Mathematics Test 244

Result

Mathematics Test 244

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Weekly Quiz Competition

Question 1
4 / -1

If λ is a root of the equation x² + 3x + 1 = 0, then tan^–1λ + tan^–1(1/λ) is

A
π/2

B
–π/2

C
π/3

D
none of these

Solution
Question 2
4 / -1

Number of integral values of ‘b’ for which the origin and the point (1, 1) lies on the same side of the straight line a²x + aby + 1 = 0, for all a ϵ R – {0} is

A
4

B
3

C
5

D
none of these

Solution

Calculation:

For same side of a²x + aby + 1 = 0 of (0, 0) & (1, 1), we get:

⇒ 1 × (a² + ab + 1) > 1

⇒ a² + ab + 1 > 0

This is true for all values of a except 0.

∴ Δ > 0 and coefficient of a² must be positive.

⇒ b² − 4 < 0

⇒ |b| < 2

⇒ b ∈ {− 1 , 0 , 1}

∴ The number of integral values of b is 3.

The correct answer is Option 2.
Question 3
4 / -1

A
a straight line parallel to x-axis

B
a straight line parallel to y-axis

C
a parabola

D
a circle

Solution
Question 4
4 / -1

The maximum value of f(x) = |x ln x| in x ∈ (0, 1) is

A
1/e

B
e

C
1

D
none of these

Solution
Question 5
4 / -1

The slope of the line touching both the parabolas y² = 4x and x² = –32y is

A

B
3/2

C
1/8

D
2/3

Solution
Question 6
4 / -1

A
Domain of f (x) is [-1,1]

B
Maximum value of g (x) is 3/4

C
Maximum value of h (x) is 1/4

D

Solution
Question 7
4 / -1

If (R̅ - S̅).t̂ = 0, (R̅ - S̅).n̂ = 0 (R̅ - S̅).b̂ =0 and where t̂, n̂, b̂ form a right handed triad of orthogonal vectors, then –

A
R̅ = S̅

B
R̅ × S̅ = 0̅

C
R̅ .S̅ = 0

D
R̅ = 0

Solution
Question 8
4 / -1

If the four letter words (need not to meaningful) are to be formed using the letter from the word "MEDITERRANEAN" such that the first letter is R and the fourth letter is E, then the total number of all such words is:

A
110

B
59

C

D
56

Solution
Question 9
4 / -1

A
2/3

B
3/2

C
2

D
1/2

Solution
Question 10
4 / -1

A
1/3

B
4/3

C
8/3

D

Solution