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JEE Main 5 Years at a Glance, 1., , If sum, , of all, , 8cos x| COS, , the, , solutions, , o, , of the, , equation, , 4., , If5(tan x-cos x), , i n (0. m) is k, (a), , then k is equal to:, , 13, , (a), 2., , 3., , 9, , b)9, , 2018, (c), , 20, , 9, , 5., , (d), , PQR is a triangular park with PQ=PR=200 m. AT.V. tower, stands at the mid-point of QR. If the angles of elevation of, the top of the tower at P, Q and R are respectively 45°, 30°, and 30°, then the height ofthe tower (in m) is:, [20181, , (a) 9(1+ 3), , (c)18(1+ 3), , the foot of the tower, is., , Online 20181, , (b), , (b), , 9, , 5, , (c), , 3, , (d), , Let a vertical tower AB have its end A on the level ground., Let C be the mid-point of AB and Pbe a point on the ground, such that AP =2AB. If ZBPC ==B, then tan ß is equal to, , (a), 6., , If 0Sx, , (c), , (b), , 9, <, , 4, , (d), , 9, , 27t, then the number of real values of x, which, , satisfy the equation, , coS x +cos 2x +cos 3x +cos 4x, 7., , =, , 2016, , 0 is:, 3, , (d) 5, (a) 7, A man is walking towards a vertical pillar in a straight path,, b), , a, , change, min) by the car to reach, , 2017], , 2017, , (a) 50, (b) 1003 (c) 50/2 (d) 100, A man on the top of a vertical tower observes a car moving, at uniform speed towards the tower on a horizontal road. If, it takes 18 min, for the angle of depression of the car to, from 30° to 45°, then after this, the time taken (in, , 2cos 2x +9, then the value ofcos 4x is, , =, , 9, , (c), , at a uniform speed. At a certain point A on the path, he, observes that the angle of elevation of the top of the pillar is, 30°. After walking for 10 minutes from A in the same direction,, at a point B, he observes that the angle of elevation of the, , top ofthe pillar is 60°. Then the time taken (in minutes) by, 2, , (d) 18 (V3 -1), , him, from B to reach the pillar, is:, (a) 20, (b) 5, (c) 6, , 20161, (d), , 10

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8., , Ifm and M are the minimum and the maximum values of, 1, 4+sin 2x-2 cos" x, x¬ R, then M - m is equal to:, 2, , Online 2016], 9, , (a), 9., , (b), , 4, , 15, 4, , (a), 13., , 7, , (c), , (d), , 4, , 4, , Online 2016], (b) 6, (c) 4, (a) 2, (d) 8, If the angles of elevation of the top of a tower from three, , collinear points A, B and C, on a line leading to the foot of, , 11., , 12., , (b) 2:3, , ()3:1, , a, , Let, , fk (x) =*(sinx+cos" x), , where, , xe, , R and k21., , K, , Then f4(x)-fo (x) equals, , (d), , bird is sitting on the top ofa vertical pole 20 m high and its, elevation from a point O on the ground is 45°. It flies off, horizontally straight away from the point O. After one, second, the elevation of the bird from O is reduced to 30°., , 2014, , 2014], , (a) 20/2, , (b) 20(3-1), , (c) 40(2-1), , ()40(3-V2), (p*q*0), then c o t t i s equal, , P-, , )3:2, , and 2C= 60°. Then the ordered, AABC, =2+3, b, Online 2015, pair (ZA, ZB) is equal to, (b) (105°, 15°), (a) (45°, 75°), () (15°, 105°), (d) (75°,45°), In, , 6, , [Online 2014], , to:, , 2015, , AB: BC, is:, , 1:3, , (c), , A, , 14. If cosect=, , the tower, are 30°, 45° and 60° respectively, then the ratio,, , (a), , 12, , Then the speed (in m/s) ofthe bird is, , The number of x e [0, 2t] for which, , 2 sin x+ 18cos x -V2cos" x + 18sin* x = 1 is, , 10., , (b), , 4, , b), , (a), 15., , Vp, , (c), , Vpq, , (d pq, , Thenumber of values of o in [0, 27t] for which, 2sin'a-7 sin- a+7 sin o=2, is:, , Online 2014], (a), , 6, , (b), , 4, , (c), , 3, , (d), , 1

