If the determinant `|[a+p, l+x, u+f], [b+q, x+y, v+g], [c+r, n+z, w+h]|` splits into exactly `K` determinants of order 3, each element of which contains only one term, then the values of `K` is

If the determinant |{:(x+a,p+u,l+f),(y+b,q+v,m+g),(z+c,r+w,n+h):}| splits into exactly K determinants of order 3, each elements of which contains only one term, then the value of K is 8

If f(x)=x^3+3x^2+4x+ bsinx+ c cosx AA x in R is a one-one function then the value of b^2 + c^2 is

The value of the determinant |(bc,ca,ab),(p,q,r),(1,1,1)| , where a, b and c respectively the pth,qth and rth terms of a H.P. is

Figure shows a series LCR circuit connected to a variable frequency 230 V source. L = 5.0 H, C = 80muF, R = 40 Omega . (a) Determine the source frequency which drives the circuit in resonance. (b) Obtain the impedance of the circuit and the amplitude of current at the resonating frequency. (c) Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency.

Prove that: |{:(a, b, c), (x, y, z), (p, q, r):}|=|{:(y, b, q), (x, a, p), (z, c, r):}|

A farmer mixes two brands P and Q of cattle feed. Brand P, costing Rs. 250 per bag, contains 3 units of nutritional element A, 2.5 units of element B and 2 units of element C. Brand Q costing Rs. 200 pre bag contains 1.5 units of nutritional element A, 11.25 units of element B, and 3 units of element c. The minimum requirements of nutrients A,B and C are 18 units, and 24 units respectively. Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag? What is the minimum cost of the mixture per bag.

If the system of linear equations x+a y+a z=0,\ x+b y+b z=0,\ x+c y+c z=0 has a non zero solution then System is always non trivial solutions System is consistent only when a=b=c If a!=b!=c then x=0,\ y=t ,\ z=-t\ AAt in R If a=b=c\ t h e n\ y=t_1, z=t_2,\ x=-a(t_1+t_2)AAt_1, t_2 in R

f: R rarrR be defined by f(x) =x/2+3, g: R rarr R be defined by g(x) = 2x-K . If fog = gof then find the value of K.

Let x_1,x_2,x_3,………,x_n be n observations . Let W_i = lx_i + k for i=1,2,……,n, where l and k are constants. If the mean of x_i's is 48 and their standard deviation is 12, the mean of w_i's is 55 and standard deviation of w_i's is 15, the values of l and k should be ..........