Mathematics Test 182

Result

Mathematics Test 182

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Weekly Quiz Competition

Question 1
4 / -1

Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n are, respectively,

A
4, 7

B
7, 4

C
4, 4

D
7, 7

Solution
Question 2
4 / -1

A

B

C

D

Solution
Question 3
4 / -1

A

B

C

D

Solution
Question 4
4 / -1

A
a negative integer

B
a whole number

C
a real number

D
a natural number

Solution

Therefore, P(K + 1) is true, when P(k) is true.

Hence, from the principle of mathematical induction, the statement is true for all natural numbers n.
Question 5
4 / -1

If the roots of the equation (x – a) (x – b) + (x – b) (x – c) + (x – c) (x – a) = 0 are equal, then a² + b² + c² =

A
a + b + c

B
2a + b + c

C
3abc

D
ab + bc + ca

Solution
Question 6
4 / -1

The true statement for the graph of in equations 3x + 2y ≤ 6 and 6x + 4y ≥ 20, is

A
Both graphs are disjoint

B
Both do not contain origin

C
Both contain point (1, 1)

D
None of these

Solution
Question 7
4 / -1

A
1

B
2

C
3

D
4

Solution
Question 8
4 / -1

A
0

B
20C₁₀

C
-20C₁₀

D

Solution
Question 9
4 / -1

If the ratio of H.M. and G.M. of two quantities is 12 : 13 then the ratio of the numbers is

A
1 : 2

B
2 : 3

C
3 : 4

D
None of these

Solution
Question 10
4 / -1

Given a family of lines a(2x + y + 4) + b(x – 2y – 3) = 0, the number of lines belonging to the family at a distance √10 from P(2, –3) is

A
0

B
1

C
2

D
4

Solution

The length of perpendicular from P(2, –3) on the given family of lines