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Question : The bar chart given below shows the annual production (in 1000 tonnes) of coffee of a country for the years 2018 to 2022. What is the average production (in 1000 tonnes) of coffee for the years 2018, 2019, and 2020?
Option 1: 530
Option 2: 810
Option 3: 720
Option 4: 640
Correct Answer: 640
Solution : Production of coffee in 2018 = 700 (in 1000 tonnes) Production of coffee in 2019 = 550 (in 1000 tonnes) Production of coffee in 2020 = 670 (in 1000 tonnes) Average = $\frac{\text{Sum of yearly production}}{{\text{Total number of years}}}$ = $\frac{700+550+670}{3}$ = $\frac{1920}{3}$ = $640$
Question : Akham Lakshmi Devi, a recipient of the Sangeet Natak Akademi award, is renowned for which of the following dances?
Option 1: Kathak
Option 2: Odissi
Option 3: Sattriya
Option 4: Manipuri
Correct Answer: Manipuri
Solution : The correct option is Manipuri.
Akham Lakshmi Devi is renowned for the Manipuri dance form. She was a renowned Manipuri dancer and advocate, showcasing this traditional dance style from the northeastern state of Manipur. Akham Lakshmi Devi was conferred with the Sangeet Natak Akademi Award
Question : What will be the value of $\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$?
Option 1: $\frac{1}{\sqrt{2}}$
Option 2: $\sqrt{3}$
Option 3: $1$
Option 4: $\frac{1}{\sqrt{3}}$
Correct Answer: $1$
Solution : Given: $\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$ = $\frac{\sin (90^{\circ}-60^{\circ}) \sin (90^{\circ}-50^{\circ}) \sin (90^{\circ}-40^{\circ}) \sin (90^{\circ}-30^{\circ})}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$ = $\frac{\cos 60^{\circ} \cos 50^{\circ} \cos 40^{\circ} \cos 30^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos
Question : Which state of India has made rainwater harvesting compulsory for all houses?
Option 1: Haryana
Option 2: Maharashtra
Option 3: Tamil Nadu
Option 4: Punjab
Correct Answer: Tamil Nadu
Solution : The correct option is Tamil Nadu.
The first state in India that mandates rooftop rainwater harvesting systems for every home is Tamil Nadu. The act of collecting and storing rainwater as opposed to letting it run off is called rainwater harvesting. Rainwater is collected
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 $2\sec A$.
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