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364k views 4-9 20 62 62 47 61 0 Ashish Bajpai Saurabh deshmukh Dedicated on 16 September 2018 Chemistry "Thank a lot sir for making excellent revision course last year because of you I loved maths and cracked jee without coaching, you are great si." Ashish Bajpai Referral ID: AshishBajpai

9th January Maths 1st Shift Solution Q1 to Q5

n + 1, n e N (the set the ntegral I. For *2 of natural numbers), 2sin(2 -1 sin20x2-1) 2sin(x2-1) +sin2(x2-1) dx is equal to (where c is a constant of integration) (a) ^loge sec2 (b) logee (1+c (c) loge lsec(x2-1)l+c (d) loge |seq-2 2 2 2 2 2

2403 15 2. If the fractional part of the number is , then k is equal to 15 (a) 6 (b) 8(c) 14 (d) 4

3. Let f: R- R be a function defined as 5, f xs1 a+bx, if 1<x<3 .Then fis f(x)- 30, x25 (a) continuous if a --5 andb - 10 (b) continuous if a 5 and b -5 (c) continuous if a - 0 and b-5 (d) not continuous for any values of a and b

4. The value of |cosxp dx is (a) 4/3 (b) -4/3 (c) 0 (d) 2/3

5. Axis of a parabola lies along x-axis. Ifits vertex and focus are at distances 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it? (a) (6,4/2) (c) (5, 2V6)

1. For x2 ^ n + 1, n e N (the set the ntegral of natural numbers), 2sin(2 -1) -sin2(x2-1) 2sin x2 - 1)+sin 2(x2-1) dx is equal to (where c is a constant of integration) (a) loge sec (b) logec (-1c 2 2 2 log sec(x-1) +c 2 e2 (d) loge |sec|-2 T C

1. Let 2 sin(x- 2 sin(x2+ sin 2(x2 -1) -1) - sin 2(x^ -1) dx Put x2-1 = t 2x dx = dt 1 2sint - sin 2t dt 22sint+sin 2t 1 1- cost 2V1 cost loge Sec +loge sec Option A & D correct

2002(2) 403 234 100 (15 +1)100 15 2. Consider, _ = 15 15 Which can be written as (15A1) 8+ 15 15 Here, 8 is an integer. 403 8 .. Fractional part of Given 15 15 15 Option B is Correct

5 if x S 1 a + bx,f 1<x <3 3. Given, f(x) - 30, if Also,f(3)b15,(3) a 3b,(3)b 15 Also,f(5) = 30,f(5-) = b + 25,f(5*) = 30 (iii) From (i), (ii) and (iii), clearly, f is not continuous for any values of a and Option D is correct.

Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively 5. from the origin, on the positive x-axis then which of the following points does not lie on it? (a) (6, 4V2) (c) (5, 2V6)

5. We have, vertex A(2,0) and focus S(4, 0). 01(2,0) S(4,0) :. Equation of parabola will be Clearly, (8, 6) will not lie on this parabola. Option D is Correct.