Mathematics Test 198

Result

Mathematics Test 198

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Weekly Quiz Competition

Question 1
4 / -1

The equation to the directrix of a parabola if the two extremities of its latus rectum are (2, 4) and (6, 4) and the parabola passes through the point (8, 1) is

A
y – 5 = 0

B
y – 6 = 0

C
y – 1 = 0

D
y – 2 = 0

Solution

focus is (4, 4) & D can be y = 6 or y = 2

where ‘O’ is origin and S is the focus and D is directrix
Question 2
4 / -1

then the maximum value of Δ is

A
3

B
9

C
10

D
13

Solution

Apply R₃ → R₃ → R₁, we get

= (3cos θ – sin θ)² So, maximum value of Δ equals 10.
Question 3
4 / -1

The number of solution(s) of the equation

(where z = x + iy, x, y ∈ R, i² = –1 and x ≠ 2)

A
0

B
1

C
2

D
3

Solution
Question 4
4 / -1

Two circles of radii r₁ and r₂ are both touching the coordinate axes and intersecting each other orthogonally. The value of r₁/r₂ (where r₁ > r₂) equals

A
2 + √3

B
√3 + 1

C
2 – √3

D
2 + √5

Solution

Circle is (x – r)² + (y – r)² = r²

⇒ x² + y² – 2xr – 2yr + r² = 0

Hence the circles are x² + y² – 2xr₁ – 2yr₁ + r₁² = 0 ......(1)
Question 5
4 / -1

Let X and Y be two matrices satisfying this relations

then Tr.(X) – Tr.(Y) equals

[Note : Tr.(P) denotes trace of matrix P.]

A
5

B
4

C
3

D
2
Question 6
4 / -1

The differential equation dx/dy = 3y/2x represents a family of hyperbolas (except when it represents a pair of lines) with eccentricity can be

A
√2

B

C

D
√3

Solution
Question 7
4 / -1

Line L, perpendicular to the line with equation y = 3x – 5, contains the point (1, 4). The x-intercept of L, is

A
12

B
13

C
14

D
15

Solution
Question 8
4 / -1

Let A = [a_ij] (1 ≤ i , j ≤ 3) be a 3 × 3 matrix and B = [b_ij] (1 ≤ i , j ≤ 3) be a 3 × 3 matrix such that

If det. A = 4, then the value of det. B is

A
0

B
4

C
8

D
16

Solution

B = AA^T.

Hence, det.

B = |AA^T| = |A| |A^T| = |A|² = 4² = 16.
Question 9
4 / -1

Number of words that can be formed using all the letters of the word GARGEE if no two alike letters are together, is

A
84

B
62

C
240

D
None

Solution

Number of words when G's are separated but E's are together = 3! × ⁴C₂ = 36

∴ Number of ways when no two alike letters are together = 120 – 36 = 84
Question 10
4 / -1

If acute angle between the line and xy plane is α and acute angle between the planes x + 2y = 0 and 2x + y = 0 is β then (cos²α + sin²β) equals

A
1

B
1/4

C
2/3

D
3/4

Solution