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Question : In trapezium $ABCD$, $AB \parallel CD$ and $AB = 2CD$. Its diagonals intersect at $O$. If the area of $\triangle AOB=84\;\mathrm{cm^2}$ then the area of $\triangle COD$ is equal to:
Option 1: 72 cm2
Option 2: 21 cm2
Option 3: 42 cm2
Option 4: 26 cm2
Correct Answer: 21 cm2
Solution :
In trapezium $ABCD$, $AB \parallel CD, AB = 2CD$ and area of $\Delta AOB=84\;\mathrm{cm^2}$. In $\triangle AOB$ and $\triangle COD$, $\angle AOB=\angle COD$ (Vertically opposite angles) $\angle ABO=\angle CDO$ (Alternate angles) $\angle BAO=\angle DCO$ (Alternate angles) So, $\triangle AOB\sim\triangle COD$ Using the theorem,
Question : Reserve Bank of India was nationalised in:
Option 1: 1947
Option 2: 1948
Option 3: 1949
Option 4: 1951
Correct Answer: 1949
Solution : The correct answer is 1949.
RBI was established under the Reserve Bank of India Act 1934. It was established on the recommendation of Hilton Young Commission also known as Royal Commission on Indian Currency and Finance. It was nationalised on 1st January 1949 on the
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 number.
Marriages, birthday celebrations, meetings, conferences, seminars and many similar events layout (1) ________multi-course feasts with plenty of starters followed by the main course. Later, (2) __________of food get dumped into dustbins, (3) __________of its value to the hungry poor. Most such gatherings serve buffets. The (4) _________of food wastage is more when people help themselves. They (5). ____________more than what they can eat only to waste the (6) ________Similar wastage is seen when hotels serve (7) _________breakfast buffets. Wherever food is free and (8) _________plenty, people take more. Those fortunate to have (9) __________food forget the plight of those who do not have (10) __________to eat. Millions of people die of malnutrition and hunger in India.
Question: Select the most appropriate option to fill in the blank No. 8.
Option 1: for
Option 2: in
Option 3: by
Option 4: of
Correct Answer: in
Solution : The correct choice is the second option.
Explanation: The preposition "in" is used to indicate a situation or condition, and in this context, it appropriately connects the idea that food is free with its abundance during events and gatherings.
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.
Many forests are cleared to (1)____ way for palm oil plantations. Palm oil is the most (2) ____produced vegetable oil and is found in half of all supermarket products. It's cheap, versatile and can be added to (3)_____ food and personal products like lipstick and shampoo. (4) _____popularity has (5)______ people to clear tropical forests to grow more palm trees.
Question
Select the most appropriate option to fill in the blank number 2.
Option 1: commonly
Option 2: casually
Option 3: lovingly
Option 4: usually
Correct Answer: commonly
Solution : The right choice is the first option.
Explanation: The word "commonly" is used to convey that palm oil is the most frequently or commonly produced vegetable oil. It indicates that palm oil is widely and regularly produced among various vegetable oils. In the context
Question : In a circle with a centre at O(0,0) and a radius of 5 cm, AB is a chord of length 8 cm. If OM is perpendicular to AB, then the length of OM is:
Option 1: 2.5 cm
Option 2: 3 cm
Option 3: 4 cm
Option 4: 1 cm
Correct Answer: 3 cm
Solution : Given , AB = 8 cm We know that the perpendicular from the centre of a circle to a chord bisects the chord. AM = MB = $\frac{1}{2}×8=4$ cm OA = 5 cm From ∆ AOM, OA2 = OM2 + AM2
Question : Select the most appropriate ANTONYM of the given word. voluntary
Option 1: discretional
Option 2: optional
Option 3: mandatory
Option 4: uncompelled
Correct Answer: mandatory
Solution : The correct choice is the third option.
Explanation: "Voluntary" implies an action or decision made willingly, without coercion or external pressure. To find an antonym, we should look for a term that denotes actions or situations that are obligatory or required. "Mandatory" fits this
Question : Which is greater $\sqrt[3]{2}$ or $\sqrt{3}$?
Option 1: Cannot be compared.
Option 2: $\sqrt[3]{2}$
Option 3: $\sqrt{3}$
Option 4: Both are equal.
Correct Answer: $\sqrt{3}$
Solution : Taking LCM of the given indices i.e., LCM of 2 and 3 is 6. $\Rightarrow \sqrt[3]{2}=2^\frac{1}{3}=2^\frac{2}{6}=\sqrt[6]{2^2}=\sqrt[6]{4}$ $\Rightarrow \sqrt{3}=3^\frac{1}{2}=3^\frac{3}{6}=\sqrt[6]{3^3}=\sqrt[6]{27}$ Thus, $\sqrt{3}$ is greater. Hence, the correct answer is $\sqrt{3}$.
Question : Identify whether the given statements about p-block elements are correct or incorrect.
Statement A: In p-block elements, the last electron enters the outermost p orbital.
Statement B: The non-metals and metalloids exist only in the p-block of the periodic table.
Option 1: Both Statements A and B are correct.
Option 2: Only Statement A is correct.
Option 3: Both Statements A and B are incorrect.
Option 4: Only Statement B is correct.
Correct Answer: Both Statements A and B are correct.
Solution : The correct option is Both Statements A and B are correct.
In p-block elements, the last electron is added to the outermost p orbital. The p-block includes elements whose outermost electrons are in the p subshell.
Non-metals and
Question : An article is marked at 100% above its cost price. After allowing two successive discounts of 5% and 20% respectively on the marked price, it is sold at $x$% profit. What is the value of $x$?
Option 1: 48
Option 2: 75
Option 3: 72
Option 4: 52
Correct Answer: 52
Solution : Given: An article is marked at 100% above its cost price. After allowing two successive discounts of 5% and 20% respectively on the marked price, it is sold at $x$% profit. Use the formula, Profit percentage = $\frac{\text{SP – CP}}{\text{CP}}\times 100$, where $SP$, $CP$ are
Question : The sum of all prime numbers between 58 and 68 is:
Option 1: 179
Option 2: 178
Option 3: 187
Option 4: 183
Correct Answer: 187
Solution : List of all the prime numbers between 58 and 68 = 59, 61 and 67 Now, (59 + 61 + 67) = 187 Hence, the correct answer is 187.
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