Mathematics Test

Result

Mathematics Test - 11

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Weekly Quiz Competition

Question 1
1 / -0

A
0

B
2/3

C
4/3

D
None of these

Solution
Question 2
1 / -0

A
[1/√2, 1]

B
[0, 1]

C
[1/2, 1]

D
[3/4, 1]

Solution
Question 3
1 / -0

A

B

C

D
None of these

Solution
Question 4
1 / -0

A

B

C

D

Solution
Question 5
1 / -0

The solution of the equation x² dy/dx = x² + xy + y² is

A
tan^-1(y/x) = log x + C

B
tan^-1(x/y) = log x + C

C
tan^-1 (x/y) = log y + C

D
none of these

Solution
Question 6
1 / -0

The solution of the boundary value problem 2y dy/dx + y² cot x = 2 cos x, y(π/2) = 1 is

A
y² = sin x

B
y = sin² x

C
y² = cos x + 1

D
None of these

Solution
Question 7
1 / -0

What is the solution of the equation (y log y) dx + (x - logy) dy = 0?

A
x = C/log y + log y

B
y = C/log x + log x

C
(x + 1) log y = c

D
None of these

Solution
Question 8
1 / -0

The solution of the differential equation dy/dx + y/x = x² is

A
4xy = x⁴ + 4c

B
xy = x⁴ + c

C
1/4xy = x⁴ + c

D
None of these

Solution
Question 9
1 / -0

The order and degree of differential equation d²s/dt²+ 4 = 0 are

A
2, 2

B
2, 3

C
3, 2

D
None of these

Solution

The order is 2 and degree is 1.
Question 10
1 / -0

The equation of the plane through the line of intersection of planes x + y + z + 3 = 0 and 2x − y + 3z + 1 =0 and parallel to the line x/1 = y/2 =z/3 is

A
x − 5y + 3z = 7

B
x − 5y + 3z = − 7

C
x + 5y + 3z = 7

D
none of these

Solution

Any plane through the given line is 2x − y + 3z + 1 + λ (x + y + z + 3) = 0 If this plane is parallel to the line x/1 = y/2 = z/3, then the normal to the plane is also perpendicular to the above line.
∴(l₁l₂ + m₁ m₂ + n₁ n₂ = 0
⇒ (2 + λ) 1 + (λ −1) 2 + (3 + λ) 3 = 0
⇒ λ= -3/2
and the required plane is
2x − y + 3z + 1 + (-3/2) (x + y + z + 3) = 0
⇒ x − 5y + 3z − 7 = 0
or
x − 5y + 3z = 7
Question 11
1 / -0

If g [f(x)] = |sin x| and f[g(x)] = (sin√x)² then,

A
f(x) = sin² x, g(x) = √x

B
f(x) = sin x, g(x) = |x|

C
f(x) = x², g(x) = sin√x

D
f and g cannot be determined

Solution
Question 12
1 / -0

A
1/4 log (x⁴+1) +C

B
– log (x⁴ + 1) + C

C
log (x4 + 1) + C

D
None of these

Solution
Question 13
1 / -0

If g(x) satisfies the conditions of Rolle’s theorem in [1, 2] and g′(x) = f(x), then is equal to

A
1

B
3

C
0

D
2

Solution

As g(x) satisfies the condition of Rolle’s theorem in [1, 2], g(x) is continuous in the interval and
g(1) = g(2).
Question 14
1 / -0

Which of the following is logically equivalent to ∼ (∼p ⇒ q) ?

A
p ∨ q

B
p ∨ ∼ q

C
∼p ∨ q

D
∼p ∨ ∼q

Solution
Question 15
1 / -0

If the mean of a binomial distribution is 25, then its standard deviation lies in the interval

A
[0, 5)

B
(0, 5]

C
[0, 25)

D
(0, 25]

Solution