Mathematics Test 68

Result

Mathematics Test 68

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Weekly Quiz Competition

Question 1
4 / -1

Let S be a non-empty subset of R (R is the set of Real Numbers). Consider the following statement:

P: There is a rational number x ∈ S such that x > 0

A
There is no rational number x ∈ S such that x ⩽ 0

B
Every rational number x ∈ S satisfies x ⩽ 0

C
x ∈ S and x ⩽ 0 ⇒ x is not rational

D
There is a rational number x ∈ S such that x ⩽ 0
Question 2
4 / -1

The equation of the tangent to the curve y = x + 4 / x², that is parallel to the x-axis, is

A
y = 1

B
y = 2

C
y = 3

D
y = 0
Question 3
4 / -1

Solution of the differential equation cos x dy = y (sin x−y) dx, 0 < x < π / 2 is

A
y sec x = tan x+c

B
y tan x = sec x + c

C
tan x = (sec x + c) y

D
secx = (tan x + c) y
Question 4
4 / -1

The area bounded by the curves y = cos x and y=sin x between the ordinates x = 0 and x = 3π / 2 is

A
4 √2 + 2

B
4 √2 - 1

C
4 √2 + 1

D
4 √2 - 2
Question 5
4 / -1

If two tangents drawn from a point P to the parabola y²= 4x are at right angles, then the locus of P is

A
2x + 1 = 0

B
x = −1

C
2x − 1 = 0

D
x = 1
Question 6
4 / -1

For all x ∈ R, x² + 2ax + 10−3a > 0, then the interval in which ‘a’ lies is

A
a < −5

B
−5 < a < 2

C
a > 5

D
2 < a < 5