Mathematics Test 249

Result

Mathematics Test 249

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Weekly Quiz Competition

Question 1
4 / -1

The number of solution in [0, 2π] of the equation

A
2

B
4

C
6

D
8

Solution

∴ The number of solutions is 8.

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

A
5

B
13

C
12

D
15

Solution
Question 3
4 / -1

A

B

C

D

Solution

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

(where c is a constant of integration), then values of P and Q are respectively

A

B

C

D

Solution
Question 5
4 / -1

The distance of the point having position vector î - 2ĵ - 6k̂, from the straight line passing through the point (2, -3, -4) and parallel to the vector 6î + 3ĵ - 4k̂ is units.

A

B
341/61

C

D

Solution
Question 6
4 / -1

A vector is inclined to X-axis at 45°, Y-axis at 60° and at an acute angle to Z-axis if is normal to a plane passing through the point (-√2, 1, 1), then equation of the plane is

A
√2x + y + z = 0

B
x + √2y + z = 1

C
-√2x + y + 2z = 5

D
x + y + √2z = 1

Solution
Question 7
4 / -1

The particular solution of the differential equation (1 + y²)dx - xy dy = 0 at x = 1, y = 0, represents

A
circle

B
pair of straight lines

C
hyperbola

D
ellipse

Solution

∴ The given differential equation represents a hyperbola.
Question 8
4 / -1

The coefficient of a¹⁰b⁷c³ in the expansion of (bc + ca + ab)¹⁰ is

A
140

B
150

C
120

D
160

Solution
Question 9
4 / -1

Let A be the set of even natural numbers that are < 8 & B be the set of prime integers that are < 7 The number of relations from A to B are

A
3²

B
2^9-1

C
9²

D
2⁹

Solution

Calculation:

Given, A is the set of even natural numbers less than 8.

⇒ A = {2, 4, 6}

⇒ m = n(A) = 3

B is the set of prime numbers less than 7.

⇒ B = {2, 3, 5}

⇒ n = n(B) = 3

∴ Number of relations = 2^mn = 2⁹

∴ The number of relations from A to B are 2⁹.

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

If α₁, α₂,...., α_n are in A.P. with common difference θ, then the sum of the series sec α₁ sec α₂ + sec α₂ sec α₃ + ....+ sec α_n-1 sec α_n = k(tan α_n - tan α₁) where k =

A
sin θ

B
cos θ

C
sec θ

D
cosec θ

Solution