JEE Advanced Physics 1000+ Questions PDF (Solved) | IIT-JEE PYQs + Hard Problems

124 CBSE QUESTION BANK of MATHEMATICS Class XII
Question 41. If y= SIn'(6xNl- 9x 1
then find dy
3/2 3V2
Solution : Here, y =sin-'(6x1-9x2) ’ y= sin(2x 3ry1- (3x))
Put 3x = sin
y =sin(2 sin By1 - sin e) ’ y= sin-(2sin 9cos 9)
y= sin (sin 20) ’ y= 20 y=2 sin(3x)
dy 2
x3 =
6

de 1-(3x? Ang

1Mark

? PREVIQUSYEARS QUESTIONS FOR 2023
I. Determine the value of kfor which the following function is continuous at =3.
( +3 -36
,T 3
f(z) = C-3
C=3
(2017 CBSE)
2. If the following function f(r) is continuous at z = 0, then write the value of k.
3c
sin
2
f(æ) = [2017 CBSE Compl]
C =0

I<0
3. Determine the value of the constant 'k' so that the function f(¢) = z is continuous at
3, C0
I=0. [2017 Delhil
dy
4. Ify =log(cos e), then find [2019 CBSE)
dz

5. Ify =cosec (cot N), then find dy
d
[2019 CBSE)
6. Differentiate cos(sin (r)»} with respect toz. (2019CBSE Compl!
7. Differentiate ysin(e") with respect to z. [2019 CBSE Compt.
dy if sin
8. Find da +cos y=1. [2019 CBSE ComplJ

9. Ify = Ae + Be Tthen d'y is equal to :
da (2020 CBSE
(a) 25y (b) 5y (c) -25y (d) 15y
-9
T3
10. If the function fdefined as: f(z) = T-3 is continuous at r=3, find the value of k.
k, C=3
[2020CBSE]

, 125
CONTINUITY AND DIEFERENTIABILITY
log, then equals:
Ify=
11.

(b) -2 (2020CBSEJ
(C) (d)
12. Let fr) = lu|,;for all xeR check its (2020 CBSEJ

thefunction f(x) = (3 -8, if xs5
atr= 0.differentiability
13. If 2k, if x>5 1S continuous. then the value of k is :

(a, 4 [2022 CBSEJ
(e) (a)
14. Thefunction f(r) =[], where (c] is the greatest integer function that is less than or equal to z, 1s
continuOus at :
(a)4 (b) -2 [2022 CBSE)
(c) 1.5 (d) 1
tan- (e), then dy is equal to :
15. Ify=
1 1
(a (b) 2
1+e (C (d)
+e-2x
[2022 CBSE]
16. fe-z) =z°,thendy) is equal to :
dz 1)
3 (2022CBSE]
(a)2 (b) -2 (c) 3 (d)

dy is equal to:
17. Ify=e then
da
(a) -y (b) y (c) c (d) - [202? CBSE)

18. Ifr =t+1,y =2at, then d'y at t= ais:
da?
1 1
1 (c) (d) 0
(a) (b) -202 2,2 (2022 CBSE]


19. The function f(«) =
for T< I is:
|2- for z>1
(a) not differentiable at x = 1 (b) differentiable at r = 1
(c) not continuous at z = 1 (d) neither continuous nor differentiable at =l
(2022 CBSEJ
20. Ify= sin(2 sinc), then (1 - y is equal to :
(a) -*y1 +4y (b) -y1 -4y (c) y1- 4y (d) y1 +4y [2022 CBSE)

ANSWERS

1. k=12 3. k=-3 4. -e tane")
2

e cos(e)
, COsec(cot væ) cot(cot v) cosec N 6. -2r cos(a sin(sin
2y/sin(e")
2/z