Mathematics Test 300

Result

Mathematics Test 300

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Weekly Quiz Competition

Question 1
4 / -1

A

B

C

D

Solution
Question 2
4 / -1

A stone thrown vertically upward satisfied the equation s = 64t - 16t², where s is in metre and t is in second. What is the time required to reach the maximum height by the stone?

A
1 s

B
2 s

C
3 s

D
4 s

Solution

Given, s = 64t - 16t²,

So, the function s(t) is maximum when,

s'(t) = 0 and s"(t) < 0

⇒ s'(t) = 64 - 16(2t) = 0

⇒ 64 = 32 t

⇒ t = 2

And at t = 2, s"(t) = -32 < 0

So, s(t) is maximum at t = 2.

So, The time required to reach the maximum height by the stone is 2s.

∴ The correct answer is an option (2).
Question 3
4 / -1

The area (in sq. units) of the smaller region lying above the X-axis and bounded between the circle x²+ y²= 2ax and the parabola y²= ax is

A

B

C

D

Solution
Question 4
4 / -1

A

B

C

D

Solution
Question 5
4 / -1

A

B

C

D

Solution

Given,

Expression = cot⁻¹ [ (√(1−sin x) + √(1+sin x)) / (√(1−sin x) − √(1+sin x)) ]

Let A = (√(1−sin x) + √(1+sin x)) / (√(1−sin x) − √(1+sin x))

Multiply numerator and denominator by conjugate of denominator:

⇒ A = [(√(1−sin x) + √(1+sin x))²] / [(1−sin x) − (1+sin x)]

⇒ A = [1−sin x + 1+sin x + 2√((1−sin x)(1+sin x))] / [−2sin x]

⇒ A = [2 + 2√(1−sin²x)] / (−2sin x)

⇒ A = [2 + 2cos x] / (−2sin x)

⇒ A = −(1 + cos x) / sin x

⇒ A = −cot(x/2) [Using identity: cot(x/2) = (1 + cos x) / sin x]

⇒ cot⁻¹(A) = cot⁻¹(−cot(x/2))

⇒ cot⁻¹(cot(π − x/2)) = π − x/2

∴ Required value is π − x/2
Question 6
4 / -1

If y(x) is a solution of the differential equation

A

B
-1

C

D
1

Solution

The differential equation is:

Hence, the correct answer is Option (c).
Question 7
4 / -1

Let the point P of the focal chord PQ of the parabola y²=16x be (1,−4). If the focus of the parabola divides the chord PQ in the ratio m:n, gcd (m,n) = 1,. Then m²+ n² is equal to

A
10

B
37

C
17

D
26

Solution
Question 8
4 / -1

Let the area of the triangle formed by a straight line L : x + by + c = 0 with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line L makes an angle of 45^∘ with the positive x-axis, then the value of b²+ c²is

A
93

B
83

C
97

D
90

Solution
Question 9
4 / -1

The centroid of a variable triangle ABC is at the distance of 5 units from the origin. If A = (2,3) and B = (3,2),then the locus of C is

A
A circle of radius 225 unit

B
A rectangular hyperbola

C
A circle of diameter 30 units

D

Solution
Question 10
4 / -1

A
c²

B
−c²

C
-1

D
1

Solution