Mathematics Test 207

Result

Mathematics Test 207

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Weekly Quiz Competition

Question 1
4 / -1

Let A and B be two sets in a universal set U. Then,

A
A - B = A' - B'

B
A - (A - B) = A ∩ B'

C
A - B = A' ∩ B'

D
A ∪ B = (A - B) ∪ (B - A) ∪ (A ∩ B)

Solution
Question 2
4 / -1

A
1- i√3

B
-1 + i√3

C
i√3

D
-i√3

Solution
Question 3
4 / -1

If the normal at the point (bt₁², 2bt₁) on a parabola meets the parabola again at the point (bt₂², 2bt₂), then

A

B

C

D

Solution
Question 4
4 / -1

A

B

C

D

Solution
Question 5
4 / -1

The differential equation whose solution is Ax² + By² = 1, where A and B are arbitrary constants, is of

A
second order and second degree

B
first order and second degree

C
first order and first degree

D
second order and first degree

Solution

Given: Ax² + By² = 1

As the solution has two constants, the order of the differential equation is 2,

So, our choices (2) and (3) are discarded from the list, only choices (1) and (4) are possible.

Again, Ax² + By² = 1 ... (*)

Differentiating (*) w.r.t. x,
Question 6
4 / -1

The volume of a parallelepiped whose sides are given by

A
4/13

B
4

C
2/7

D
None of these

Solution
Question 7
4 / -1

In an experiment with 15 observations on x, the following results were available.

∑x² = 2830, ∑x = 170

One observation, which was 20, was found to be wrong and was replaced by the correct value 30. Then, the corrected variance was

A
188.66

B
177.33

C
8.33

D
78.00

Solution

∑x = 170 and ∑x² = 2830

Increase in ∑x = 10 ∑x' = 170 + 10 = 180

Increases in ∑x² = 900 - 400 = 500

Then,

∑(x')² = 2830 + 500 = 3330
Question 8
4 / -1

The general solution of sin x - 3 sin 2x + sin 3x = cos x - 3 cos 2x + cos 3x is

A

B

C

D

Solution

(sin x + sin 3x) - 3 sin 2x = (cos x + cos 3x) - 3 cos 2x

∴ sin 2x (2 cos x - 3) = cos 2x (2 cos x - 3)

⇒ cos x = 3/2 or tan 2x = 1

cos x = 3/2 is impossible.

∴ tan 2x = 1
Question 9
4 / -1

The statement p → (q → p) is equivalent to

A
~p v q v ~p

B
~p v ~ q v p

C
~p ∧ ~ q v p

D
~p v ~ q ∧ p

Solution
Question 10
4 / -1

The function f(x) = x^1/x has a maximum value at

A
x = e

B
x = e^-1

C
x = e²

D
x = 0

Solution

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