Mathematics Test 146

Result

Mathematics Test 146

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Weekly Quiz Competition

Question 1
4 / -1

Let a, b and c be positive constants. The value of ‘a’ in terms of ‘c’ if the value of integral is independent of ‘b’ equals

A

B

C

D

Solution
Question 2
4 / -1

Let are three vectors along the adjacent edges of a tetrahedron, if then volume of tetrahedron is

A
1 / √2

B
2 / √3

C

D
2√2 / 3

Solution
Question 3
4 / -1

Let ω be a complex cube root of unity with ω ≠ 1. A fair die is thrown three times. If r₁, r₂ and r₃ are the numbers obtained on the die, then the probability that

A
1/18

B
1/9

C
2/9

D
1/36

Solution

A dice is thrown thrice n(s)=6 x 6 x 6

Favorable events, ω^r1 + ω^r2 + ω^r3

(r₁,r₂,r₃) are ordered 3 triples which can take values.

(1,2,3)(1,5,3)(4,2,3)(4,5,3)

(1,2,6)(1,5,6)(4,2,6)(4,5,6)

i.e, 8 ordered pairs and each can be arranged in 3! ways.

3!=6
Question 4
4 / -1

A ray of light travels along a line y = 4 and strikes the surface of a curves y² = 4 (x + y), then equations of the line along which reflected ray travel is

A
x = 0

B
x = 2

C
x + y = 4

D
2x + y = 4

Solution

Focus is (0,2)

Point os interflection property of parabola, reflected ray passes through the focus.

X = 0 is required line.
Question 5
4 / -1

A triangle ABC having vertices A (5, 1), B (–1, –7) and C (1, 4) respectively. If L1 be the line mirror passing through C and parallel to AB, a light ray emanating from point A and goes along the direction of internal bisector of the angle A, which meets the mirror at E and BC at D. Then sum of the area of ΔACE and ΔABC is

A
19/2 sq. units

B
38 sq. units

C
19 sq. units

D
75/2 sq. units

Solution
Question 6
4 / -1

The number of different ways in which the persons A, B, C having 6 one rupee coins, 7 one rupee coins, 8 one rupee coins respectively donate 10 one rupee coins collectively is equal

A
44

B
45

C
46

D
47

Solution
Question 7
4 / -1

Let a = cos^–1 (cos 20), b = cos^–1 (cos 30) and c = sin^–1 sin (a + b) then maximum value of sin (2 (a+b+c) x) + cos² ((a+b+c) x) is

A
√5+1 / 2

B
√5 -1 / 2

C
√3 -1 / 2

D
1

Solution
Question 8
4 / -1

A rectangle ABCD of dimensions r and 2r is folded along diagonal BD such that planes ABD and CBD are perpendicular to each other. Let the position of the vertex A remains unchanged and C₁ is the new position of C.

The distance of C₁ from A is equal to

A
2√5r / 5

B
2√10r / 5

C
√85r / 5

D
√4r / 5

Solution

Let the rectangle ABCD initially lies in xy plane with B King at origin BC' along x - axis and BA
Along y-axis.

Equation of BD in xy-plane is y = 2x
Question 9
4 / -1

A rectangle ABCD of dimensions r and 2r is folded along diagonal BD such that planes ABD and CBD are perpendicular to each other. Let the position of the vertex A remains unchanged and C₁ is the new position of C.

If ∠∠ABC₁ = θ, then cos θ is equal to

A
1/5

B
2/5

C
2/√5

D
4/5

Solution

Let the rectangle ABCD initially lies in xy plane with B King at origin BC' along x - axis and BA
Along y-axis.

Equation of BD in xy-plane is y = 2x
Question 10
4 / -1

A square ABCD of diagonal 2a is folded along the diagonal AC so that the planes DAC and BAC are at right angle. The shortest distance between DC and AB is

A
2a/√3

B
√2a

C
2a/√5

D
√3a/2

Solution

When folded coordinates will be D(0,0,a);C(a,0,0);A(−a,0,0);B(0,−a,0)

Equation of DC is,

∴ Shortest distance = 2a/√3