# RD SHARMA Solutions for Class 12-science Maths Chapter 12 - Higher Order Derivatives

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## Chapter 12 - Higher Order Derivatives Exercise MCQ

Question 27

If  then  is equal to

a. 25y

b. 5y

c. -25y

d. 15y

Solution 27

Given:

Differentiating the above equation w.r.t x, we get

Differentiating the equation (i) w.r.t x, we get

Question 28

If  then  equals

a.

b.

c.

d.

Solution 28

Given:

Differentiating the above equation w.r.t x, we get

Again differentiating w.r.t x, we get

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Correct option: (d)

Question 6

If y = a + bx2, a,b arbitarary constansts, then

Solution 6

Question 7

If f (x) = (cos x + i sin x) (cos 2x + i sin 2x) (cos 3x + i sin 3x)…. (cos nx + i sin nx) and f (1) = 1, then f'' (1) is equal to

Solution 7

Question 8

Solution 8

Question 9

If f"(x)= then (1-x2) f"(x) - x f"(x)=

(a) 1

(b) -1

(c) 0

(d) none of these

Solution 9

Question 10

Solution 10

Question 11

Let f (x) be a polynomial. Then, the second order derivative of f (ex) is

(a) f"(ex)e2x + f'(ex)ex

(b) f"(ex)ex + f'(ex)

(c) f"(ex)e2x + f"(ex)ex

(d) f"(ex)

Solution 11

Question 12

If y = a cos (loge x) + b sin (loge x), then x2 y2 + xy1 =

(a) 0

(b) y

(c) - y

(d) none of these

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

If y = sin (m sin -1 x), then (1-x2) y2 - xy1 is equal to

(a) m2y

(b) my

(c) -m2y

(d) none of these

Solution 15

Question 16

If y = (sin-1 x)2, then (1-x2 )y2 is equal to

(a) xy1 + 2

(b) xy1 - 2

(c) - xy1 + 2

(d) none of these

Solution 16

Question 17

If y = e tanx, then (cos2 x) y2 =

(a) (1 - sin 2x) y1

(b) - 1 (1 + sin 2x) y1

(c) (1+ sin 2x) y1

(d) none of these

Solution 17

Question 18

Solution 18

Question is incorrect.

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

If y1/n + y-1/n = 2x, then (x2 - 1) y2 + xy1 =

(a) -n2y

(b) n2y

(c) 0

(d) none of these

Solution 22

Question 23

Solution 23

Question 24

If y = xn-1 log x then x2y2+(3 -2n) xy1 is equal to

(a) -3

(b) 1

(c) 3

(d) none of these

Solution 24

Question 25

If xy - log e y = 1 satisfies the equation x (yy2 + ) - y2 + λyy1 = 0, then λ =

(a) -3

(b) 1

(c) 3

(d) none of these

Solution 25

Question 26

If y2 = ax2 + bx + c, then

(a) a constant

(b) a function of x only

(c) a function of y only

(d) a function of x and y

Solution 26

## Chapter 12 - Higher Order Derivatives Exercise Ex. 12.1

Question 1(i)
Solution 1(i)
Question 1(ii)
Solution 1(ii)
Question 1(iii)

Find the second order derivative of log(sinx).

Solution 1(iii)

Question 1(iv)
Solution 1(iv)

Question 1(v)
Solution 1(v)
Question 1(vi)
Solution 1(vi)
Question 1(vii)
Solution 1(vii)
Question 1(viii)

Solution 1(viii)

Question 1(ix)
Solution 1(ix)
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5

Solution 5

Question 6

Solution 6

Question 7
Solution 7
Question 8
Solution 8
Question 10

Solution 10

Question 11
Solution 11

Question 12
Solution 12
Question 13

Solution 13

Question 14

If , find

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17
Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Solution 34

Question 35

Solution 35

Question 36

Solution 36

Question 37

Solution 37

Question 38

Solution 38

Question 39

Solution 39

Question 40

Solution 40

Question 41

Solution 41

Question 42

Solution 42

Question 43

Solution 43

Question 44

Solution 44

Question 45

Solution 45

Question 46

Solution 46

Question 47

Solution 47

Question 49

Solution 49

Question 50

Solution 50

Question 51

Solution 51

Question 52

Solution 52

Question 53

Solution 53

Question 9

If  prove that  and

Solution 9

Given:

Differentiating 'x' w.r.t  we get

Differentiating 'y' w.r.t  we get

Dividing (ii) by (i), we get

… (iii)

Differentiating above equation w.r.t x, we get

Hence,

Question 48

If  find

Solution 48

Given:

Differentiating 'x' w.r.t t, we get

Differentiating 'y' w.r.t t, we get

Dividing (ii) by (i), we get

Differentiating above equation w.r.t x, we get

Hence,

## Chapter 12 - Higher Order Derivatives Exercise Ex. 12VSAQ

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

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