`l^2+m^2+n^2` is equal to
(a)`0`
(a)`1`
(a)`-1`
(a)None of these

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

If f(x)=((x^(l))/(x^(m)))^(l+m)((x^(m))/(x^(n)))^(m+n)((x^(n))/(x^(l)))^(n+l) then f'(x) is equal to (a) 1 (b) 0 (c) x^(l+m+n) (d) none of these

(1)/(1)+(1)/(1+2)+(1)/(1+2+3)+.........2020 terms =(m)/(n) where m, n are coprime natural numbers then (m)/(n-1) is equal to (1) 1 (2) 2 (3) 3 (4) None of these

If A=[(1,1),(1,0)] and n epsilon N then A^n is equal to (A) 2^(n-1)A (B) 2^nA (C) nA (D) none of these

If n=2m+1,m in N uu{0}, then int_(0)^((pi)/(2))(sin nx)/(sin x)dx is equal to (i)pi(ii)(pi)/(2)(iii)(pi)/(4) (iv) none of these

A B C is a right-angled triangle in which /_B=90^0 and B C=adot If n points L_1, L_2, ,L_nonA B is divided in n+1 equal parts and L_1M_1, L_2M_2, ,L_n M_n are line segments parallel to B Ca n dM_1, M_2, ,M_n are on A C , then the sum of the lengths of L_1M_1, L_2M_2, ,L_n M_n is (a(n+1))/2 b. (a(n-1))/2 c. (a n)/2 d. none of these

L_(1) is a line passing through the point A(n,n+1) having slope, n, L_(2) is a line passing through the point B(-n, n^(2)) and is perpendicular to L_(1) , If L_(1) and L_(2) intersect on y-axis, then n is equal to ________ (n gt 0)

lim_(x rarr oo)(a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-2)+...+a_(n))/(b_(0)x^(m)+b_(1)x^(m-1)+b_(2)x^(m-2)+...+b_(m)) ; m, n>0 is equal to A. 0 when m > n B. oo when m C. (a_(0))/(b_(0)) when m=n D. none of these

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) If the angle between the lines is 60^(@) then the value of l_(1)(l_(1)+l_(2))+m_(1)(m_(1)+m_(2))+n_(1)(n_(1)+n_(2)) is

If one root of the equation lx^(2)+mx+n=0 is (9)/(2) equal to (l,m and n are positive integers) and (m)/(4n)=(l)/(m), then l+n is equal to