Mathematics Test 130

Result

Mathematics Test 130

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Weekly Quiz Competition

Question 1
4 / -1

The foci of a hyperbola coincide with the foci of the ellipse .The equation of the hyperbola if its eccentricity is 2, is

A

B

C

D
none of these

Solution
Question 2
4 / -1

Four persons are asked the same question by an interviewer. If each has, independently, a probability 1/6 of answering correctly, then the probability that at least one of them answers correctly is

A

B
2/3

C
1/36

D
none of these

Solution

Let denote the event that the i^th person answers the question correctly.
P(at least one of them answers correctly)
Question 3
4 / -1

Let for all is a root of the equation f(x) = 0 then

A
b = 1

B
b = 2

C
b = 12

D
b = – 1

Solution
Question 4
4 / -1

A variable chord passing through the fixed point P on the axis of the parabola cuts the parabola at the points A & B. The co-ordinates of the point P such that constant is

A

B

C

D

Solution

Let the point P be (h, 0). Hence equation of the chord passing through P(h, 0) in parametric form is given by
Question 5
4 / -1

Sum to n terms of the series

A

B

C

D
none of these

Solution
Question 6
4 / -1

The value of the limit is

A
10!

B
¹⁰C₁₀

C
¹⁰C₁

D
10¹⁰

Solution
Question 7
4 / -1

If z and ω are two non-zero complex numbers such that |zω| = 1 and arg(z) – arg(ω) = π/2, the is equal to

A
– i

B
1

C
-1

D
i

Solution

so, modulus of this complex number is 1 and argument is -π/2. so complex no. is "-i"
Question 8
4 / -1

If 0<x<1, then is equal to

A

B
x

C

D

Solution
Question 9
4 / -1

The function defined by

A
Invertible

B
Injective but not surjective.

C
Surjective but not injective

D
Neither injective nor surjective.

Solution

From graph we can see that, for two value of ‘x’, f(x) has same value so f(x) is not injective.
Also, range of f(x) is [0, 1)
Question 10
4 / -1

Let a₁, a₂, a₃, .... be terms of an A.P

A
7/2

B
2/7

C
11/41

D
41/11

Solution