The pdf contains multiple type questions on the topic CONTINUITY AND DIFFERENTIABILITY.
The pdf contains the most important questions and covers all the topics in depth.
Answers have been also given on the last page.
Q1. The derivative of 2x + y = sin y is :
2
(A) cos y
2
(B) cos y + 3
2
(C)
cos y− 3
(D) None of these.
Q2. dy
If sin x + y = log x , then dx is equal to :
1−x
(A) x sin y
1−x
(B) x cos y
1+x
(C) x cos y
(D) None of these.
Q3. dy
If 2x + 3x = sin x, then dx is equal to :
cos x+2
(A) 3
cos x−2
(B) 3
(C) cos x + 2
(D) None of these.
Q4. dy
If y = √sin x + y , then dx is equal to :
cos x
(A) 2y−1
cos x
(B)1−2y
sin x
(C) 1−2y
sin x
(D).2y−1
Q5. dy
If cos y = x cos(a + y) with cos α = 1, then dx is equal to :
sin2 (a+y)
(A) sin a
ZIET, BHUBANESWAR Page 1
, cos2 (a+y)
(B) sin a
(C) sin2 (a + y)sinα
(D) None of these.
Q6. dy
If y x = ey−x , then dx is equal to :
1+logy
(A) ylog y
(1+logy)2
(B) y log y
1+logy
(C) (log y)2
(1+logy)2
(D) log y
Q7. dy
If x = ex−y then dx is equal to
x−y
(A) x log x
y−x
(B) log x
y−x
(C) x log x
x−y
(D) log x
Q8. dy
If x = at 2 and y = 2at , then dx is equal to :
(A) t
1
(B) t
−1
(C) t2
(D) None of these.
Q9. dy
If x = a(cos θ + θ sin θ and y = a(sinθ − θcosθ), then dx is equal to :
(A) tan θ
(B) cos θ
(C) sin θ
(D) cot θ
Q10. The derivative of cos−1 (2x 2 − 1) w. r. t cos −1 x is :
(A) 2
−1
(B)
2√1−x2
2
(C) x
(D) 1 − x 2 .
ZIET, BHUBANESWAR Page 2
, Q11. The derivative of sin2 x w. r. t ecos x is:
2cosx
(A) ecosx
2cosx
(B) − ecosx
2
(C) ecosx
(D) None of these.
Q12. d2 y
If y = cos −1 x , then derivative of dx2 in term of y alone is :
(A) – cot y cosec 2 y
(B) cosec y cot 2 y
(C) coty cosec y
(D) None of these.
Q13. dy
If y = log a x + log x a + log a a , then dx is equal to :
1
(A) x + x log a
log a x
(B) + log x
x
1
(C) x log a + x log a
1 log a
(D) x log a + x(log x)2
Q14. dy
If y = (tan x)sin x , then dx is equal to :
(A) sec x + cos x
(B) sec x + log tan x
(C) (tan x)sin x
(D) None of these.
Q15. d2 y
If x = f(t)and y = g(t) then dx2 is equal to :
g′ (t)ˈ
(A)
f′ (t)
g′′ (t)f′ (t)−g′ (t)f′′ (t)
(B) 3
[g′ (t)]
g′′ (t)f′ (t)−g′ (t)f′′ (t)
(C) 2
[g′ (t)]
(D) None of these.
Q16 d2 y
If y= Ae5x + Be−5x , then dx2 =
(A) 25y (B) 5y (C) -25y (D) 15y
ZIET, BHUBANESWAR Page 3
, Q17 d2 y
If x = t 2 and y = t 3 then dx2 =
3 3 3 3
A)2 (B)4t (C)2t (D)4
Q18 2 dy
If y= x x then dx =
2 +1 2 +1
(A) )x X (B)x X (1+2 log x) (c) (1+2 log x) (D) x 2 + 1
Q19 dy
If y =(sinx)x then dx =
(A)(sinx)x (B) (x cot x + log sin x) (c) (sinx)x (x cot x + log sin x) (D)(sinx)x (cot x +
log sin x)
Q20 dy
. If x= 4t , y= 4/t then dx
1 1 1
A)− (B)t 2 (C) )t2 (D) −
t2 t3
Q21 dy
.If x= log t , y= sint t then dx
(A) sint (B) t sint (C) cost (D) t cost
Q22 dy
.If x= a secθ , y=b tanθ then dx
b b
(A) cosec θ (B) cosec θ (C) - a cosec θ (D) sec θ
a
Q23 d2 y
If y=4 x 3 + x +7 then dx2 =
(A) 12x (B) 24x (C ) 24 (D) 12
Q24 d2 y
.If y= log x then dx2 =
1 1
(A) -1 (B) (C) − (D) x
x x2
Q25 d2 y
y= cos2 x + 3x then dx2 =
A) 3x (B) cos2x (C) 3cos2x (D) – 2cos2x
Q26 d2 y
.y=x 3 logx then dx2 =
A) x(5+6 logx) (B) x (C) (5+6 logx) (D) log x
Q27 dy
.If 4x+9 then dx =
(A) 4x+9 (B) 4x+9 log4 (C) log4
(D) log x +4
Q28 dy
. If αtanx then dx =
(A) αtanx (B) sec 2 x (C) sec 2 x log α
tanx 2
(D)α sec x log α
ZIET, BHUBANESWAR Page 4
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