Mathematics Test

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Mathematics Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

Every continuous function is

A
increasing

B
decreasing

C
not differentiable always

D
differentiable
Question 2
1 / -0

Area bounded by the curve xy² = a² (a - x) and y-axis is

A
π a²/2

B
π a²

C
3 π a²

D
3 π a²/2
Question 3
1 / -0

Let f(x) = [cos x + sin x], 0 < x < 2π where [x] denotes the greatest integer less than or equal to x. The number of points of discontinuity of f(x) is

A
6

B
5

C
4

D
3

Solution

Solution
Question 4
1 / -0

The term independent of x in the expansion of ((2x) - (3/x))⁶ is

A
4320

B
216

C
-216

D
-4320
Question 5
1 / -0

The lines 2x - 3y = 5 and 3x - 4y = 7 are the diameters of a circle of area 154 square units. The equation of the circle is

A
x²+y²+2x−2y=62

B
x²+y²−2x+2y=47

C
x²+y²+2x−2y=47

D
x²+y²−2x+2y=62

Solution

The correct option is B x²+y²−2x+2y=47

Centre of circle = Point of intersection of diameters = (1, –1)

Now area = 154 ⇒ πr²=154 ⇒ r=7

Hence the equation of required circle is(x−1)²+(y+1)²= 72 ⇒ x²+y²−2x+2y = 47.
Question 6
1 / -0

Coordinates of two points are A(1,0) and B(-1,0) and Q is a point which satisfies AQ-BQ = + 1. The locus of the point Q is

A
12x²+4y²=3

B
12x²-4y²=3

C
12x²-4y²+3=0

D
12x²+4y²+3=0

Solution

Solution

Option B is correct.
Question 7
1 / -0

The equation of tangent at point (1,2) to the parabola y²=4x is

A
x-y+1=0

B
x+y+1=0

C
x+y-1=0

D
x-y-1=0
Question 8
1 / -0

The number of solutions of the equation

A
1

B
2

C
3

D
4
Question 9
1 / -0

The area bounded by the curve y=sinx, y=0, x=0 and x=(π/2) is

A
π

B
2π

C
1

D
2
Question 10
1 / -0

The family of curves, in which the subtangent at any point to any curve is double the abscissa, is given by

A
x = cy²

B
y = cx²

C
x² = cy²

D
y = cx

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Re-Attempt Weekly Quiz Competition

Mathematics Test - 4

Result

Mathematics Test - 4

Score

-

Rank

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SHARING IS CARING

Question 1

increasing

decreasing

not differentiable always

differentiable

Question 2

π a2/2

π a2

3 π a2

3 π a2/2

Question 3

6

5

4

3

Solution

Question 4

4320

216

-216

-4320

Question 5

x2+y2+2x−2y=62

x2+y2−2x+2y=47

x2+y2+2x−2y=47

x2+y2−2x+2y=62

Solution

Question 6

12x2+4y2=3

12x2-4y2=3

12x2-4y2+3=0

12x2+4y2+3=0

Solution

Question 7

x-y+1=0

x+y+1=0

x+y-1=0

x-y-1=0

Question 8

1

2

3

4

Question 9

π

2π

1

2

Question 10

x = cy2

y = cx2

x2 = cy2

y = cx

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π a²/2

π a²

3 π a²

3 π a²/2

x²+y²+2x−2y=62

x²+y²−2x+2y=47

x²+y²+2x−2y=47

x²+y²−2x+2y=62

12x²+4y²=3

12x²-4y²=3

12x²-4y²+3=0

12x²+4y²+3=0

x = cy²

y = cx²

x² = cy²