BSc CS Sem 2 BSc CS Semester 2 (2021 2022) May 2022 COMPUTER SCIENCE Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 Attempt all multiple choice questions: 40 marks
   • A) A function is said to be invertible if and only if it is
   • B) Gradient of f(x,y) = x3 + 2xy? at (1,1) is
   • C) 3x2dx is
   • a) b) 2*log2 +c
   • E) Integrating factor of differential equation +
   • F) Area under the curve y = x? over the interval [-1,1] is
   • G) Solution of differential equation is
   • b) logy
   • d) logy = 7 te
   • H) Unit vector of 3i + 4j is
   • c)2 d) does not exist
   • K) Which of the following is not true?
   • L) There is no change in function f at point u in the direction of vector v if
   • a) Dis in the direction of Vf b) is in the direction of —Vf
   • c) 0 is perpendicular to Vf d) makes angle Vf
   • M) f xsinx dx is
   • N) The interval in which the function f(x) = is increasing is
   • O) Rate of change of one variable with respect to another is called
   • a) continuity b) integral
   • C) derivative d) inflexion
   • P) Critical point of the function f(x) = x? + 6x is
   • Q) is
   • a) log|x| +c +c
   • R) Absolute maximum value of f(x) = x* — 4x in [1, 3] is ‘S) A function f(x) is concave up on an interval I if for all x
   • T) Derivative of e? is
2. Q2 Attempt the following (solve any 02) [10
   • i) Divide 100 into two parts such that sum of their squares is minimum
   • ii) Draw the graph of the curve y = 4 — 3x2 4 ili) Find the intervals in which the function f (x) = 2x3 — 12x? + 18x + 15 is increasing J iv) Find the horizontal and vertical asymptotes of the function f(x) =
3. Q3 Attempt the following (solve any 02) [10
   • i) Use method with a step size of 0.25 to find approximate solution of initial value
   • ii) Estimate f, using Simpson’s rule where n = 4
   • iii) Solve the differential equation:
   • iv) Find the area bounded between the graph of cosx, sinx and y-axis on [0, 7/4]
4. Q4 Attempt the following (solve any 02) {10 marks]
   • i) Find second order derivatives of the function
   • ii) Find the local extrema or saddle points of the function
   • iii) Find the directional derivative of the function f(x,y) = x? + at the point (-2, -3) in the direction of the vector = i+ j
   • iv) Find the equation for the tangent plane and parametric equation for normal line to the surface x* + 4y = z? at the point (1,4,3)
5. Q5 Attempt the following (solve any 01) [ 5 marks
   • i) Find the absolute maximum and minimum values of the function
   • ii) Solve the differential equation: = —4xy?
   • iii) Let z = x = t? and y = t? Use chain rule to find =

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