This set of Engineering Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Implicit Differentiation”.
3. Find the differentiation of x4 + y4 = 0
a) – x3⁄y4
b) – x4⁄y3
c) – x3⁄y3
x4 + y4 = 0
4x3 + 4y3 dy⁄dx = 0
dy⁄dx = – x3⁄y3
dy⁄dx = Sec2 (x)Sec(x) ex + Sec2 (x)Tan(x) ex + ex Tan(x)Sec(x)
dy⁄dx = Sec2 (x) ex [Sec(x)+Tan(x)] + ex Tan(x)Sec(x)
6. Implicit functions are those functions
a) Which can be solved for a single variable
b) Which can not be solved for a single variable
c) Which can be eliminated to give zero
d) Which are rational in nature.
Explanation: Implicit functions are those functions, Which can not be solved for a single variable.
For ex, f(x,y) = x3 +y3 -3xy = 0.
8. If Sin(y)=Sin(-1) (y) then
a) (1-y2 )(1 – Cos2 y) = 1
b) (1-y2 )(1 – Sin2 y) = 1
c) (1-y2 )(1 – Siny)=1
d) (1-y2 )(1 – Cosy)=1
9. If Cos(y)=Cos(-1) (y) then
a) (1 – y2 )(1 – Cos2 (y))=1
b) (1 – y2 )(1 – Cos(y))=1
c) (1 – y2 )(1 – Sin2 (y))=1
d) (1 – y2 )(1 – Sin(y))=1
Explanation: Cos(y)=Cos(-1) (y)
Differentiating both sides
-Sin(y) = -1/√(1-y2 )
(1 – y2 )(1 – Cos2 (y)) = 1.
11. If the velocity of car at time t(sec) is directly proportional to the square of its velocity at time (t-1)(sec). Then find the ratio of acceleration at t=10sec to 9sec if proportionality constant is k=10 sec/mt and velocity at t=9sec is 10 mt/sec
Differentiating w.r.t time we get
dv(t)⁄dt = 2kv(t-1) dv(t – 1)⁄dt
a(t) = 2*10*10 a(t-1)
a(t)⁄a(t – 1) = 200.
12. If z(x,y) = 2Sin(x)+Cos(y)Sin(x) find d2z(xy)⁄dxdy= ?
13. If the car is having a displace from point 1 to point 2 in t sec which is given by equation y(x) = x2 + x + 1. Then,
a) Car is moving with constant acceleration
b) Car is moving with constant velocity.
c) Neither acceleration nor velocity is constant.
d) Both aceleration and velocity is contant.
Explanation: y(x) = x2 + x + 1
Velocity is , v = dy⁄dx = 2x + 1 (not constant)
Acceleration is a = dy⁄dx = 2 (constant).
Sanfoundry Global Education & Learning Series – Engineering Mathematics.
To practice all areas of Engineering Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.