Mathematics Test

Result

Mathematics Test - 5

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Weekly Quiz Competition

Question 1
4 / -1

If the axes are rotated through an angle of 30° in the clockwise direction, the point (4, 2√3) in the new system is

A
(2, 3)

B
(2, √3)

C
(√3, 2)

D
(√3, 5)

Solution
Question 2
4 / -1

Determine the position of the point (2,−3) with respect to the hyperbola x²/9 −y²/25 = 1

A
Inside the hyperbola

B
Outside the hyperbola

C
On the hyperbola

D
Cannot be determined from the given information.

Solution
Question 3
4 / -1

The point P on the ellipse 4x² + 9y² = 36 is such that the area of the ΔP F₁ F₂ = √10Sq units, where F₁. F₂ are Foci. Then P has the coordinates

A
(± 3/√2, √2)

B
(3/2, 2)

C
(-3/2, -2)

D
None

Solution
Question 4
4 / -1

The given diagram represents

A
An onto function

B
A constant function

C
An one-one function

D
Not a function

Solution

Since the input 2 gives two different images.

Therefore, f is not a function.

Option D is not correct
Question 5
4 / -1

A
I

B
0

C
2I

D
1/2I

Solution
Question 6
4 / -1

The degree and order of the differential equation

[1+2(dy/dx)²]^3/2 = 5d²y/dx² are

A
1, 2

B
2, 2

C
3, 1

D
4, 3

Solution

The order is the highest numbered derivative in the equation, While the degree is the highest power to which a derivatives is raised.

Hence the order of given equation is 2 and the degree is 2.

So the correct answer is B.
Question 7
4 / -1

If x = a cosθ + a log tanθ/2 and y = a sinθ, then dy/dx is equal to

A
cot θ

B
tan θ

C
sin θ

D
cos θ

Solution
Question 8
4 / -1

The equation x²/8−t + y²/t−4 = 1 will represent an ellipse if

A
t ∈ (1, 5)

B
t ∈ (2, 8)

C
t ∈ (4, 8) − {6}

D
t ∈ (4, 10) − {6}

Solution
Question 9
4 / -1

On the line y = 2x − 1, what is the approximate distance between the points where x = 1 and x = 2?

A
2.24

B
2.27

C
2.31

D
2.42

Solution
Question 10
4 / -1

The continuously differentiable function y=f(x),x∈(0,π) satisfying y′ = 1 + y², y(0) = 0 = y(π) is

A
tanx

B
x(x−π)

C
(x−π)(1−e^x)

D
not possible

Solution