Mathematics Test 201

Result

Mathematics Test 201

Score
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Rank
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Weekly Quiz Competition

Question 1
4 / -1

A
1/35

B
1/14

C
1/10

D
1/5

Solution
Question 2
4 / -1

Number of integral solutions of the equation

[Note : where [x] denotes the greatest integer less than or equal to x and sgn x denotes signum function of x.]

A
2

B
3

C
5

D
7

Solution
Question 3
4 / -1

The area bounded by the curve y = x² + 4x + 5 , the axes of co-ordinates & the minimum ordinate is

A

B

C

D
8/3

Solution
Question 4
4 / -1

The differential equation of all parabolas having their axis of symmetry coinciding with the axis of x has its order and degree respectively

A
(2, 1)

B
(2, 2)

C
(1, 2)

D
(1, 1)

Solution

equation (x - a)² + y² = (x - b)² [S = (a, 0) ; D : x = b

y² = (b² - a²) + 2x (a - b)

differentiate twice to get
Question 5
4 / -1

Number of roots of the equation x² –2x–log₂ |1 – x | = 3 is

A
4

B
2

C
1

D
0

Solution
Question 6
4 / -1

Let F(x) be the primitive of w.r.t. x. If F(10) = 60 then the value of F(13), is

A
66

B
132

C
248

D
264

Solution
Question 7
4 / -1

is continuous at x = 0, then

[Note : {x} denotes fractional part of x.]

A
f(x) is differentiable at x = 0

B
k = 1

C
f(x) is continuous but not differentiable at x = 0

D
f(x) is continuous every where in its domain.

Solution
Question 8
4 / -1

A
sin x - 6 tan^-1 (sin x) + C

B
sin x - 2 sin^-1 x + C

C
sin x - 2 (sin x)^-1 - 6 tan^-1 (sin x) + C

D
sin x - 2 (sin x)^-1 + 5 tan^-1 (sin x) + C

Solution
Question 9
4 / -1

Point 'A' lies on the curve and has the coordinate where x > 0. Point B has the coordinates (x, 0). If 'O' is the origin then the maximum area of the triangle AOB is

A

B

C

D

Solution
Question 10
4 / -1

A
f (x) is continuous for all x when a = 5.

B
f (x) is discontinuous for all x.

C
f (x) is continuous for all x = 2nπ – tan^–1 (3/4) , n ∈ I when a = 5.

D
f (x) is continuous for all x = 2nπ – tan^–1 (4/3) , n ∈ I when a = 5.

Solution