Mathematics Test 219

Result

Mathematics Test 219

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Question 1
4 / -1

If f (x) = cos (log x), then, has the value

A
- 2

B
-1

C
1/2

D
None of these

Solution
Question 2
4 / -1

The angle between the lines

A
π/3

B
π/2

C
π/4

D
None of these

Solution

After solving it, we get x = 3/2

y = x makes an angle of 45 degrees with the x-axis.

x = 3/2 is a line parallel to y-axis i.e. perpendicular to x-axis.

So, angle between these two lines is 45°.

The angle between these two lines is π/4.
Question 3
4 / -1

A
0

B
1/32

C
1/8

D
1/16

Solution
Question 4
4 / -1

The sum of series 1/2! + 1/4! + 1/6! + …is

A

B

C

D

Solution
Question 5
4 / -1

If f(x) = [x]/[x] , x ≠ 0 where [.] denotes the greatest integer function, then f'(1)

A
is -1

B
is ∞

C
is zero

D
does not exist

Solution
Question 6
4 / -1

A

B

C

D

Solution
Question 7
4 / -1

In a triangle ABC, medians AD and BE are drawn. If AD = 4, DAB = π/6 and ABE = π/3, then the area of ΔABC is

A
16/3

B
32/3√3

C
64/3

D
8/3

Solution
Question 8
4 / -1

The foot of the perpendicular from (0, 2, 3) to the line

A
(3, 2, -1)

B
(-2, 3, 4)

C
(2, -1, 3)

D
(2, 3, -1)

Solution

Let N be the foot of the perpendicular from the point (0, 2, 3) on the given line

Any point on (1) is (5r - 3, 2r + 1 and 3r - 4).

If this point is N, then direction ratios of NP are

(5r - 3 - 0, 2r + 1 - 2, 3r - 4 - 3)

i.e. (5r - 3, 2r - 1, 3r - 7)

Since PN is to the given line,

∴ 5(5r - 3) + 2(2r - 1) + 3(3r - 7) = 0

⇒ 38r - 38 = 0

⇒ r = 1

∴ N is (5 - 3, 2 + 1, 3 - 4) i.e. (2, 3, -1).
Question 9
4 / -1

In a binomial distribution, mean is 3 and variance is 3/2. The probability distribution is

A

B

C

D

Solution
Question 10
4 / -1

If 0 < sin^-1x < 1 and 1 + sin^-1 x + (sin^-1 x)² + … up to infinity = 2, then x is equal to

A
π/6

B
π/4

C
π/3

D
None of these

Solution

Given that 1 + sin^-1 x + (sin^-1 x)² + … is an infinite geometric series.

So,