Question – 1

Question – 2

Question – 3

Question – 4

Question – 5

Question – 6

Question – 7

Question – 8

Question – 9

Question – 10 & Question – 11

Question – 12

Question – 13

Question – 14

Question – 15

Question – 16

Question – 1

Question – 2

Question – 3

Question – 4

Question – 5

Question – 6

Question – 7

Question – 8

Question 8. Find the value of k, if the following function is continuous {\displaystyle f(x)=\begin{cases} \frac{log (1+ax)-log (1-bx)}{x}, & \text{ if } x\ne 0 \\ k, & \text{ if } x=0 \end{cases} }

Question – 9

Question – 10

Question – 11

Question – 12

Question – 13

Question – 14

Question – 15

Question – 16

Question – 17

Question – 18 and Question – 19

Question – 1

Question – 2

Question – 3

Question – 4

Question – 5

Question – 17

Question – 18

Question – 20

Question – 21, 22

Question – 31

Question – 32

Question – 33

Question – 34

Question – 19

Question – 1, 2, 3

Question – 4, 5

Question – 6

Question – 7, 8

Question – 1, 2

Question – 3

Question – 4, 5

Question – 6

Question – 7

Question – 8

Question – 9

Question – 10

Question – 11, 12

Question – 13, 14

Question – 15

Question – 1

Question – 2, 3

Question – 4, 5

Question – 6, 7

Question – 8, 9, 10

Question – 2

Question – 3

Question – 1

Question – 4

Question – 5

Question – 6

Question – 7

Question – 8

Question – 9

Question – 10

Question – 11

Question – 12

Question – 13

Question – 14

Question – 15

Question – 16

Question – 17

Question – 18

Question – 1

Question – 2

Question – 3

Question – 4

Question – 5

Question – 6

Question – 7

Question – 8

Question – 9

Question – 10

Question – 11

Question – 1, 2, 3, 4

Question – 5

Question – 6

Question – 7

Question – 8

Question – 9

Question – 10

Question – 11

Question – 13

Question – 14

Question 14. If { \displaystyle y = Ae^{mx} + Be^{nx}} , show that { \displaystyle \frac{d^2{y}}{dx^2} - (m + n)\frac{dy}{dx} + mny = 0 } .

Question – 12

Question – 15

Question – 16

Question – 17

Question – 1

Question – 2

Question – 3

Question – 4

Question – 5

Question – 6

Question – 7

Question – 8

Question – 9

Question – 10

Question – 11

Question – 12

Question – 13

Question – 14

Question – 15

Question 15. If { \displaystyle (x - a)^2 + (y - b)^2 = c^2 } , for some c > 0, prove that {\displaystyle \frac{\left[ 1 + \left( \frac{dy}{dx}\right )^2 \right ]^{\frac{3}{2}}}{\frac{d^2y}{dx^2}} } is a constant independent of a and b.

Question – 16

Question – 17

Question – 18, 21

Question – 19

Question – 20

Question – 22

Question – 23