`("lim")_(x->oo)sum_(x=1)^(20)cos^(2n)(x-10)` is equal to (a) 0 (b) 1 (c) 19 (d) 20

lim_(x rarr oo)(1)/(1+n sin^(2)nx)is equal to -1 (b) 0 (c) 1 (d) oo

(lim)_(x rarr)(sin^(4)x-sin^(2)x+1)/(cos^(4)x-cos^(2)x+1) is equal to (a) 0( b) 1 (c) (1)/(3)(d)(1)/(2)

lim_(x rarr oo)((x^(2)+2x-1)/(2x^(2)-3x-2))^((2x+1)/(2x-1)) is equal to (a) 0 (b) oo(c)(1)/(2) (d) none of these

(lim_(x rarr oo)(sqrt(x^(2)-1))/(2x+1) is equal to 0b*-1c1/2d.1

lim_(x rarr oo){(1)/(1-n^(2))+(2)/(1-n^(2))+(n)/(1-n^(2))} is equal to 0 (b) -(1)/(2)(c)(1)/(2)(d) none of these

(lim)_(x->0)((cos x)^(1//3)-(cos x)^(1//2))/(sin^2x) equals a. 1/12 b. 1/6 c. 1/3 d.1/2

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"):}

lim_(x rarr oo)x(((x)/(x+1))^(x)-(1)/(e)) is equal to (A) (-1)/(2e) (B) (1)/(2e) (C) (1)/(e) (D) oo

lim_(x rarr oo)(cot^(-1)(x^(-a)log_(a)x))/(sec^(-1)(a^(x)log_(x)a)),(a>1) is equal to (a)2(b)1(c)(log)_(a)2(d)0