Mathematics Test 138

Result

Mathematics Test 138

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
4 / -1

A
4

B
3

C
6

D
2

Solution
Question 2
4 / -1

The equation of a circle C₁ is x²+ y²− 4x − 2y − 11 = 0. A circle C₂ of radius 1 unit rolls on the outside of the circle C₁ touching it externally. The locus of the centre of C₂ has the equation

A
x²+ y²− 4x − 2y − 20 = 0

B
x² + y² + 4x − 2y − 20 = 0

C
x² + y² − 3x − 2y − 11 = 0

D
None of these

Solution
Question 3
4 / -1

Two vertices of a triangle are (3, -2) and (-2, 3) and its orthocentre is (- 6, 1). The coordinates of its third vertex are-

A
(1, 6)

B
(-1, 6)

C
(1, -6)

D
None of these

Solution
Question 4
4 / -1

The equation of the common tangent to the equal parabolas y² = 4ax and x² = 4ay is

A
x + y + a = 0

B
x + y = a

C
x - y = a

D
None of these

Solution

Any tangent to y² = 4ax is It touches x² = 4ay if
has equal roots.
So m³ + 1 = 0, i e , m = -1 Hence, the common tangent is y = - x - a
Question 5
4 / -1

A line makes angles of 45° and 60° with the positive directions of x and y axes respectively. An angle, which the line can make with the positive direction of z-axis is:

A
60°

B
40°

C
80°

D
100°

Solution

Let α , β , γ be the angles, which the line makes with the positive directions of x-axis, y-axis and z-axis respectively

Hence the line makes an angle of 60° with the positive direction of z-axis
Question 6
4 / -1

If ln(x + y) = 2xy, then y′ (0) is equal to

A
1

B
-1

C
2

D
0

Solution
Question 7
4 / -1

If the fourth term of is equal to 200 and x > 1, then x is equal to

A
10√2

B
10⁴

C
100

D
10

Solution
Question 8
4 / -1

If the line 3x + 2y = 13 divides the area enclosed by the curve, 9x²+ 4y²− 18x − 16y − 11 = 0 into two parts then the ratio of the larger area to the smaller area is

A

B

C

D
None of these

Solution

E quation o f given curve is

It can be reduced to  which is the equation of ellipse having it’s principal axis parallel to coordinate axes
⇒  lt's area = πab = π (2) ( 3) = 6π
From the figure we can see that points of intersection of  and line 3x + 2y = 13, have x = 1, 3
⇒ Smaller area between ellipse and line
Question 9
4 / -1

The third vertex of the triangle whose centroid is (7,−2, 5) and whose other two vertices are (2, 6, −4) and (4,−2, 3) is

A
(15,−10, 16)

B
(10,−12, 16)

C
(13,−14, 11)

D
(6,−11, 10)

Solution

Let A (2, 6, - 4) and B (4, - 2, 3) be the two given vertices of the triangle. Let C (α , β, γ) be the third vertex
Since G (7, - 2, 5) is the centroid of ΔABC,
Question 10
4 / -1

The least positive integral value of m, if

A
4

B
6

C
2

D
1

Solution