Mathematics Test 165

Result

Mathematics Test 165

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Question 1
4 / -1

The value of is :-

(where x, y, z are distinct positive real numbers)

A
π

B
π/4

C
π/2

D
3π/4

Solution
Question 2
4 / -1

A line 'L' passing through P(1, 2, 1) and perpendicular to both the line. If the position vector of point Q on 'L' is (a, b, c) such that (PQ)² = 35, then (a + b + c) can be

A
4

B
5

C
6

D
7

Solution
Question 3
4 / -1

If A₁, A₃, A₅ ,......., A_2n–1 are 'n' skew symmetric matrices of same order, then B = will be :-

A
Symmetric matrix

B
Skew symmetric matrix

C
Neither symmetric nor skew symmetric matrix

D
Data is inadequate

Solution

B = A₁ + 3A₃³+ 5A₅⁵ + .......... + (2n–1) A_2n–1^2n–1

taking transpose both sides, then we get

⇒ B^T = – B

⇒ B is skew symmetric matrix
Question 4
4 / -1

A
np(1 – p)

B
np

C

D

Solution
Question 5
4 / -1

A box contains 12 mangoes out of which 5 are rotten. Two mangoes are taken out together. If one of them is found to be good then the probability that the other is also good is

A
3/8

B
7/22

C
28/33

D
None of these

Solution
Question 6
4 / -1

(where [k] denotes greatest integer function less than or equal to k.)

A
0

B
1

C
2

D
1/2

Solution

In I₁ → Apply king property and add

⇒ 2I₁ = 2 + 2I₂

⇒ I₁– I₂ = 1
Question 7
4 / -1

The area bounded by y = | x | and y = x² – 2, is :-

A
8/3

B
20/3

C
16/3

D
None of these

Solution
Question 8
4 / -1

Solution of the differential equation , if y (1) = 0, is :-

A

B

C
x = ye^y

D

Solution
Question 9
4 / -1

ABCD is a quadrilateral with If its area is k times of area of parallelogram with AB and AD as its adjacent sides, then k is :-

A
5

B
5/2

C
4

D
6

Solution
Question 10
4 / -1

The locus of centre of circle which cuts off the intercept on the co-ordinate axes of given length is a conic, whose eccentricity is :-

A
1

B
1/√2

C
√2

D
√3

Solution