Mathematics Test

Result

Mathematics Test - 2

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Question 1
1 / -0

Monica's average expenses for 4 days is Rs 6.0. She spent Rs 7.70 on first day, Rs 6.30 on second day. If she spent 10 on third day , How much did she spend on the 4th day?

A
Rs 2

B
Rs 3

C
Rs 4

D
Rs 0

Solution

Required Amount = 24 - ( 7.70 + 6.30 + 10)

= 24 - 24 = 0
Question 2
1 / -0

In a single throw of two dice, find the probability of the first dice always occur odd number and sum of two dice is greater than 5.

A
1/4

B
2/3

C
3/4

D
1/3

Solution

We know that in a single throw of two dice, the total number of possible outcomes is (6 × 6) = 36

Let S be the sample space. Then, n(S) = 36

Let E = first dice always occur odd number and sum of two dice is greater than 5. Then,

E = {(1,5 ), (1, 6), (3, 3), (3, 4), (3, 5), (3, 6), (5,1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)}

∴ n(E) = 12

So, the probability that first dice always occur odd number and sum of two dice is greater than 5
Question 3
1 / -0

A
2 × 2

B
4 × 1

C
1 × 4

D
None of these

Solution

If a matrix has m rows and n columns then its order is m × n. Clearly, in the given matrix, the number of rows and columns are each 2. So, its order is 2 × 2.
Question 4
1 / -0

The ratio of the two numbers is 5 : 7 and their LCM is 105. If X is the ratio of the sum of the numbers and the difference of the numbers. What is the value of X?

A
18

B
21

C
6

D
12

Solution
Question 5
1 / -0

For a positive integer n, if the mean of the binomial coefficient in the expansion of

(a + b)^{2n – 3} is 16, then n is equal to-

A
4

B
5

C
7

D
9

Solution
Question 6
1 / -0

If the system of linear equations :

x+ 3y +7z = 0

-x + 4y +7z = 0

(sin3θ)x+ (cos2 θ)y +2z = 0 has a non-trivial solution, then the number of values of θ lying in the interval [0, π], is-

A
one

B
two

C
three

D
more then three

Solution
Question 7
1 / -0

The number of integral values of m for which the equation, (1 + m2) x2 – 2(1 + 3m) x + (1 + 8m) = 0, has no real root, is:

A
1

B
2

C
3

D
infinitely many

Solution
Question 8
1 / -0

A man spends Rs 1,800 per month on an average for the first four mouths and Rs 2,000 per month for the nest 8 months and saves Rs 5,600 a year. What is his average monthly income ?

A
Rs 5,400

B
Rs 3,500

C
Rs 4,400

D
Rs 2,400

Solution

Total expenditure during first four months = 1,800 x 4 = Rs 7,200

Total expenditure during the next 8 months = 2,000 x 8 = Rs 16,000 Saving = Rs 5,600

Total of expenditure and saving (equal to income the year) = 7,200 + 16,000 + 5,600 = Rs 28,800

Average monthly income = 28,000/12 = Rs 2,400
Question 9
1 / -0

Six bells commencing tolling together toll at intervals of 2, 4, 6, 8,10 and 12 seconds respectively.In 30 minutes how many times do they toll together?

A
12

B
16

C
18

D
15

Solution

1. L.C.M of 2, 4, 6, 8, 10 and 12 is 120.

so, the bells will toll together after 120 seconds i.e. 2 minutes .

In 30 minutes the bells toll together 30/2 + 1 = 16 times.
Question 10
1 / -0

The average of 5 numbers is 9 and the average of the last three numbers is 5.Find the average of the first two numbers.

A
45

B
15

C
25

D
35

Solution

Sum of 5 numbers = 9 x 5 = 45

Sum of last three numbers = 15

The average of 1st two numbers = 45-15/2 = 30/2 = 15.