Mathematics Test

Result

Mathematics Test - 32

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
3 / -1

A line makes angles \(\alpha, \beta, y\) with \(x\) -axis, \(y\) -axis and z-axis respectively then \(\cos 2 \alpha+\cos 2 \beta+\cos 2 y\) is equal to-

A
2

B
-1

C
0

D
1

Solution

\(\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1\)
\(\Rightarrow \frac{1+\cos 2 \alpha}{2}+\frac{1+\cos 2 \beta}{2}+\frac{1+\cos 2 \gamma}{2}=1\)
\(\Rightarrow \cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma=-1\)
Question 2
3 / -1

A
2

B
1

C
√2

D
2√2

Solution
Question 3
3 / -1

The area bounded by the curve y = x | x |, x-axis and the ordinates x = 1, x = -1 is given by

A
0

B
1/3

C
2/3

D
None of these

Solution
Question 4
3 / -1

A
24

B
36

C
48

D
12

Solution
Question 5
3 / -1

If sin (A + B + C) = 1, tan (A - B) = 1/√3, sec(A + C) = 2,

A
A = 120°, B = 60°, C = 0°

B
A = 60°, B = 30°, C = 0°

C
A = 90°, B = 60°, C = 30°

D
None of these

Solution
Question 6
3 / -1

If f(x) = | x |³, then f′(0) =

A
0

B
1/2

C
-1

D
None of these

Solution
Question 7
3 / -1

The probability that a man will live 10 more years is 1/4 and the probability that his wife will live 10 more years is 1/3. The probability that neither of them will be alive in 10 years is

A
11/12

B
1/2

C
7/12

D
None of these

Solution

Probability that a man will live 10 more years = 1/4

Probability that man not live 10 more years = 1 - 1/4 = 3/4

Probability that his wife will live 10 more years = 1/3

Probability that his wife not live 10 more years = 1 - 1/3 = 2/3

Then, probability that neither will be alive in 10 years = (3/4) x (2/3) = 1/2
Question 8
3 / -1

The differential equation of all non - horizontal lines in a plane is

A
d²y/dx² = 0

B
dx/dy = 0

C
dy/dx = 0

D
d²x/dy²= 0

Solution
Question 9
3 / -1

In how many ways can 8 students be arranged in a row?

A
8!

B
7!

C
8

D
7

Solution

Required number of ways = 8!
Question 10
3 / -1

A
1

B
2

C
-1

D
-2

Solution