Mathematics Test

Result

Mathematics Test - 10

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
2.5 / -0.83

The only correct statement about the matrix A is

A
A2= I

B
A = (–1) I, where I is a unit matrix

C
A-1does not exist

D
A is a zero matrix

Solution
Question 2
2.5 / -0.83

Find the real numbers x and y such that : (x + iy)(3 + 2i) = 1 + i

A
x = 5/13 , y = 1/13

B
x = 5/3 , y = 1/3

C

D
x = 15/13 , y = 1/13

Solution

(x + iy)(3 + 2i) = (1 + i)
x + iy = (1 + i)/(3 + 2i)
x + iy = [(1 + i) * (3 - 2i)] / [(3 + 2i)*(3 - 2i)]
x + iy = (3 + 3i - 2i + 2) / [(3)² + (2)² ]
x + iy = (5 + i)/[ 9 + 4]
= (5 + i) / 13
=>13x + 13iy = 5+i
13x = 5 13y = 1
x = 5/13 y = 1/13
Question 3
2.5 / -0.83

Express the following in standard form : (2 –√3i) (2 + √3i) + 2 –4i

A
3 + 4i

B
4i

C
9 - 4i

D
13 + 4i

Solution

Given: (2 −√3i)(2+√3i) + 2 −4i

(2 −√3i)(2+√3i) = 7

⇒7 + 2 - 4i

⇒9 - 4i
Question 4
2.5 / -0.83

Find the reciprocal (or multiplicative inverse) of -2 + 5i

A

B

C

D

Solution

-2 + 5i
multiplicative inverse of -2 + 5i is
1/(-2+5i)
= 1/(-2+5i) * ((-2-5i)/(-2-5i))
= -2-5i/(-2)^2 -(5i)^2
= -2-5i/4-(-25)
= -2-5i/4+25
= -2-5i/29
= -2/29 -5i/29
Question 5
2.5 / -0.83

The number of ways in which 6 “+ “and 4 “–“signs can be arranged in a line such that no two “–“signs occur together is

A
P(10,4)

B
C(10,4)

C
C(7,4)

D
none of these

Solution

′+′signs can be put in a row in one way creating seven gaps shown as arrows:
Now 4 ′−′signs must be kept in these gaps. So, no tow ′−′signs should be together.
Out of these 7 gaps 4 can be chosen in 7C4 ways.
Question 6
2.5 / -0.83

On a railway track, there are 20 stations. The number of tickets required in order that it may be possible to book a passenger from every station to every other is

A
C(20,2)

B
P(20,2)

C
400

D
none of these

Solution

Number of tickets selected from first station =20
from second =19
.... for last station =0
We have to select 2 consecutive stations
so total number of possible tickets = P(20,2)
Question 7
2.5 / -0.83

A class is composed 2 brothers and 6 other boys. In how many ways can all the boys be seated at the round table so that the 2 brothers are not seated besides each other?

A
720

B
1440

C
3600

D
4320

Solution

Take 1 person from 6 and fix him and 5 others can arranged in -- 5! ways=120

there are 6 places left in which 2 brothers can sit

so they can choose any 2 places from 6 - 6C2 ways=15

2 brothers can arrange themselves in 2! ways=15*2=30

total ways=120*30=3600
Question 8
2.5 / -0.83

The minim um value of the s um of re al numb ers a _–5 , a_–4 , 3a_–3 , 1, a₈ and a₁₀ with a >0 is

A
7

B
8

C
9

D
5

Solution

Using AM > GM

⇒ Sum = 8
Question 9
2.5 / -0.83

Let a₁ , a₂ , a₃ , ..., a₁₀₀ be an arithmetic progression with a₁ = 3 and For any integer n with 1 ≤n ≤20. let m=5n. If S_m /S_n does not depend on n, then a₂ is

A
7

B
8

C
9

D
6

Solution
Question 10
2.5 / -0.83

Let a₁ , a₂ , a₃ , ..... be in harmonic progression with a₁ = 5 and a₂₀ = 25. The least positive integer n for which a_n <0 is

A
22

B
23

C
24

D
25

Solution