# Multiple Choice Questions of Math For Diploma Entrance Exam

### MCQs of Math For Diploma Entrance Exam Set-II

1. If a coin is tossed twice, then the probability of getting at least one tail is...........

Since only one coin is tossed twice, it is an independent event.
In 1ˢᵗ trial:
Probability of getting tail
i.e. P(T₁)=1/2
Again, In 2ⁿᵈ trial:
Probability of getting tail
P(T₂) = 1/2
∴ Probability of getting tail in both trial
i.e. P(T)=P(T₁)×P(T₂)
=1/2×1/2
=1/4

2. Two numbers are in the ratio 4:5, If their sum is 180, what will be the first number?

Let the first and second number be 4x and 5x respectively.
According to the question,
4x+5x=180
or,9x=180
or, x=180/9=20
∴First number=4×20=80
Second number=5×20=100

3. The distance between the parallel lines 3x+5y=11 and 3x+5y= -23 is............units

4. The perpendiculars drawn from the vertices of the triangle on their opposite sites meet at a point. This point is known as...........

5. A piece of wire 44 cm long is bent into the form of a circle. Then, the diameter of the circle is...........

6. The area of the circle centered at (1,2) and passing through (4,6) is..........

7. In an examination, a student required 40% marks to pass it. A student getting 185 marks fails by 15 marks, then the total marks is.........

Since, the student failed by 15 marks even though getting 185 marks.
40% marks =185+15= 200
or, 1% marks = 200/40= 5
or, 100% marks= 5×100= 500
Hence, the total marks =500

8. The sum of all odd numbers between 0 and 100 is..........

Odd numbers between 0 and 100 is 1,3,5,.......99.
1ˢᵗ term(a) = 1
2ⁿᵈ term(b) = 3
Common difference(d) = 3-1= 2
last term(tₙ) = 99
No. of terms(n) = ?
We know that,
a + (n-1)d = tₙ
or, 1 + (n-1)2 = 99
or, (n-1)2 = 99-1
or, n-1 = 98/2
or, n = 49+1
or,n = 50

Now, We know that,
Sum of odd numbers(Sₙ)=n²
or,S₅₀=50²=2500

9. If 18,a,b,-3 are in A.P., then a+b=.........

Given, 18,a,b, -3 are in A.P.
1ˢᵗ term(a)= 18
No. of terms(n) = 4
Last term(tₙ) = -3
We know that,
a + (n-1)d = tₙ
or, 18 + (4-1)d = -3
or, 3d = -3-18
or, d = -21/3
or, d = -7

Again, we know that,
a = 1ˢᵗ term(a) + d = 18 - 7 = 11
b = 1ˢᵗ term(a) + 2d= 18 + 2 × (-7)= 18 - 14 = 4

∴a + b= 11 + 4 = 15

10. The geometric mean between the two numbers 2 and 16 is...........

Given,
1ˢᵗ term(a) = 2
Last term(b) = 16
Geometric Mean(GM) = ?
We know that,
GM = √ab
= √2×16
=√32
= √2²×2²×2
= 4√2

11. Two lines represented by ax²+2hxy+by²=0 will be perpendicular to each other if...........

12. The equation ax²+2hxy+by²+2gx+2fy+c=0 represents a circle if.............

The correct answer is 'a=b & h=0'

13. The point of intersection of the lines 3x-4y-10=0 and 5x+3y-7=0 is...........

14. The product of √-5 and √-9 is..........

√-5×√-9
=√45
=√5×3²
=3√5

15. The inverse of matrix (³₁ ²₁) is..........

16. A square matrix A is said to be non-singular if.............

The correct answer is |A|≠0 that means when determinant of the square matrix is not equal to 0, it is called non- singular matrix.

17. The formula for calculating the sum of the first 'n' odd natural numbers is..........

18. The value of sin18° is.........

19. A function f(x) is odd if..........

The correct answer is f(-x)= -f(x).

20. B⊂A, then n(A∪B) = ..............

The correct answer is 'n(A)' because set A contains every element of set B as set A is superset of subset B.

21. The set {{Φ}, {1},{2},{1,2}} is............of {1,2}.

The given set is subset of {1,2}.

22. A function f(x) is even if..........

23. The product of matrices Aₘₓₙ and Bₚₓₛ exists if.........

The correct answer is 'n=p' because the product of any two matrices is only possible when the number of columns of first matrix is equal to the number of rows of second matrix.

24. The ratio of the ages of father and son is 9:4. If the son is 24 years old, what is the father's age?

25. The equation of the line parallel to y-axis is.........

The equation of any line parallel to y-axis is x=a.

26. If median=4 and mean=3, then mode=.............