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Question : What is the area of a triangle having a perimeter of 32 cm, one side of 11 cm, and the difference between the other two sides is 5 cm?
Option 1: $8\sqrt{30}$ cm2
Option 2: $5\sqrt{35}$ cm2
Option 3: $6\sqrt{30}$ cm2
Option 4: $8\sqrt{2}$ cm2
Correct Answer: $8\sqrt{30}$ cm2
Solution : Let the sides of the triangle be $a$, $b$, and $c$. Given Perimeter = 32 cm ⇒ $a+b+c=32$ ...... equation (1) One side, let $a$ =11 cm Also, the difference between the other two sides, $b−c=5$........ equation (2) Performing equation (1) + equation
Question : Directions: Which of the following interchange of signs would make the given equation correct? 13 + 26 × 2 – 5 ÷ 4 = 6
Option 1: ÷ and +
Option 2: + and –
Option 3: × and –
Option 4: × and ÷
Correct Answer: × and ÷
Solution : Given: 13 + 26 × 2 – 5 ÷ 4 = 6
Replace the given symbols in the options one by one with the original symbols in the given equation. First option: ÷ and + = 13 ÷ 26 × 2 – 5
Question : Select the INCORRECTLY spelt word.
Option 1: Difficulty
Option 2: Thesaurus
Option 3: Dictionary
Option 4: Dinoshauraus
Correct Answer: Dinoshauraus
Solution : The correct option is the fourth option.
Explanation: The correct spelling of the word is dinosaur. Dinosaurs are a group of extinct reptiles that lived millions of years ago. They varied greatly in size, shape, and habitat and are known for their dominance on Earth
Question : Find out the area of the triangle of base 7 cm and the corresponding height of 12 cm.
Option 1: 42 cm2
Option 2: 54 cm2
Option 3: 43 cm2
Option 4: 44 cm2
Correct Answer: 42 cm2
Solution : Area of a triangle = $\frac{1}{2}$ × Base × Height Given the base ($b$) is 7 cm and the height ($h$) is 12 cm. So, the area = $\frac{1}{2}$ × 7 × 12 = 42 cm2 Hence, the correct answer is 42
Question : Directions: What will come in the place of the question mark (?) in the following equation if + and – are interchanged and × and ÷ are interchanged? 49 × 7 ÷ 13 – 87 + 12 = ?
Option 1: 167
Option 2: 166
Option 3: 159
Option 4: 171
Correct Answer: 166
Solution : Given: 49 × 7 ÷ 13 – 87 + 12 = ?
On, interchanging the symbols with each other, we get – = 49 ÷ 7 × 13 + 87 – 12 = 7 × 13 + 87 – 12 = 91 + 87 –
Question : Simplify the following expression: $\frac{1-\sin A}{\cos A}+\frac{\cos A}{1-\sin A}$
Option 1: $2 \cos A$
Option 2: $2 \tan A$
Option 3: $2 \sec A$
Option 4: $2 \sin A$
Correct Answer: $2 \sec A$
Solution : $\frac{1-\sin A}{\cos A}+\frac{\cos A}{1-\sin A}$ $=\frac{(1-\sin A)^2+\cos^2A}{\cos A(1-\sin A)}$ $=\frac{1+\sin^2 A-2\sin A+\cos^2A}{\cos A(1-\sin A)}$ $=\frac{1+1 -2\sin A}{\cos A(1-\sin A)}$ $=\frac{2 -2\sin A}{\cos A(1-\sin A)}$ $=\frac{2(1 -\sin A)}{\cos A(1-\sin A)}$ $=\frac{2}{\cos A}$ $=2\sec A$ Hence, the correct answer is $2\sec A$.
Question : A is twice as fast as B and B is thrice as fast as C. The journey covered by C in $1\frac{1}{2}$ hour will be covered by A in:
Option 1: 15 minutes
Option 2: 30 minutes
Option 3: 1 hour
Option 4: 10 minutes
Correct Answer: 15 minutes
Solution : Given: A is twice as fast as B and B is thrice as fast as C. The journey is covered by C in $1\frac{1}{2}$ hour. Let the speed of C be $x$ metre/min. So, the speed of B will be $3x$ metre/min. And the
Question : The Chhatrapati Shivaji Maharaj Terminus was formerly known as ______.
Option 1: Elizabeth Terminus Station
Option 2: James Terminus Station
Option 3: George Terminus Station
Option 4: Victoria Terminus Station
Correct Answer: Victoria Terminus Station
Solution : The correct answer is Victoria Terminus Station.
The Chhatrapati Shivaji Terminus touches the Arabian Sea coast and is located in Mumbai, in Western India. The Victoria Terminus Station was the previous name of the Chhatrapati Shivaji Maharaj Terminus. It is one of
Question : The following pie chart shows the percentage expenditure of a country on different heads. The total expenditure is INR 1,680 (in billions). Study the chart and answer the question.
The expenditure on Education is what percentage less than the expenditure on Defence?
Option 1: 150%
Option 2: 50%
Option 3: 100%
Option 4: 125%
Correct Answer: 50%
Solution : Expenditure on Education = 6% Expenditure on Defence = 12% Required percentage = $\frac{12-6}{12}$ × 100 = 50% Hence, the correct answer is 50%.
Question : Which of the following chemicals is used as a preservative to slow browning and discolouration in foods and beverages during preparation, storage, and distribution?
Option 1: Nitrous oxide
Option 2: Phosgene
Option 3: Sulphites
Option 4: Chlorine
Correct Answer: Sulphites
Solution : The correct answer is Sulphites.
Sulphites is a sulphur-containing compound that has been used for centuries to prevent discolouration and slow browning during the storage and distribution of many foods. When some fruits are cut, the exposure of the flesh to oxygen results in
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