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1., , Let, , S(x), , when x is rational, , {0,, , =, , (a) 0, , 2., , (b), , 1, , (d), , None of these, , 5., , lim -n+1, , _, , 6., , (c) n+, , (d) None, , 13., , (a), , dx, 0, , e-l, , (d), , 1+ x-+x# 1+x, (b), , 8., , 0, , (b), , 1, , 1, , lim, , (a), 9., , Let, , o, , (d), , (c), , Iffx), , lim, , 1, , X, , None of these, , 10, , +, , (d) 100, , 1S, , Then lim, , (b) -1/12, , (c) 2/3, , 1-cos(ax +bx+ C), (x-a), , a, , (c)(a-, , sinlog(+3x), A, , (b) (h, 4, 3, , (6), , is, , (d), , + c=, , 0,, , equal to:, , -B), , (d) None of these, , 3, , (d), , X, , n 4), , 15., , 1/3, , Evaluate limn, , x-2, , 1-xy, , for all x, yE R, , arm, (xy# 1) a, , 4, , 3, , 3, , b) log 10, , (d), , +, , 3, , (d), , x-x-2, x -2x- sin(x-2), , log 5 log2, , (c)log, , 16. lim, , x+y, , =2. Then, f, (b), , (a), , ß be the roots of ax +bx, , (a) 0, , 1S, , 2, , f)= "|, , is equal to, , Sin x, , 1/6, and, , (4-1), , (d) 200, , +Y, , (cos x 2 - (cos x)3, x0, , (c)100, , (a)(In4, , equal to, , lim+1+(x+2), +(x +100)0, +10, (a), , 0, , ()n 4y, , (C)(a+B+Y)x+5+Y-1, 7., 7., , b), , The value of lim, , 14., is, , 50, , 4, , c), , 1+-4 x-, , () 16, , (o), , 2, , 99, , n(n-1), , 1, , then, , -Sin 2x, T1+cos 4x, , x0, , (b) e2, , (a) e, If, , 2, , + x +l,, f)1000, f'(1)=mf (0), where m is equal to, , 0., then the value, , n-n-1, , nco, , (d), , 100, , (a), , n, , 4, , For the function, , 12., , of a, , (b) n, , (c), , lim, , fx)=+ +, , x2, , (a), , (x+1), , (b), , (b), , (c)x, , (sin nx) [(a -n}nx tanx], , x>0, , a))x-b\x-, , lim, , (x-1), , Evaluate, , -, , If lim, , then, , (d) es, , c)e5, , (b)-1, , lim t b x +ea, =2, , (a) 2, , 11., , (b) e, , 1, , 10. If, , 1, , dy, Ify=(1 +x4) (1 +x2) (1 -x4), thenis, equal to, dx, (a), , 4., , X0, , For xeR, limn, (a) e, , 3., , then lim f(x) is:, , when x is irrational, , 1-2, , (a) 0, , (b), , (c), , (d), , 0, , 1sequal to, , None of these, , 2

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17., , If z, = COS, , t1Sin, wherer, , = 1, 2. 3..., , ,, , n, , then, , 24, , lim z122Z3 -..n 1S equal to, , lim, , sin(Tt cosXequals, , 0, , (b), , (a)T, (a) cosd+isin 0, , (b), , (c), , (d), , a/2, , cos(a/2)-isin(a/2), 25., , If, , +1, x<0, , 18, Iff (x)= {0, , a#l, , , X =0 then lim f(x)exists for al, , (b), , Let f(r) =4 and, , 20., , given by, (a) 2, , a-1, , (d) a#2, , 1S, , 0+, , 4, , (a), , =, , (c), , cos+sine, , lim, , 4, , 27., , ()-2 (d) 2, , 4, , S (x) =4. Then lim, , x2, , non-zero number is, (b) 2, , 3, , (d), , (d) 4, , 3, , F....+nl/cos2, , 22. The value of lim |1 cos +2/cos x++/cos x, , 28., , (d), , (c), , n, , (b), , 83, , (d), , 0, , +, , x, , +X+1,, , 100 99, , (d) 200, , (c) 100, , (b) 0, , 50, , lim (sec x - tan x) is equal to, , (a), , 29., , 7cosx, , (b), , 0, , 0, , (c), , 2, , sin(sgn(x), (sgn(x), , lim, , is, , where, , (d), , 1, , 3, , denotes the greatest, , integer function, is equal to, , (b) 1, , 0, , (d) does not exist, , (c)-1, , nn+1), 2, , 30., , (C), , For the function, , (a), , 1+v2+x -v3, The value of limnX2, X-2, a), , a=-2, b=4, , a=4, b=-2, , XT/2, , x L2, , 23., , (c), , (d) None of these, , f'l)=mf'(0), where mis equal to, , x-2, , x-1(cOS X isa finite, x", , (c), , (a), , (b), , 0, then, , ax +bx, then, b), , f(x)=, , J(2)-2/ (x).is, , (c)-4, x0, , 0, , to, , (b) a=3 and b =9/2, (d) a=3 and b=-9/2, , (a) a=4, b =2, , (a), , b)-2, , (cos, 21. The integer n for which lim, , (a), , 1, , Xa, , a#0, , (b), , The value of, , 19., , a = - 3 and b = 9/2, , ( c ) a = - 3 and b = -9/2, , x-1,x>0, (a), , (d), , Tw2, , +b) exists and is equal, , sin 3x + ax, , lim, (x, X0, , (a), , x, , (c), , T, , Iffx) |cos x], then f, =, , is equal to, , is, , a), , 43, , b), , 2, , (d) None of these, , None of these, , Answer key, JEE Main 5 Years at a Glance, , (6)|, , 2, , (c)3 c)4, , (b) 5 a ) 6 (b)7, , (a)8, , (a) 9(c)10 (b), , EXERCISE-1: Concept Builder (Topicwise), , 1, , c), , 7 (b) 13 6) 19 (b) 25 (a) 31 (d37 ()43 (d) 49 (d) 55, , 2, , (d), , 3, , (c), , 4, , (c) 10, (d)16, , 5, 6, , (c), (a), , (b), (c), , 8, , (6)14, , 9(c)15, 11, , (d), , 20, , (c)| 21, (a)22, , (d)| 17 (b)23, , 38, , (a), , 44 (a), , (a)|27 (d)33 (d)39, , (d), , 45, , (b)26, , (b)28, (d), , 29, , (a), , 32, , (b), , 50 (c)| 56, , (a) 51 (c)57 (b), , d)34c)40 (c)46 (c) 52(b)58, (b)35 (a)41 (d)47 (c) 53 (c) 59, , 12 (a)18 (a) 24 (b)|30(a) 36, , (c), , (b), , (a)42 (a)|48|(6)54 (a)60, , (b), , (d), , (a), , EXERCISE-2:Concept Applicator, , (c)7 d) 10 (d)13 (b)16 (b)19 (d)22 (b)25, (b), , 8, , b)11(a)14d)17C)20 (c) 23 (a) 26, , (a), , 28, , (b)29, , (a), (a), , 6 ) 6 (a)9 (c)12 (c)15 (a) 18 (b)21 ()24 (b)27 (c)30b