Mathematics Test

Result

Mathematics Test - 6

Score
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Weekly Quiz Competition

Question 1
1 / -0

If f(x) = log (1 + x) - log (1 - x) and log (g(x)) = log (3x + x3) - log (1 + 3x2), then what is the value of f(g(x))?

A
g(f(x))

B
2g(f(x))

C
3g(x)

D
3f(x)

Solution
Question 2
1 / -0

Directions: Refer to the following functions:

A(x, y, z) = Max {max (x, y), min (y, z), min (x, z)}

B(x, y, z) = Max {max (x, y), min (y, z), max (x, z)}

C(x, y, z) = Max {min (x, y), min (y, z), min (x, z)}

D(x, y, z) = Min {max (x, y), max (y, z), max (x, z)}

Max (x, y, z) = Maximum of x, y and z.

Min (x, y, z) = Minimum of x, y and z.

Assume x, y and z as distinct integers.

For what condition, will A(x, y, z) be equal to Max (x, y, z)?

A
When x is maximum

B
When y is maximum

C
When z is maximum

D
Either (1) or (2)

Solution

Let us assign some values to x, y and z.

Put x = 1, y = 2, z = 3.

Now, A(x, y, z) = Max (2, 2, 1) = 1.

B (x, y, z) = Max (2, 2, 2) = 2

C (x, y, z) = Max (1, 2, 1) = 1

D (x, y, z) = Min (2, 3, 1) = 3

Max (x, y, z) = Min (1, 2, 3) = 1

Min (x, y, z) = Max (1, 2, 3) = 3

They will be equal only when z has the minimum value among the three, and x or y has the maximum value.

1. You might have checked by options and option 1 satisfies, but option 2 also satisfies.

2. You might have checked by options and option 2 satisfies, but option 1 also satisfies.

3. We can simply ignore this option as for x = 1, y = 2 , z = 3, it does not satisfy.
Question 3
1 / -0

A
1

B
2

C
5

D
7

Solution
Question 4
1 / -0

A
x/√(1+x²)

B
x

C
x√(1+x²)

D
√(1+x²)

Solution
Question 5
1 / -0

If the sum of odd coefficients of (1+z)⁵ is x, find the number of solutions of a+b+c+d=x where -x

A
³⁴C₃

B
³³C₃

C
³⁵C₃

D
³⁶C₄

Solution
Question 6
1 / -0

A
1

B
2

C
1/2

D
3/2

Solution
Question 7
1 / -0

The number of values of k for which the system of equations (k + 1) x + 8y = 4k and

kx + (k + 3)y = 3k - 1 has infinitely many solutions is

A
0

B
1

C
2

D
infinite

Solution
Question 8
1 / -0

The eccentricity of an ellipse with its centre at the origin is 1/2. If one of the directrix is x = 4, then the equation of the ellipse is

A
4x² + 3y² = 1

B
3x² + 4y² = 12

C
4x² + 3y² = 12

D
3x² + 4y² = 1

Solution
Question 9
1 / -0

A
1/10010

B
1/10110

C
100/10110

D
1/10100

Solution
Question 10
1 / -0

A
e

B
1/2e

C
2e

D
none of these

Solution