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Question : The circumferences of the two circles are touching externally. The distance between their centres is 12 cm. The radius of one circle is 7 cm. Find the diameter (in cm) of the other circle.
Option 1: 12
Option 2: 10
Option 3: 8
Option 4: 5
Correct Answer: 10
Solution : When two circles touch each other externally, the distance between their centres is equal to the sum of their radii. ⇒ Distance = 12 = 7 + Radius of other circle ⇒ Radius of other circle = 12 – 7 = 5 cm So, the
Question : Yogita sold a plasma TV at a 20% gain to Shyamla, and Shyamla sold it to Deepa at a 10% profit. If Deepa had to pay Rs. 33,000 for the plasma TV, find the cost price of the plasma TV for Yogita.
Option 1: Rs. 30,000
Option 2: Rs. 25,000
Option 3: Rs. 35,000
Option 4: Rs. 40,000
Correct Answer: Rs. 25,000
Solution : Let the cost price of the plasma TV for Yogita be Rs. $x$. According to the question, $x×\frac{120}{100}×\frac{110}{100}=33000$ ⇒ $x=33000×\frac{100}{120}×\frac{100}{110}$ ⇒ $x =25000$ Hence, the correct answer is Rs. 25,000.
Question : Directions: A and B are a married couple. C and D are brothers. C is the brother of A. How is D related to B?
Option 1: Brother
Option 2: Son-in-law
Option 3: Cousin
Option 4: Brother-in-law
Correct Answer: Brother-in-law
Solution : As per the instructions given, the family tree will be –
Here, the quadrilateral represents the male, and the circular figure represents the female in the figure.
So, D is the brother-in-law of B. Hence, the fourth option is correct.
Question : The least six-digit number, which is a perfect square, is:
Option 1: 100489
Option 2: 10000
Option 3: 100256
Option 4: 100255
Correct Answer: 100489
Solution : The least six-digit number is 100000. Using the long division method to find its square root, we see that it is not a perfect square. ⇒ (316)2 = (100000 – 144) = 99856, a 5-digit number. But (317)2 = 100489, a 6-digit number.
Question : Comprehension: In the following passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each blank. I had seen the magic shop from afar several times. I had passed (1)______ once or twice, a shop window of (2)______ little objects, magic balls, magic hens, wonderful cones, magic dolls, and all those (3)______ of things. But never had I thought of going in (4)______ one day. Gip hauled me by my finger—right (5)______ to the window. Question: Select the most appropriate option to fill in the blank no. 3.
Option 1: pattern
Option 2: sort
Option 3: shape
Option 4: design
Correct Answer: sort
Solution : The second option is the correct choice.
The word sort is appropriate in the context as it refers to a category or type of magical objects that the magic shop sells. It conveys the idea of a variety of magical items available in the shop
Question : The table shows the number of boys and girls in the schools. Which school has the minimum number of students?
Option 1: 2
Option 2: 3
Option 3: 5
Option 4: 1
Correct Answer: 5
Solution : The minimum number of students in the school = Number of boys + Number of the girls. The minimum number of students in the school 1 = 44 + 56 = 100 The minimum number of students in the school 2 = 34 + 45
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the highlighted part of the sentence. In case no improvement is needed, select "No Improvement".
There are schools in either sides of the road.
(1) schools on either side
(2) school on either side
(3) school on either sides
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The correct choice is the first option.
Since one is talking about multiple schools on both sides of the road, one should use the plural form "schools" instead of "school". "Side" must be used in the singular form because it refers to one of those
Question : The following pie chart shows the number of workers of different categories A, B, C, D, E, F, G, and H of a factory in 1995. If the number of workers in Category B increased by 10% and the number of workers in Category D decreased by 5% in 1996, then what is the total no. of workers in Categories B and D in 1996, if no. of workers in B was 1500 in the year 1995?
Option 1: 4025
Option 2: 4500
Option 3: 5000
Option 4: 4000
Correct Answer: 4025
Solution : Number of workers in Category B was 1500 in the year 1995. It is given that 15% of the workers are in Category B. So, 15% of the workers are in Category B = 1500 $\therefore$ 25% of workers in Category D $= \frac{1500}{15}×25=2500$ In
Question : How do Pteridophytes reproduce?
Option 1: With the help of seeds
Option 2: With the help of spores
Option 3: With the help of pollens
Option 4: With the help of budding
Correct Answer: With the help of spores
Solution : The correct answer is With the help of spores.
Pteridophytes are plants that do not produce any flowers for seeds, and they are also called cryptograms. They are usually found in damp and shady places. Pteridophytes reproduce with the help of
Question : Simplify the given expression $\frac{(x^3-y^3)(x+y)}{x^2+x y+y^2}$.
Option 1: $x - y$
Option 2: $x^2-y^2$
Option 3: $x + y$
Option 4: $x^2+y^2$
Correct Answer: $x^2-y^2$
Solution : $\frac{(x^3-y^3)(x+y)}{x^2+x y+y^2}$ = $\frac{(x-y)(x^2+x y+y^2)(x+y)}{x^2+x y+y^2}$ = $(x-y)(x+y)$ = $x^2-y^2$ Hence, the correct answer is $x^2-y^2$.
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