Mathematics Test 248

Result

Mathematics Test 248

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Weekly Quiz Competition

Question 1
4 / -1

If the slope of one of the lines represented by ax² + (2a + 1)xy + 2y² = 0 is reciprocal of the slope of the other, then the sum of squares of slopes is

A

B
82/9

C
97/36

D
2

Solution
Question 2
4 / -1

A

B

C

D

Solution
Question 3
4 / -1

If the mean and S.D. of the data 3, 5, 7, a, b are 5 and 2 respectively, then a and b are the roots of the equation

A
x² - 10x + 18 = 0

B
2x² - 20x + 19 = 0

C
x² - 10x + 19 = 0

D
x² - 20x + 18 = 0

Solution

Note that the required quadratic equation is expressed as

x²- (a + b)x + ab = 0

x²- 10x + 19 = 0

∴ The required equation is x² - 10x + 19 = 0.

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

A linguistic club of a certain Institute consists of 6 girls and 4 boys. A team of 4 members to be selected from this group including the selection of a Captain (from among these 4 members) for the team. If the team has to include atmost one boy, the number of ways of selecting the team is

A
95

B
260

C
320

D
380

Solution

Calculation:

Case I : No boy is included.

Selecting 4 girls from 6 girls = ⁶C₄

Selecting 1 captain from selected members = ⁴C₁

Total number of ways = ⁶C₄ × ⁴C₁ = 60

Case II : One boy is included.

Selecting 3 girls and 1 boy from given members = ⁶C₃ × ⁴C₁.

Selecting 1 captain from the selected members = ⁴C₁.

Total Number of ways = ⁶C₃ × ⁴C₁ × ⁴C₁ = 320.

∴ Total Number of ways = 320 + 60 = 380.

The correct answer is Option 4.
Question 5
4 / -1

The range of values of x for which ƒ(x) = x³ + 6x² – 36x + 7 is increasing in

A
(-∞, -6) ∪ (2, ∞)

B
(-6, 2)

C
(∞, -2) ∪ (6, ∞)

D
(-6, 2]

Solution

Calculation:

Given, f(x) = x³ + 6x² - 36x + 7

⇒ f'(x) = 3x² + 12x - 36

= 3(x²+ 4x - 12)

For f(x) to be increasing,

f'(x) > 0

⇒ 3 (x² + 4x - 12) > 0

⇒ x²+ 4x - 12 > 0

⇒ (x + 6) (x - 2) > 0

⇒ x ∈ (- ∞, −6) ∪ (2, ∞)

∴ The range of x is (- ∞, −6) ∪ (2, ∞).

The correct answer is Option 1.
Question 6
4 / -1

A
nπ, n ∈ ℤ

B

C

D

Solution
Question 7
4 / -1

The co-ordinates of the point, where the line meets the plane 2x + 4y - z = 3, are

A
(3, -1, -1)

B
(3, 1, -1)

C
(3, -1, 1)

D
(-3, -1, -1)

Solution
Question 8
4 / -1

A
4

B
2

C
-1

D
-3

Solution

Calculation:

Given, f(x) is continuous x = 0

⇒ k² = 16

⇒ k = 4

∴ The value of k is 4.

The correct answer is Option 1.
Question 9
4 / -1

The graphical solution set for the system of inequations

x - 2y ≤ 2, 5x + 2y ≥ 10, 4x + 5y ≤ 20, x ≥ 0, y ≥ 0 is given by

A
Fig. 2

B
Fig. 4

C
Fig. 1

D
Fig. 3

Solution

Calculation:

Feasible region lies on origin side of x - 2y = 2, 4x + 5y = 20 and on non-origin side of 5x + 2y = 10, in 1^st quadrant.

∴ The correct graphical solution set is Fig. 2.

The correct answer is Option 4.
Question 10
4 / -1

If two vertices of a triangle are A(3, 1, 4) and B(-4, 5, −3) and the centroid of the triangle is G(-1, 2, 1), then the third vertex C of the triangle is

A
(2, 0, 2)

B
(-2, 0, 2)

C
(0, -2, 2)

D
(2, -2, 0)

Solution

Calculation:

Let the coordinates of C be C = (x, y, z)

Given, A(3, 1, 4) and B(-4, 5, −3) and the centroid of the triangle is G(-1, 2, 1)