t+1) is equidistant from the axes.

Find the value of (log)_2(2 9 3-2)+(log)_2(12 3 3+4+4 9 3)dot

Find the value of log_(2) (2root(3)9-2) + log_(2)(12root(3)3+4+4root(3)9) .