Mathematics Test 102

Result

Mathematics Test 102

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Weekly Quiz Competition

Question 1
4 / -1

for what values of a, f(x) is continuous at x = 0 :

A
1, –1/4

B
1, 0

C
1/4, –1

D
None
Question 2
4 / -1

If f(x) = + 2; then f^–1 (y) = ?

A
1/2 log₁₀(y-1 / y-3)

B
1/2 log₁₀(y-3 / y-1)

C
1/2 log₁₀(y-1 / 3 - y)

D
1/2 log₁₀(y-1 / y)
Question 3
4 / -1

dx = ax + b ln (4e^x + 5e^–x) + c; then:

A
a = –1/8, b = 7/8

B
a = 1/8, b = –7/8

C
a = 1/8, b = 7/8

D
a = –1/8, b = –7/8

Solution
Question 4
4 / -1

The area bounded by the loop of the curve 4y² = x² (4 – x²) is

A
7/3 sq. units

B
8/3 sq. units

C
11/3 sq. units

D
16/3 sq. units

Solution
Question 5
4 / -1

Equation of the curve satisfying
xdy – ydx = dx; y(1) = 0 is :-

A
y = x²sin(logx)

B
y² = x(x – 1)²

C
y² = x²(x – 1)

D
y = xsin(logx)

Solution
Question 6
4 / -1

An ellipse, with foci at (0, 2) and (0, –2) and minor axis of length 4, passes through which of the following points ?

A
(1, 2√2)

B
( 2, √2)

C
(2, 2√2)

D
(√2, 2)

Solution

given that be = 2 and a = 2

(here a < b)

∵ a² = b²(1 – e²)

∴ b² = 8

∴ equation of ellipse x²/4 + y²/8 = 1
Question 7
4 / -1

A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point :

A
(3, 10)

B
(2,3)

C
(1,5)

D
(3,5)

Solution
Question 8
4 / -1

Find minimum value of 8 sin²θ + 2cosec²θ. Where θ ∈ R :-

A
10

B
2

C
8

D
12

Solution
Question 9
4 / -1

A
is singleton

B
Contains exactly two numbers only one of which is positive

C
Contains exactly two positive numbers

D
is empty

Solution
Question 10
4 / -1

The length of the perpendicular drawn from the point (2, 1, 4) to the plane containing the lines and is :

A
√3

B
1/√3

C
1/3

D
3

Solution