# Basic Mathematics (BCA) Questions

## Section A

Multiple Choice Questions (3 Marks each)

1. In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach
mathematics and 4 teach physics and mathematics. How many teach physics?
a) 36
b) 12
c) 24
d) 28
1. For the propositional variables 𝑝 and 𝑞, 𝑝 → 𝑞 is False when
a) Both 𝑝 and 𝑞 are True
b) Both 𝑝 and 𝑞 are False
c) 𝑝 is False and 𝑞 is True
d) 𝑝 is True and 𝑞 is False
1. For the usual sets, which one of the following is incorrect?
a) The algebraic structure (𝑁,×) has the identity element as 1
b) The algebraic structure (𝑁, +) has the identity element as 0
c) The algebraic structure (𝑍,×) has the identity element as 1
d) The algebraic structure (𝑍, +) has the identity element as 0
1. Let us consider a circle of radius 7 cm. If an arc of this circle subtends an angle of 20 radian to the centre, then what is the area of the sector such formed?
a) 140 cm2
b) 490 cm2
c) 70 cm2
d) 980 cm2
1. A bag contains 3 red balls, 4 green balls and 5 blue balls. The probability of choosing 2 red balls,
1 green ball and one blue ball is
a) 2/27
b) 1/15
c) 4/33
d) 3/29

6. What is the value of the following limit?

lim┬(n→∞)⁡〖(2n^2-3n+7)/(n^2+5n+35)〗

a) 0
b) 1/5
c) 7
d) Does not exist.

7. d/dx (e^x sin⁡x )=?

a) e^x (sin⁡x+cos⁡x)
b) e^x (sin⁡x-cos⁡x)
c) (sin⁡x+cos⁡x)
d) e^x cos⁡x

8. ∫[e^x+3/√(1-x^2 )] dx=?

a) e^x+3 cos^(-1)⁡x+C
b) e^x-3 sin^(-1)⁡x+C
c) e^x+3 tan^(-1)⁡x+C
d) e^x+3 sin^(-1)⁡x+C

9. The sum of the order and degree of the following differential equation is
((d^2 y)/(dx^2 ))^3-7x(dy/dx)^2+2y=sin⁡ x

a) 4
b) 5
c) 6
d) 2

10. The value of the determinant |(2&[email protected]&-1)| is

a) 10
b) −14
c) 1
d) −10

## Section B

a) Show that (a_n )→0where a_n=1/2^n
b) If f(x)=e^x show that f^’ (x)=e^x.
c) Evaluate ∫〖sin⁡  5x cos⁡  2x dx〗
d) Integrate the function 1/((1+e^x ) (1+e^(-x) ) ) with respect to x by substitution method.
e) Solve dy/dx-(y cos⁡x+sin⁡y+y)/(sin⁡x+x cos⁡y+x)=0
f) Evaluate the determinant Δ=| (0&2&[email protected]&4&[email protected]&0&4) |