Mathematics Test 263

Result

Mathematics Test 263

Score
-
out of -
Rank
-
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TIME Taken - -

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Weekly Quiz Competition

Question 1
4 / -1

A

B

C

D
None of these

Solution
Question 2
4 / -1

If m₁, m₂, m₃ and m₄ are, respectively the magnitudes of the vectors

then the corect order of m₁, m₂, m₃ and m₄ is

A
m₃ < m₁ < m₄ < m₂

B
m₃ < m₁ < m₂< m₄

C
m₃ < m₄< m₁ < m₂

D
m₃ < m₄ < m₂ < m₁

Solution
Question 3
4 / -1

A
1/8√3

B
1/√3

C
8√3

D
√3

Solution
Question 4
4 / -1

The area bounded by y = x|sin x| and X - axis between x = 0, x = 2π is

A
2 π sq units

B
3 π sq units

C
π sq units

D
4π sq units

Solution
Question 5
4 / -1

the eccenricity of the hyperbola

A
3/4

B
3/5

C
√41/4

D
√41/5

Solution
Question 6
4 / -1

If θ is the angle between the tangents from (-1, 0) to the circle x² + y² - 5x + 4y - 2 = 0, then θ is equal to

A
2 tan^-1 (7/4)

B
tan^-1(7/4)

C
2 cot^-1(7/4)

D
cot^-1(7/4)

Solution
Question 7
4 / -1

Let S_k be the sum of an infinite GP series whose first term k is k and common ratio is k/(k + 1) (k> 0). Then, the value of is equal to

A
log_e 4

B
log_e 2 - 1

C
1 - log_e 2

D
1 - log_e 4

Solution
Question 8
4 / -1

Let z₁ ≠ z₂ and |z₁| = |z₂|. If z₁ has positive real part and z₂ has negative imaginary part.

A
real and positive

B
zero or purely imaginary

C
real and negative

D
None of the above

Solution
Question 9
4 / -1

Where [] denotes the greater function is equal to

A
0

B
1

C
-1

D
does not exist

Solution
Question 10
4 / -1

A
an equilateral triangle

B
an isosceles triangle

C
collinear

D
right angled triangle
Solution
- Given Vectors:
- A = 7i - 11j + k
- B = 5i + 3j - 2k
- C = 12i - 8j - k
- Step 1: Calculate Lengths of the Sides
- The lengths of the sides are calculated using the distance formula:
- Distance AB:
- AB = B - A = (5 - 7)i + (3 + 11)j + (-2 - 1)k = -2i + 14j - 3k
- |AB| = √((-2)² + (14)² + (-3)²) = √(4 + 196 + 9) = √209
- Distance BC:
- BC = C - B = (12 - 5)i + (-8 - 3)j + (-1 + 2)k = 7i - 11j + k
- |BC| = √((7)² + (-11)² + (1)²) = √(49 + 121 + 1) = √171
- Distance AC:
- AC = C - A = (12 - 7)i + (-8 + 11)j + (-1 - 1)k = 5i + 3j - 2k
- |AC| = √((5)² + (3)² + (-2)²) = √(25 + 9 + 4) = √38
- Step 2: Determine the Type of Triangle
- The lengths are:
- |AB| = √209
- |BC| = √171
- |AC| = √38
- Triangle Type Analysis:
- a) Equilateral Triangle: All sides equal. (Not applicable here)
- b)Isosceles Triangle: At least two sides equal. (Not applicable here)
- c)Right-Angled Triangle: Check if |AC|² + |BC|² = |AB|²: (38 + 171 = 209) (True)
- Therefore, it is a right-angled triangle.