Mathematics Test 225

Result

Mathematics Test 225

Score
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Rank
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Weekly Quiz Competition

Question 1
4 / -1

In a town of 10000 families, it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then the number of families that buy none of these newspapers is

A
4000

B
4300

C
4500

D
5000

Solution

Number of families who buy none of A, B and C = N - n(A ∪ B ∪ C),

where N = Total number of families.

n(A): Number of Newspaper A readers.

n(B): Number of Newspaper B readers.

n(C): Number of Newspaper C readers.

Number of families who buy none of A, B and C = 10000 - {n(A) + n(B) + n(C) - n(A ⌒ B) - n(B ⌒ C) - n(A ⌒ C) + n(A ⌒ B ⌒ C)}

= 10000 - 4000 - 2000 - 1000 + 500 + 300 + 400 - 200

= 4000

Number of families who buy none of A, B and C = 4000
Question 2
4 / -1

If |z - 4| < |z - 2|, then its solution is given by

A
Re(z) > 0

B
Re(z) < 0

C
Re(z) > 3

D
Re(z) > 2

Solution

|z - 4| < |z - 2|

or, |(a - 4) + ib| < |(a - 2) + ib| (By taking z = a + ib)

⇒ (a - 4)² + b² < (a - 2)² + b²

⇒ -8a + 4a < -16 + 4

⇒ 4a > 12

⇒ a > 3

⇒ Re(z) > 3
Question 3
4 / -1

If the lines x + 2ay + a = 0, x + 3by + b = 0 and x + 4cy + c = 0 are concurrent, then a, b and c are in

A
AP

B
HP

C
GP

D
None of these

Solution
Question 4
4 / -1

A
zero

B
1/4

C
1/5

D
1/30

Solution
Question 5
4 / -1

A

B

C

D

Solution
Question 6
4 / -1

then the solution of the equation is

A

B

C

D

Solution
Question 7
4 / -1

If P (x, y, z) is a point on the line segment joining Q (2, 2, 4) and R (3, 5, 6) such that projections of on the axes are 13/5 , 19/5 , 26/5 , respectively, then in what ratio does P divide

A
1 : 2

B
3 : 2

C
2 : 3

D
1 : 3

Solution
Question 8
4 / -1

A
0

B

C

D

Solution
Question 9
4 / -1

The equation

A
no solution

B
one solution

C
more than one real solution

D
none of these

Solution
Question 10
4 / -1

How many of the integers less than 5 satisfy the given inequality?

A
6

B
5

C
3

D
4

Solution

x ≠ 2

Case 1:

(x + 2)(x + 3) ≥ 0 and x - 2 > 0

x ≤ -3, x ≥ - 2 and x > 2

So, x > 2

Case 2:

(x + 2)(x + 3) ≤ 0 and x - 2 < />

-3 ≤ x ≤ -2 and x < />

So, -3 ≤ x ≤ -2

Integers that satisfy the given inequality and are less than 5 = -3, -2, 3 and 4

Hence, total number of such integers = 4