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Question : If $\sin \theta=\frac{1}{2}$, then the value of $\left(3 \cos \theta-4 \cos ^3 \theta\right)$ is:
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: – 1
Correct Answer: 0
Solution : Given, $\sin \theta=\frac{1}{2}$ ⇒ $\theta = 30^\circ$ Now, $\left(3 \cos \theta-4 \cos ^3 \theta\right)=-\cos 3\theta$ ⇒ $\left(3 \cos \theta-4 \cos ^3 \theta\right)=-\cos 90^\circ$ ⇒ $\left(3 \cos \theta-4 \cos ^3 \theta\right)=0$ Hence, the correct answer is 0.
Question : Study the given graph and answer the question that follows. The following graph shows the distribution of the cost percentage of different items.
If a person purchased all the items for INR 3,00,000, then the cost of a TV is less than that of a laptop by:
Option 1: INR 40,000
Option 2: INR 55,000
Option 3: INR 50,000
Option 4: INR 45,000
Correct Answer: INR 45,000
Solution : According to the question Cost of TV is 15% ie. 0.15 × 300000 = 45000 The cost of Laptop is 30% i.e. 0.30 × 300000 = 90000 Now, Difference = Cost of laptop – Cost of TV = 90000 – 45000 = 45000 Hence,
Question : The following pie chart shows the percentage distribution of different fruits in a market. There are $15,000 \mathrm{~kg}$ of oranges in the market. Find the quantity of musk melon and watermelon together.
Option 1: 25,000 kg
Option 2: 5,000 kg
Option 3: 20,000 kg
Option 4: 10,000 kg
Correct Answer: 25,000 kg
Solution : Given: 15% of orange = 15000 kg ⇒ 1% = 1000 kg percentage distribution of musk melon and watermelon together = (20 + 5) = 25% So, 25% = 25 × 1000 = 25000 kg Hence, the correct answer is 25000 kg.
Question : A chord of a circle is equal to its radius of length 9 cm. Find the angle subtended by it in the major segment.
Option 1: $90^\circ$
Option 2: $60^\circ$
Option 3: $30^\circ$
Option 4: $120^\circ$
Correct Answer: $30^\circ$
Solution : The length of the chord(AB) = radius(OB) = 9 cm When the length of the chord and the radius are equal, the triangle formed is equilateral. The angles of an equilateral triangle are $60^\circ$ $\therefore$ The angle subtended in the major segment is half of
Question : The table given below shows the number of scissors sold by five shopkeepers.
What is the ratio of the number of scissors sold by R to the sold by S?
Option 1: 5 : 8
Option 2: 8 : 3
Option 3: 9 : 5
Option 4: 5 : 9
Correct Answer: 9 : 5
Solution : The number of scissors sold by R = 45 The number of scissors sold by S = 25 So, the required ratio = $\frac{45}{25} = \frac{9}{5}$ Hence, the correct answer is 9 : 5.
Question : Directions: A circular sheet of paper is folded in a particular manner, punched once, and then unfolded. Find out how the paper was folded and punched from amongst the answer figures.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : When the given unfolded paper is folded, it will look like –
Hence, the second option is correct.
Question : Directions: The bar chart given below shows the percentage distribution of the production of various models of mobile manufacturing in 2007 and 2008. The total production in 2007 was 35 lakh mobile phones, and in 2008, the production was 44 lakh. Study the chart and answer the following questions:
What was the difference in the number of B type mobiles produced in 2007 and 2008?
Option 1: 3,55,000
Option 2: 2,70,000
Option 3: 2,25,000
Option 4: 1,75,000
Correct Answer: 3,55,000
Solution : As per the given graph, The total production of mobile phones in 2007 = 35 lakh The total production in 2008 = 44 lakh The number of mobiles of model B manufactured in 2007 = 15% of 35 lakh = 5,25,000 The number of mobiles
Question : What is the sum of all two-digit numbers which are divisible by 9?
Option 1: 565
Option 2: 535
Option 3: 585
Option 4: 475
Correct Answer: 585
Solution : Sum of an arithmetic series = $\frac{n}{2} × (\text{first term + last term})$ ⇒ Two digit numbers divisible by 9: 18, 27, 36,..., 99 (Total terms = 10) So, the sum = $\frac{10}{2} × (18 + 99) = 585$ Therefore, the sum of all two-digit
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.
Calcium supplements, commonly (1) _______women are helpful (2) ________ warding off osteoporosis. More than just (3) ________ grams a day, (4) ________, can lead to stomach upset and even kidney stones. Niacin proven in reducing cholesterol levels can be dangerous (5) ________doses to those who suffer from heart problems. Question
Select the most appropriate option to fill in the blank number 5.
Option 1: in little
Option 2: in large
Option 3: in big
Option 4: in huge
Correct Answer: in large
Solution : The correct option is the second option.
Explanation: The phrase in large doses specifies the amount of niacin that can be dangerous. It indicates that while niacin is effective in reducing cholesterol levels, taking it in large quantities can pose risks, especially
Question : Directions: Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number. 4 : 25 :: 6 : 49 :: 8 : ?
Option 1: 80
Option 2: 82
Option 3: 85
Option 4: 81
Correct Answer: 81
Solution : Given: 4 : 25 :: 6 : 49 :: 8 : ?
Like, 4 : 25→(4 + 1)2 = (5)2 = 25 And, 6 : 49→(6 + 1)2 = (7)2 = 49 Similarly, follow the same pattern for 8 : ?→(8
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