Mathematics Test

Result

Mathematics Test - 17

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Question 1
1 / -0

A

B

C

D

Solution
Question 2
1 / -0

A

B

C

D

None of these

Solution

Since the real part of z is negative & imaginary part of z is positive, so the point lies in IInd quadrant.
Question 3
1 / -0

Out of 30 guests, twenty like tea and fifteen like coffee, also each guest likes at least one of the two drinks. How many guests like both tea and coffee?

A
5

B
4

C
6

D
3

Solution

Let A be the set of guests who like tea.

Let B be the set of guests who like coffee.

Then is the set of guests who like at least one drink, and

is the set of guests who like both drinks.

We have n(A) = 20, n(B) = 15, n(A∪B) = 30

From the formula we get

30 = 20 + 15 - n(A∩B)

n(A∩B) = 35 – 30 = 5

So, n(A∩B) = 5.

Hence, 5 guests like both drinks.
Question 4
1 / -0

The Value of X in two dimensional planes is also called as

A
Abscissa

B
grade

C
Aplicate

D
Ordered pair

Solution

The value of x is also known as x-coordinate or Abscissa and the value of y are called y-coordinate or ordinate in two dimensional plane ofCartesian system.

Abscissa is a signed measure of the point’s projection on the primary axis. It is rarely used in three dimensional geometry.

The value of z-coordinate in three dimensional diagrams is called applicate.

Ordered pair consists of both abscissa and ordinate i.e. (x, y).
Question 5
1 / -0

A
x ϵ (-∞, -1) ∪ (3, ∞)

B
x ϵ (-∞, -2) ∪ (3, ∞)

C
x ϵ (-∞, -1) ∪ (2, ∞)

D
x ϵ (-∞, -0) ∪ (3, ∞)

Solution
Question 6
1 / -0

Equation x(1+y²)dx+tan⁻¹ydy = 0 is satisfied by

A

$y=\pm \tan (\sqrt{\left.c-x^{2}\right)}$

B

$y=\pm(\sqrt{\tan (c-x)}$

C

$y=\pm \tan \sqrt{c}-4 x^{2}$

D

$y=\pm \tan \sqrt{c}-x^{2}$

Solution
Question 7
1 / -0

A multiple choice question has 5 alternates, one or more than one correct. Find the least number of chances which would be given to a student such that probability of giving a correct answer is more than 1/3.

A
9

B
10

C
11

D
12

Solution

There are two options, select or not select each of the five alternatives. But we cannot choose the case of not selecting any alternate.

Hence, Total number of cases
Question 8
1 / -0

If $f (x) = \log (\frac{1 + x}{1 - x})$ and Ig(x) = $(\frac{3 x + x^{3}}{1 + 3 x^{2}})$ then what is f [g(x)] equalto?

A
−f(x)

B
3[f(x)]

C
[f(x)]3

D
−3[f(x)]

Solution

$f[g(x)]=\log \left[\frac{1+g(x)}{1-g)(x)}\right]=\log \left[\frac{1+3 x^{2}+3 x+x^{3}}{1+3 x^{2}-3 x-x^{3}}\right]$

$=\log \left(\frac{1+x}{1-x}\right)$
$=3 \log \left(\frac{1+x}{1-x}\right)$
$=3 f(x)$
Question 9
1 / -0

If A and B are two subsets of a set X such that n (X) = 900, n (A) = 400, n (B) = 600 and n (A∩B) = 250. Then, n (A'∩B') = ?

A
13

B
150

C
180

D
250

Solution

Given n (A) = 400, n (B) = 600 and n (A∩B) = 250

n (A∪B) = n (A) + n (B) - n (A∩B) = 400 + 600 - 250 = 750

n (A∪B) = 750

n [(A∪B)’] = (900 – 750) = 150

According to De - Morgan’s law, n [(A∪B)’] = n (A'∩B')

So, n (A'∩B') = 150
Question 10
1 / -0

In a group of buffaloes and ducks, the total number of feet was more than twice the total number of heads, so find the number of buffaloes in the group.

A
6

B
12

C
8

D
None of these

Solution