Mathematics Test 215

Result

Mathematics Test 215

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Weekly Quiz Competition

Question 1
4 / -1

If A = {θ : 2cos²θ + sin θ ≤ 2} and then A ∩ B is equal to

A

B

C

D
None of these

Solution
Question 2
4 / -1

Let a relation R be defined by R = {(4, 5), (1, 4), (4, 6), (7, 6), (3, 7)}. The relation R^-1oR is given by

A
{(1, 1), (4, 4), (7, 4), (4, 7), (7, 7)}

B
{(1, 1), (4, 4), (4, 7), (7, 4), (7, 7), (3, 3)}

C
{(1, 5), (1, 6), (3, 6)}

D
None of these

Solution
Question 3
4 / -1

A

B

C

D
0

Solution
Question 4
4 / -1

The function

A

B

C

D

Solution
Question 5
4 / -1

If f(a + b - x) = f(x), then is equal to

A

B

C

D

Solution
Question 6
4 / -1

For all the real values of x, if f(x) + f(x + 8) = f(x + 4) + f(x + 12), g(x) f(x) dx and g(1) = 2, then the value of g(12) is

A
2

B
24

C
12

D
4096

Solution

f(x) + f(x + 8) = f(x + 4) + f(x + 12)

Replacing x by x + 4, we get

f(x + 4) + f(x + 12) = f(x + 8) + f(x + 16)

Subtracting one from the other, we get

f(x) = f(x + 16)

g'(x) = f(x + 16) - f(x)

g'(x) = 0

g(x) = k

g(1) = 2

∴ k = 2

∴ g(12) = 2
Question 7
4 / -1

If the lines represented by the equation 3y² - x² + 2- √3x - 3 = 0 are rotated about the point (√3, 0) through an angle 15°, one in clockwise direction and other in anticlockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is

A
y² - x² + 2√3x + 3 = 0

B
y² - x² + 2√3x - 3 = 0

C
y² - x² - 2√3x + 3 = 0

D
y² - x² + 3 = 0

Solution

The given equation of the pair of straight lines can be rewritten as
Question 8
4 / -1

If then the value of is

A
5

B
3

C
-5

D
-3

Solution
Question 9
4 / -1

A box contains 100 tickets numbered 1 to 100. If 2 tickets are drawn successively without replacement from the box, what is the probability that all the tickets bear numbers divisible by 10?

A
0.04

B
0.4

C
0.001

D
0.009

Solution

No. of tickets numbered from 1 to 100, divisible by 10 = 10

Let,

Event (A) = Drawing 2 tickets successively without replacement which are divisible by 10.
Question 10
4 / -1

A

B

C

D

Solution