Mathematics Test 144

Result

Mathematics Test 144

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Question 1
4 / -1

A vector of magnitude 9 and perpendicular to both the vectors

A

B

C

D

Solution
Question 2
4 / -1

If x = 9 is the chord of contact of the hyperbola x² - y² = 9, then the equation of the corresponding pair of tangents is

A
9x² - 8y² + 18x - 9 = 0

B
9x² - 8y² - 18x + 9 = 0

C
9x² - 8y² - 18x - 9 = 0

D
9x² - 8y² + 18x + 9 = 0

Solution

Let (h, k) be point whose chord of contact with respect to hyperbola x² - y² = 9 is x = 9.
W e know that, chord of contact of (h, k) with respect to hyperbola x² - y² = 9 is T = 0

But it is the equation of the line x = 9.
This is possible when h = 1, k = 0 (by comparing both equations).
Againe quation of pair of tangents is T² = SS₁
Question 3
4 / -1

A

B

C

D

Solution
Question 4
4 / -1

If α, β and γ are the angles which a directed line makes with the positive directions of the co-ordinates axes, then find the value of sin²α + sin²β + sin²γ.

A
0

B
4

C
2

D
1

Solution

The direction cosines of the line are
Question 5
4 / -1

In an acute - angled triangle ABC, points D, E and F are the feet of the perpendiculars from A, B and C onto BC, AC and AB, respectively. H is the orthocentre of ΔABC. If sin A = 3/5 and BC = 39, then the length of AH is

A
50

B
42

C
55

D
52

Solution
Question 6
4 / -1

then f(x) is equal to

A
cos x

B
sin x

C
tan x

D
1

Solution
Question 7
4 / -1

If x is rational and ,⁡ then value of x is equal to

A
4, 3/5

B
4, 1/4

C
3, 1/3

D
2, 1/2

Solution
Question 8
4 / -1

The line x = c cuts the triangle with corners (0, 0), (1, 1) and (9, 1) into two regions. For the area of the two regions to be the same c must be equal to :

A
5/2

B
3

C
7/2

D
3 or 15

Solution

The area of the triagle formed by three given vertices is

1/2 × 8 × 1 = 4

Now the line x = c bisect the area of triangle in two equal parts so the area of the both the parts of the triangle must be four
Question 9
4 / -1

The number of solutions of the equation a ^f(^x) + g(x) = 0, where a > 0, g (x) ≠ 0 and has least value 1/2 is

A
One

B
Two

C
Infinite many

D
Zero

Solution

Which is impossible.
Hence, no solutions.
∴ Number of solutions = zero.
Question 10
4 / -1

The area of the curvilinear triangle bounded by the y-axis & the curve y = tan x & y = (2/3) cos x is

A

B

C

D
None of these

Solution