Mathematics Test

Result

Mathematics Test - 18

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Weekly Quiz Competition

Question 1
1 / -0

Three numbers, the first number is two times the second and the second number is three times the third number. If the average of all three is 21, then find the largest number of three numbers?

A
36

B
38

C
47

D
48

Solution

Considered III number = x

II number = 2x

I number = 4 x x = 3 × 3 = 9x = 3 × 3 = 9

Large number = 4 × 9 = 36
Question 2
1 / -0

Find the value of -

$\left|\begin{array}{ccc}w^{3} & w^{2} & w \\ w^{5} & 1 & w \\ w^{4} & w^{3} & w^{2}\end{array}\right|$

A
0

B
1

C
2

D
3

Solution
Question 3
1 / -0

Find out the value of n in the expansion (5+x/7)ⁿ,, where x¹⁰ and x¹¹ are equal.

A
75

B
110

C
395

D
225

Solution
Question 4
1 / -0

Among the following alternatives, which represents each bar is for a range of data?

A
Pie chart

B
Bar graph

C
Histogram

D
Frequency polygon

Solution

Bar graph is used to represent the grouped data with rectangular bars that can be plotted vertically or horizontally.

Histogram is also used to represent the grouped data graphically in bars. It is similar to Bar graph, but in a histogram each bar is for range of data.

Pie chart is a circular representation of grouped data.

Frequency polygons are the graphical representation of grouped data by understanding the shapes of distribution.
Question 5
1 / -0

The integral for $\int \frac{\cos^{2} x + \sin^{2} x}{\cos^{2} x \sin^{2} x} d x$ is.

A
-sin x + sec x + C

B
-cot x + tan x + C

C
cos x + sec x + C

D
tan x - cot x + C

Solution
Question 6
1 / -0

Let $f (x) = \log (1 - x) + \sqrt{x^{2} - 1} (x) = ?$ Then Domain

A
[1, ∞ ]

B
[-∞, -1 ]

C
[-1, 1 ]

D
[0, 1]

Solution

f(x) = g(x) + h(x)

g(x) is defined only when 1 – x > 0

When x < 1

Dom (g) = [-∞, 1]

h(x) is defined x² - 1 ≥ 0

When x ≥ 1 or x ≤ -1

Dom (h) = [-∞, -1] or [1, ∞]

Dom (f) = Dom (g) U Dom (h)

= [-∞, -1]
Question 7
1 / -0

A shopkeeper bought two articles for Rs.68250. He sold one at a loss of 20% and the other at a profit of 15%. If the selling price of each article is same, then the difference between their cost prices is -

A
Rs. 12500

B
Rs. 12250

C
Rs. 13500

D
Rs. 12200

Solution

Let the cost price of first and the second article be Rs.x and y respectively.
Question 8
1 / -0

The 10th term in the expansion of (x² - 2x + 1)20 is:

A
²⁰C₁₀(x – x²)¹⁰

B
²⁰C₁₀(x² – 1)¹⁰

C
²⁰C₁₀(x² – 1)₁₀

D
²⁰C₁₀(x² + 1)¹⁰

Solution

To find the general term of the binomial expansion (1 - a)n, following formula is used:

T_r + 1 = (-1)^{r n}C_r a^r

The given equation can be re - written as:

x² - 2x + 1 = 1 - x(1 - x)

Let x(1 - x) = y

So, x² - 2x + 1 = 1 - y

So, the 10th term of the expansion will be:

T₁₀= ²⁰C₁₀y¹⁰

Put the value of y as (x – x²)

T₁₀ =²⁰C₁₀(x – x²)¹⁰
Question 9
1 / -0

The largest possible set of real numbers which can be the domain of
$f (x) = \sqrt{1 - \frac{1}{x}} i s$

A
(0,1)∪(0,∞)

B
(−1,0)∪(1,∞)

C
$(- \infty, - 1) \cup (0, \infty)$

D
$(- \infty, 0) \cup (1, \infty)$

Solution
Question 10
1 / -0

A
15/4

B
17/2

C
23/2

D
14/5

Solution