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Question : In a triangle MNO, XA, XB, and XC are perpendicular bisectors on sides MN, ON, and OM respectively intersecting each other at X. If $\angle \mathrm{NMO}=55°$, then what is the value of $\angle \mathrm{NXO}$?
Option 1: 130°
Option 2: 110°
Option 3: 95°
Option 4: 125°
Correct Answer: 110°
Solution :
$\angle NXO$ is the angle made at the circumcenter of the triangle. ⇒ $\angle NXO = 2 × ∠NMO$ ⇒ $∠NXO = 2 × 55°$ ⇒ $∠NXO = 110°$ Hence, the correct answer is 110°.
Question : Comprehension:
In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.
The concept of motivation focuses on explaining what 'moves' behaviour. In fact, the term (1)_______ is derived from the Latin word 'movere', referring to the movement of activity. Most of our everyday explanation of (2)________ is given in terms of motives. Motives also help in making (3)__________ about behaviour. A person will work hard in school, in sports, in business, in music, and in many other situations, if he/she has a very strong need for (4)__________. Hence, motives are the general states that enable us to make predictions about behaviour in many different situations. In other words, motivation is one of the (5)_________ of behaviour. Instincts, drives, needs, goals, and incentives come under the broad cluster of motivation.
Question: Select the most appropriate option to fill in the blank number (5).
Option 1: meaning
Option 2: causes
Option 3: ways
Option 4: determinants
Correct Answer: determinants
Solution : The correct choice is the fourth option.
"Determinants" is the appropriate choice. It means a factor or cause that makes something happen or leads directly to a decision. It helps convey that motivation is one of the factors on which behaviour depends.
Question : The materials through which things cannot be seen are called _______.
Option 1: translucent materials
Option 2: transparent materials
Option 3: opaque materials
Option 4: pale materials
Correct Answer: opaque materials
Solution : The correct option is opaque materials.
The opaque materials are the materials through which you cannot see any light. Concrete, wood and metals are examples of opaque materials. The transparent materials are those materials from which you can see clearly. The translucent materials are
Question : Study the given bar-graph and answer the question that follows. The bar graph shows the number of bottles and the number of cups sold by five different shops during a given week.
The total number of bottles sold during the given week by the five shops taken together is approximately what percentage of the total number of cups sold during the given week by the five shops taken together?
Option 1: 96.43%
Option 2: 92.11%
Option 3: 87.22%
Option 4: 89.07%
Correct Answer: 92.11%
Solution : Total number of bottles = 81 + 39 + 63 + 77 + 90 = 350 Total number of cups = 68 + 72 + 93 + 87 + 60 = 380 Required percentage = $\frac{\text{total bottles}}{\text{total cups}}\times100$ = $\frac{350}{380}\times100$ = 92.11% Hence, the correct
Question : In $\Delta$ABC, D is the mid-point of BC and G is the centroid. If GD = 5 cm then the length of AD is:
Option 1: 10 cm
Option 2: 12 cm
Option 3: 15 cm
Option 4: 20 cm
Correct Answer: 15 cm
In a triangle, the centroid divides the median into two segments in the ratio of 2 : 1. Given that GD = 5 cm. ⇒ AG : GD = 2 : 1 ⇒ AG = 2GD = 2 × 5 cm = 10 cm
Question : Directions: Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: Some festivals are fireworks. No cracker is a firework. No bomb is a festival. Conclusions: I. No bomb is a cracker. II. Some bombs are crackers.
Option 1: Both conclusions I and II follow
Option 2: Neither conclusion I nor II follows
Option 3: Either conclusion I or II follows
Option 4: Only conclusion II follows
Correct Answer: Either conclusion I or II follows
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyze the conclusions – Conclusion (I): No bomb is a cracker – It is a possibility that the circle representing bomb and cracker does not overlap.
Question : Directions: In the following question, select the missing number from the given series. 98, 70, 42, 14, ?, – 42
Option 1: –10
Option 2: –14
Option 3: 0
Option 4: –15
Correct Answer: –14
Solution : Given: 98, 70, 42, 14, ?, – 42
Subtract 28 from each number to obtain the required missing number in the series. 98 – 28 = 70; 70 – 28 = 42; 42 – 28 = 14; 14 – 28 = –14; –14 – 28
Question : The following sentence has been split into four segments. Identify the segment that contains a grammatical error.
The earthy / fragrance of soil / after a first rain / is always refreshing.
Option 1: is always refreshing
Option 2: fragrance of soil
Option 3: The earthy
Option 4: after a first rain
Correct Answer: after a first rain
Solution : The error lies in the fourth option.
The sentence contains the wrong use of the article a, as it should be replaced with the to make the sentence grammatically accurate. The definite article the is used to refer to the
Question : Study the given pie chart carefully and answer the following question. If the scholarship has to be paid out of the donation fund, then what is the percentage of the donation fund used for this purpose (rounded off to two decimal places)? The entire fund that the school gets from different sources is equal to Rs. 10 lakh
Option 1: 74.29%
Option 2: 72.15%
Option 3: 80.25%
Option 4: 75.25%
Correct Answer: 74.29%
Solution : Given: The entire fund that the school gets from different sources is equal to Rs.10 lakh. The scholarship has to be paid out of the donation fund. The donation fund is 35% of the total fund = $1000000×\frac{35}{100}=350000$ For scholarship purposes, 26% of funds are
Question : If $x=1-y$ and $x^2=2-y^2$, then what is the value of $xy$?
Option 1: $1$
Option 2: $2$
Option 3: $-\frac{1}{2}$
Option 4: $–1$
Correct Answer: $-\frac{1}{2}$
Solution : Given: $x = 1-y$ ⇒ $x+y = 1$ Squaring both sides, we get, ⇒ $x^2+y^2+2xy=1$ Using $x^2 = 2-y^2$ ⇒ $2-y^2+y^2+2xy=1$ ⇒ $2+2xy =1$ $\therefore xy = -\frac{1}{2}$ Hence, the correct answer is $-\frac{1}{2}$.
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