Mathematics Test 142

Result

Mathematics Test 142

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Question 1
4 / -1

If the area bounded by y = ax² and x = ay², a > 0, is 1, then a is equal to

A
1

B
1/√3

C
1/3

D
- 1/√3

Solution
Question 2
4 / -1

A single letter is selected at random from the word 'PROBABILITY'. The probability that it is a vowel, is :

A
2/9

B
4/9

C
3/9

D
None of these

Solution

Out of 11 letters in the word PROBABILITYO,A,I and I are the vowels.
So probability that the letter selected is a vowel, is 4/11
Question 3
4 / -1

Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number.

A
4/7

B
8/7

C
6/7

D
2/7

Solution

Let the events be :
A : Number on the card drawn is even.
B : Number on the card is more than 3.
We are to find P(A/B).
We have : S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8,10}
and B = {4, 5, 6, 7, 8, 9, 10}
Question 4
4 / -1

A
x = 3, y = 1

B
x = 1, y = 3

C
x = 0, y = 3

D
x = 0, y = 0

Solution
Question 5
4 / -1

A

B
– 1/3

C
1/2

D
1/4

Solution
Question 6
4 / -1

A point R with x-co-ordinate 4 lies on the line segment joining the points P (2, - 3, 4) and Q (8, 0,10). Find the co-ordinates of the point R.

A
(4,−2, 6)

B
(2,−4, 6)

C
(3,−4, 2)

D
(1,−3, 4)

Solution
Question 7
4 / -1

A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The coordinates of the point A are

A
(13/5, 0)

B
(5/13, 0)

C
(- 7, 0)

D
None of these

Solution

Let the coordinates of A be (a. 0). Then the slope of the reflected ray is
Question 8
4 / -1

The points A, B and C represent the complex numbers z₁, z₂, (1−i)z₁+iz₂ (where ) respectively on the complex plane. The triangle ABC is :

A
Isosceles but not right angled

B
Right angled but not isosceles

C
Isosceles and right angled

D
None of these

Solution

Hence the triangle is isosceles and right angled.
Question 9
4 / -1

In the expansion of the term containing same powers of a and b is -

A
11^thterm

B
12^thterm

C
6^thterm

D
13^th term

Solution

∴ 13^th term contains same power of a & b.
Question 10
4 / -1

All the spades are taken out from a pack of cards. From these cards, cards are drawn one by one without replacement till the ace of spades comes. The probability that the ace comes in the 4th draw is

A
1/13

B
12/13

C
4/13

D
None of these

Solution