Mathematics Test 280

Result

Mathematics Test 280

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Weekly Quiz Competition

Question 1
4 / -1

The number of arbitrary constants in the solution of a differential equation of degree 2 and order 3 is

A
2

B
3

C
2³

D
1

Solution

Since, the number of arbitrary constants in a solution of a differential equation of order n is equal to its order.

So, number of arbitrary constants = Order of differential equation = 3
Question 2
4 / -1

If y = y(x) is the solution of the differential equation such that y(0) = 0, then y(1) is equal to:

A
log_e 2

B
2e

C
2 + log_e2

D
1 + log_e2

Solution
Question 3
4 / -1

A
x² - y² - x = 0

B
a circle

C
a hyperbola

D
an ellipse

Solution
Question 4
4 / -1

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

A

B

C
(x + 1) log y = c

D
None of these

Solution
Question 5
4 / -1

The integrating factor of dy/dx - 3y/x = x³ sin x is

A
1/x²

B
1/x³

C
x

D
x²

Solution
Question 6
4 / -1

A
6

B
7

C
2√13

D
4√3

Solution
Question 7
4 / -1

The value of k for which the points A (1, 0, 3), B (– 1, 3, 4), C (1, 2, 1) and D (k, 2, 5) are coplanar, is

A
1

B
2

C
0

D
-1

Solution
Question 8
4 / -1

Two systems of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a', b', c' from the origin, then

A

B

C

D

Solution
Question 9
4 / -1

Equation of a plane bisecting the angle between the planes 2x - y + 2z + 3 = 0 and 3x - 2y + 6z + 8 = 0 is

A
5x - y - 4z - 45 = 0

B
5x - y - 4z - 3 = 0

C
23x + 13y + 32z - 45 = 0

D
23x - 13y + 32z + 5 = 0

Solution

Equations of the planes bisecting the angle between the given planes are
Question 10
4 / -1

Let a = i + j + k, b = I – j + 2k and c = xi + (x – 2)j – k. If the vector c lies in the plane of a and b, then x equals

A
0

B
1

C
-4

D
-2

Solution