Mathematics Test 210

Result

Mathematics Test 210

Score
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Weekly Quiz Competition

Question 1
4 / -1

A
3 : 4

B
1 : 2

C
4 : 3

D
2 : 3

Solution
Question 2
4 / -1

At an election, a voter may vote for any number of candidates not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote, is

A
6210

B
385

C
1110

D
5040

Solution

Total number of ways

= ¹⁰C₁ + ¹⁰C₂ + ¹⁰C₃ + ¹⁰C₄

= 10 + 45 + 120 + 210 = 385
Question 3
4 / -1

If 2y - a is the harmonic mean between y − x and y − z , then x - a, y - a and z - a are in

A
arithmetic progression

B
geometric progression

C
harmonic progression

D
none of these

Solution

It is given that, y − x, 2(y − a) and (y − z)y - x, 2y - a and y - z are in harmonic progression.
Question 4
4 / -1

are probabilities of mutually exclusive events of a random experiment, then the range of p is

A

B

C

D

Solution
Question 5
4 / -1

The equation of the bisectors of the angles between the lines represented by the equation 2(x + 2)² + 3(x + 2)(y - 2) -2(y - 2)² = 0 is

A
3x² − 8xy − 3y² − 28x + 4y + 32 = 0

B
3x² + 8xy − 3y² + 28x − 4y + 32 = 0

C
3x² − 8xy − 3y² + 28x − 4y + 32 = 0

D
3x²− 8xy − 3y²+ 28x − 4y − 32 = 0

Solution

2(x + 2)² + 3(x + 2)(y - 2) -2(y - 2)² = 0

Assume x + 2 = X, y − 2 = Y

2X² + 3XY − 2Y² = 0

Equation of the bisectors would be
Question 6
4 / -1

The possible values of scalar kk such that the matrix A⁻¹− kI is singular, where

A
-1/2, 2

B
-1, 1/2

C
1/2, -1/2

D
-1, 1

Solution
Question 7
4 / -1

If 1 + sinθ + sin²θ + sin³θ +.....=4 + 2√3, 0 < θ < π, then

A
θ = π/3

B
θ = π/6

C
θ = π/3 or π/6

D
θ = π/3 or 2π/3

Solution
Question 8
4 / -1

If f(x) = 3x⁴ + 4x³ − 12x² + 12 the f(x) is

A
increasing in (−∞, −2) ∪ (0, 1)

B
increasing in (−2, 0) ∪ (1, ∞)

C
decreasing in (−2, 0) ∪ (0, 1)

D
decreasing in (−∞,−2) and in (1,∞)

Solution

Since, f(x) = 3x⁴ + 4x³ − 12x² + 12

f′(x) = 12x³ + 12x² − 24x

= 12x(x − 1)(x + 2)

From the above expression it is clear that f(x) is increasing in (−2, 0)∪(1, ∞) and decreasing in (−∞, −2)∪(0, 1)
Question 9
4 / -1

A man whose eye level is 1.5 meter above the ground observes the angle of elevation of a tower to be 60°. If the distance of the man from the tower is 10 meter, the height of the tower is

A

B

C

D
None of these

Solution
Question 10
4 / -1

The area bounded by the curve y = x²/ 2 , x-axis and x = 2 is

A
1/3 sq.unit

B
2/3 sq.unit

C
1 sq.unit

D
4/3 sq.unit

Solution