Mathematics Test

Question 1
1 / -0

In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.

The number of students who had taken only physics is:

A
2

B
3

C
5

D
6

Question 2
1 / -0

In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.

The number of students who had taken only two subjects is:

A
7

B
8

C
9

D
10

Question 3
1 / -0

In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.

Consider the following statements:

1. The number of students who had taken only one subject is equal to the number of students who had taken only two subject.

2. The number of students who had taken at least two subjects is four times the number of students who had taken all the three subjects.

Which of the above statements is/are correct?

A
1 only

B
2 only

C
Both 1 and 2

D
Neither 1 nor 2

Question 4
1 / -0

In the expansion of $\left(x^{3}-\frac{1}{x^{2}}\right)^{\text {n }}$ where $n$ is a positive integer, the sum of the coefficients of $x^{5}$ and $x^{10}$ is 0 . What is n equal to?

A
5

B
10

C
15

D
None of these

Question 5
1 / -0

In the expansion of $\left(x^{3}-\frac{1}{x^{2}}\right)^{n}$ where $n$ is a positive integer, the sum of the coefficients of $x^{5}$ and $x^{10}$ is 0 .

What is the value of the independent term?

A
5005

B
7200

C
-5005

D
-7200

Question 6
1 / -0

In the expansion of $\left(x^{3}-\frac{1}{x^{2}}\right)^{\text {n }}$ where $n$ is a positive integer, the sum of the coefficients of $x^{5}$ and $x^{10}$ is 0 .

What is the sum of the coefficients of the two middle terms?

A
0

B
1

C
-1

D
None of these

Question 7
1 / -0

Given that C(n, r) : C(n, r + 1) = 1 : 2 and C(n, r + 1) : C(n, r + 2) = 2 : 3.What is n equal to?

A
11

B
12

C
13

D
14

Question 8
1 / -0

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?

A
$\frac{2}{3}$

B
$\frac{8}{21}$

C
$\frac{3}{7}$

D
$\frac{9}{22}$

Question 9
1 / -0

Given that C(n, r) : C(n, r + 1) = 1 : 2 and C(n, r + 1) : C(n, r + 2) = 2 : 3.What is P(n, r) : C(n, r) equal to?

A
6

B
24

C
120

D
720

Question 10
1 / -0

The complete solution 3 tan² x = 1 is given by :

A
$x=n \pi \pm \frac{\pi}{3}$

B
$x=n \pi+\frac{\pi}{3}$ only

C
$x=n \pi \pm \frac{\pi}{6}$

D
$x=n \pi+\frac{\pi}{6}$ only

Submit Test

Mathematics Tes...

Question 1

2

3

5

6

Question 2

7

8

9

10

Question 3

1 only

2 only

Both 1 and 2

Neither 1 nor 2

Question 4

5

10

15

None of these

Question 5

5005

7200

-5005

-7200

Question 6

0

1

-1

None of these

Question 7

11

12

13

14

Question 8

23

821

37

922

Question 9

6

24

120

720

Question 10

\(x=n \pi \pm \frac{\pi}{3}\)

\(x=n \pi+\frac{\pi}{3}\) only

\(x=n \pi \pm \frac{\pi}{6}\)

\(x=n \pi+\frac{\pi}{6}\) only

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Question Analysis

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$\frac{2}{3}$

$\frac{8}{21}$

$\frac{3}{7}$

$\frac{9}{22}$