`(d ^(20))/(dx ^(20)) [ 2 cos x cos 3x]=`

Match the following : {:("Column I ", " Column II" ), ("(A)" if lim_(x to 1) (1-x) tan""(pix)/2 = k " then " sin (1/k) " is" , "(p)"4),( "(B)" if lim_(x to 5) (x^(k)-5^(k))/(x-5) = 500 " then k is " , "(q)" 1),("(C)" lim_(x to oo)(1 + 4/(x+1))^((3x-1)/3) " is equal to " e^(k) " , then k is" , "(r) A perfect sqare"), ("(D) " d^(20)/(dx^(20)) (2 cos x"," cos 3x)= 2^(4k) [ cos2x + 2^(20) . cos4k]" then k is " , "(s)" 5),(, "(t)An odd number"):}

Match the following : {:("Column I ", " Column II" ), ("(A)" if lim_(x to 1) (1-x) tan""(pix)/2 = k " then " sin (1/k) " is" , "(p)"4),( "(B)" if lim_(x to 5) (x^(k)-5^(k))/(x-5) = 500 " then k is " , "(q)" 1),("(C)" lim_(x to oo)(1 + 4/(x+1))^((3x-1)/3) " is equal to " e^(k) " , then k is" , "(r) A perfect sqare"), ("(D) " d^(20)/(dx^(20)) (2 cos x"," cos 3x)= 2^(4k) [ cos2x + 2^(20) . cos4k]" then k is " , "(s)" 5),(, "(t)An odd number"):}

(d^(20))/(dx^(20))(2cos x cos3x) is equal to (a) 2^(20)(cos2x-2^(20)cos3x)(b)2^(20)(cos2x+2^(20)cos4x)(c)2^(20)(cos2x+2^(20)sin4x)(d)2^(20)(sin2x-2^(20)sin4x)

(d^(20))/(dx^(20))(2cos x cos3x)=2^(20)(cos2x-2^(20)cos4x)(b)2^(20)(cos2x+2^(20)cos4x)(c)2^(20)(sin2x+2^(20)sin4x)(d)2^(20)(sin2x-2^(20)sin4x)

(d^(2))/(dx^(2))(2 cos x cos 3x) is equal to

int cos x cos 3x dx

(d^(20))/(dx^(20))(2cosxcos3x)= 2^(20)(cos2x-2^(20)cos4x) (b) 2^(20)(cos2x+2^(20)cos4x) (c) 2^(20)(sin2x+2^(20)sin4x) (d) 2^(20)(sin2x-2^(20)sin4x)

(d^(20))/(dx^(20))(2cosxcos3x) is equal to (a) 2^(20)(cos2x-2^(20)cos3x) (b) 2^(20)(cos2x+2^(20)cos4x) (c) 2^(20)(sin2x+2^(20)sin4x) (d) 2^(20)(sin2x-2^(20)sin4x)

(d^(20))/(dx^(20))(2cosxcos3x) is equal to (a) 2^(20)(cos2x-2^(20)cos3x) (b) 2^(20)(cos2x+2^(20)cos4x) (c) 2^(20)(sin2x+2^(20)sin4x) (d) 2^(20)(sin2x-2^(20)sin4x)

(d^(20))/(dx^(20))(2cosxcos3x) is equal to (a) 2^(20)(cos2x-2^(20)cos3x) (b) 2^(20)(cos2x+2^(20)cos4x) (c) 2^(20)(sin2x+2^(20)sin4x) (d) 2^(20)(sin2x-2^(20)sin4x)