Mathematics Test

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Mathematics Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

The curves 4x² + 9y² = 72 and x² - y² = 5 at (3, 2)

A
touch each other

B
cut orthogonally

C
intersect at 45°

D
intersect at 60°
Question 2
1 / -0

The area contained between the curve xy = a², the vertical line x = a, x = 4a (a > 0) and x -axis is

A
a² log 2

B
2a² log 2

C
a log 2

D
2a log 2
Question 3
1 / -0

Complex numbers z₁,z₂ and z₃ in A.P.

A
lie on a line

B
lie on a parabola

C
lie on ellipse

D
lie on circle
Question 4
1 / -0

From the origin chords are drawn to the circle x²+ y² - 2y = 0. The locus of the middle points of these chords is

A
x² + y² - y = 0

B
x² + y² - x = 0

C
x² + y² - 2x = 0

D
x² + y² - x - y = 0

Solution

Let P(x₁, y₁) be a point in the locus
Question 5
1 / -0

If | x | < 1, then the coefficient of xn in the expansion (1 + x + x² + x³ + ....)2 is

A
n

B
n - 1

C
n + 2

D
n + 1

Solution

1 + x + x² + x³ + ..... = (1 - x) ^-1 [∵ | x | < 1]
∴ (1 + x + x² + x³ + .....)² = [(1 - x)^-1]²
= (1 - x)^-2
Now (1 - x)^-2 = 1 + 2x + 3x² + 4x³ + ..... + (n + 1) xⁿ (∵ | x | < 1).
Hence Coefficient of xⁿ is (n + 1)
Question 6
1 / -0

The pair of lines represented by 3ax2 + 5xy + (a² - 2)y²= 0 are ⊥ to each other for

A
two values of a

B
for one value of a

C
for no value of a

D
none of these
Question 7
1 / -0

The value of f(0) so that f x = sinx / x is continuous at x = 0 is

A
1

B
2

C
3

D
3 2
Question 8
1 / -0

The tangent drawn from (α,β) to an ellipse (x²/a²)+(y²/b²)=1 touches the circle x²+y²=c² then the locus of (α,β) is

A
an ellipse

B
a circle

C
a parabola

D
none of these
Question 9
1 / -0

A
(a + b + c)²

B
(a + b + c)⁴

C
(a + b + c)³

D
(a + b + c)
Question 10
1 / -0

A
1

B
1/2

C
1/3

D
1/4

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Re-Attempt Weekly Quiz Competition

Mathematics Test - 1

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Mathematics Test - 1

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SHARING IS CARING

Question 1

touch each other

cut orthogonally

intersect at 45°

intersect at 60°

Question 2

a2 log 2

2a2 log 2

a log 2

2a log 2

Question 3

lie on a line

lie on a parabola

lie on ellipse

lie on circle

Question 4

x2 + y2 - y = 0

x2 + y2 - x = 0

x2 + y2 - 2x = 0

x2 + y2 - x - y = 0

Solution

Question 5

n

n - 1

n + 2

n + 1

Solution

Question 6

two values of a

for one value of a

for no value of a

none of these

Question 7

1

2

3

3 2

Question 8

an ellipse

a circle

a parabola

none of these

Question 9

(a + b + c)2

(a + b + c)4

(a + b + c)3

(a + b + c)

Question 10

1

1/2

1/3

1/4

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a² log 2

2a² log 2

x² + y² - y = 0

x² + y² - x = 0

x² + y² - 2x = 0

x² + y² - x - y = 0

(a + b + c)²

(a + b + c)⁴

(a + b + c)³