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Exercise-2:Concept Applicator, 1., , The expression, , 37T, , (a), , reduces to, (a) 1, 2., , when simplified, , +, , (c)sin (a/2), , The solution to the inequality cos x, , (d) sin a, , 2T, , xE, , 2nTt+2nT+, , +, , (cosx + secx), , then the, , ne, , 3, , (d) 0, , C)9, , Iftan+0 + tan, , 4, , 0=p sec20, , then, , the value of, , pis equal to:, , 9., 9., , -is, 10., , (b), , 2, , 4, , The value, , (d), , (c)1, , 3, , Period of sin 6-v3 cos, , (a), , (a) xe2nT+,2n+|;ne, Z, 6, (b), , (b), , 7, , (a), , (b) 0, , x), , 4, , 8., cot+cot|, , + cosec, , minimum value ofy, Vxe R,is, , cos(20 2Tt)tan| o 2o, sin, 4, , Ify= (sin x, , 7., , 1+sin 20, , is, , (d) 2, (c), (b) 2, oftan°20°- 33 tan 20° +27 tan 20° is:, , (d), (c) 4, b) 3, 2, Which ofthe following is correct?, (b) sin 1°<sin1, (a) sin 1°> sin 1, , 5, , (a), , 11., , Z, , 4, , TT, , 2nT, (d), , 3., , (c), , ,2nT+, , Nonë of these, , of a tower. They m e a s u r e, Two men are on the opposite side, of the tower 45° and 30°, the angle of elevation of the top, the tower is 40 m, find the, respectively. If the height of, , 4., 4, , 40, , The, , (b), , m, , range, , 109.28 m, (c) 68.280 m (d), expression, the, values o f, , 40/3, of, , is, , The value of, , (a), , Which, , -, , 1+tan 15°, , pairs of function, , () S)=,g()=11, None of these, , 2, , 15., (d), , 2, , sin, , = then range offfx) is, , x+3, , cos" x+ 3cos°, , x, , is equal to, , (b) cos x sinx, (d), , 1, , co, , 2, 16, , (b), , (d), , ()16, 16, , General solution of the equation, , 2, , 32, , 2 cot 9+2/3 cot 0+ 4cosec +8=0 is, , is identical?, , cosx ;g (x) =1, (b) f(x) sinfx +, =, , 3, , 18, , STT, 7Tt, 3TT, The value of s i n s i n s i n,Sin, 1s, 16, 16, 16, 16, , (a), , (a) Sx)=vx*.g(x) =x, , (d), , 14., , 1-tan 1is, (c), , =, , If sinx +sinx =1, then, , (a), , (d) -3/3,13], , b)3, , 1, , COS, , (c)0, , b) -6, 8], , (c)-8,6], 5., , 13., , cos x+cos', , -7,71, , (d) sin 1°, , V1+tanx V1+cot x, (a) -1,0] (b) [0, 1], (c) -1, 1] (d) None of these, , m, , Scos+3cos| +|+1, (a), , Sin x, , 12. Let fx)=-, , distance between the men., , (a), , sin 1°= sin 1, , (a), , (c), , mTttnEI, , 2nT+ n¬l, , (b), , nTt+neI, 6, , (d) 2nT +1T nET, 6

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16., , A man observes when he has climbed up, , ofthe length of, , 23., , an inclined ladder, placed against a wall, the angular, depression of an object on the floor is a and that after he, has elimbed the ladder fully, the depression is B If the, inclination of the ladder to the floor is 0, then cot, 3 cot a-cot B, 3 cot B-cot a, ., , =, , (a), , (b), , 2, , cot B-cot a, , (c), 17., , (d), , 2, , 2, , The number ofsolution oftan x +secx=2cos.xin (0, 2 7t) is, (d) 1, (c) 0, (a) 2, (b) 3, 3, , 18., , 25., , and cosB=, IfsinA=z,0<KA<, 5, , -12, , 13, , (b), , 0, , (a), , 19., , 20., , 21., , 13, , 65, , 75, , v2, , 4, , b) (0, 21)-[1, 7), , (c)0.5-, , (d) (0, 1), , 26., , 65, , (a), , PBD ,, , then AP is equal to, , 2a sin(b), , 2b sin, , C, , (c), , (c), , 50(v3 -1)m, , 50/3 m, , (d) 50 1-, , m, , (c), , 0, , sin B, cos, , A, , (a) ab=c, a=b, , but not, 4, , (C), Let, , =, , 2 sin C, , (b), , c=a, , (d), , b=c, , (d), , 2, , (d), , 4, , , then, , then sin 0 is, 4, , (a), , r-1, , whenever it is defined is, , In any triangle ABC, if, , 30., , 3, , ysec, , 28., , of, , (b), , 1-sin*x, , The value of cosec 430°+y3 sec 470° is, (c)-4, (b) 1, (a) 0, , 45°. The height of tower is, , 50 m, , 1-cosx, , 27., 27., , From the top ofa cliff50 m high, the angles ofdepression, be 30° and, the top and bottom of a tower are observed to, , (a), , tan x, , COSX, , 29. Iftan 6=, , (d), , ne I, , of the function, , Vcosec - 1, (a) 4, b)-2, , (c), , 2c sin, , neI, , nt +, , (d) nT, , sin x, , cotx, , =, , =, , (b), , ne I, , The minimum value, , S)=, , range off(x) cosx- sin x is, (a) -1, 1] (6) -1,-1] () V2/2]d) -2,-2], IfP is a point on the altitude AD of the triangle ABC such, The, , 2, , neI, , (C)nT-, , =, , a) 1. T), , ?, , 12, , TT, , ,n<B<,then, 2, (d), , 4, , 6+2, , (b), , (a) (2n +1), , 37t, , 16, , (d), , 2, , (c) 3+2 d) v6+1, 4, General solution of the equation tan 6 tan 20, 1 is, given by, , of:fx) ycos(sin x)+/log, {x}; {&} denote, , The domain, the fractional part, is, , that, , 22., , (b), , 82, , 15, , ST, , of sin, , value of sin (A - B) is, , 13, , (c), , 1, , What is the value, , (a), , 2, cot a+cot B, , cos 10°, , sin 10°, (a), , 24., , 3, , 1, , but not, , 5, , 5, , - or, , (b), , (d) None of these, , (1 +1+x ) tan y=1+ 1-x.Then sin 4 is equal to, , (a), , 4x, , (c), , x, , 2, , (d), , None of these