Mathematics Test

Result

Mathematics Test - 20

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Weekly Quiz Competition

Question 1
3 / -1

If no husband and wife play in the same game, then the number of ways in which a mixed double game can be arranged from among nine married couples is

A
756

B
1512

C
3024

D
None of these

Solution
Question 2
3 / -1

Which of the following pieces of data does not uniquely determine the acute-angled ΔABC (R = circum radius)?

A
a, sin A, sin B

B
a, b, c

C
a, sin B, R

D
a, sin A, R

Solution
Question 3
3 / -1

Find the equation of the line passing through the intersection of the lines x + 2y - 3 = 0 and 4x – y + 7 = 0 and which is parallel to y – x + 10 = 0.

A
3x + 3y + 10 = 0

B
- 3x + 3y + 10 = 0

C
- 3x + 3y - 10 = 0

D
None of these

Solution

Let the equation be x + 2y - 3 + k (4x - y + 7) = 0 ............ (i)

i.e., (1 + 4k) x + (2 - k) y + 7k - 3 = 0

i.e., y = (-1 - 4k)/(2-k) + 3 - 7k

Since it is parallel to y - x + 10 = 0 (i.e., y = x - 10), slopes are equal.

So, (- 1 - 4k)/(2 - k) = 1

- 1 - 4k = 2 - k

k = - 1

Substituting this in eq (i), we get:

The required line is x + 2y - 3 + (-1)(4x - y + 7) = 0

i.e. - 3x + 3y - 10 = 0
Question 4
3 / -1

The circles x² + y² – 10x + 16 = 0 and x² + y² = r² intersect each other at two distinct points if

A
r < 2

B
r > 8

C
2 < r < 8

D
2≤ r≤ 8

Solution

Centres of the given circles are (5, 0) and (0, 0) and their radii are 3 and r, respectively. The two circles will intersect at two distinct points if the distance between their centres is greater than the difference of their radii and less than the sum of radii.

⇒ |3 – r| < 5 < 3 + r⇒ 2 < r < 8
Question 5
3 / -1

A
an even function

B
an odd function

C
a periodic function

D
None of these

Solution
Question 6
3 / -1

A
1/4

B
1/5

C
1/6

D
1/7

Solution
Question 7
3 / -1

A
a = 1 and b = -2

B
a = 1 and b = -1

C
a = -1 and b = 1

D
a = 2 and b = -2

Solution
Question 8
3 / -1

A
A.P.

B
G.P.

C
H.P.

D
None of these

Solution
Question 9
3 / -1

What is the circumradius of a triangle with length of sides as 6 units, 8 units and 10 units?

A
4 units

B
5 units

C
3 units

D
None of the above

Solution

As the given triangle is a right triangle, the circumradius is half of the hypotenuse which is 5 units

Hence, answer option 2 is correct.
Question 10
3 / -1

A

B

C

D

Solution