Since PQ = QR, ΔPQR is isosceles. The angles opposite the equal sides are equal, so ∠QRP = ∠QPR. Let each of these angles be x. Then, x + x + 100° = 180° (sum of angles in a triangle). Solving gives x = 40°.

Each letter in ‘FLIP’ is moved one step forward to get ‘GKPJ’. Similarly, in ‘TIME’, T->U, I->N, M->J, E->F, so ‘UNJF’.

Both arguments present strong and valid points. Argument 1 highlights a potential health benefit of a vegetarian diet, while Argument 2 points out a possible drawback. Both aspects are crucial for a balanced view on dietary choices.

The series alternates between increasing even numbers and subsequent letters. After 8G, the next term is 10I.

Let original length = l and breadth = b. New length = 1.1l, new breadth = 0.9b. New area = 1.1l * 0.9b = 0.99lb. Decrease = 0.01lb, which is a 1% decrease.

“Between you and me” is correct. “Between” is a preposition and should be followed by object pronouns, which in this case are “you” and “me.”

The Vedas, a large body of religious texts, were composed during the Vedic civilization. They form the oldest layer of Sanskrit literature and the oldest scriptures of Hinduism.

GST is an Indirect Tax which has replaced many Indirect Taxes in India. It is a comprehensive, multi-stage, destination-based tax.

Profit = 20% of Cost Price = 20/100 * 500 = ₹100. So, Selling Price = Cost Price + Profit = ₹500 + ₹100 = ₹600.

Let the sum invested at 6% be x. Then, the sum invested at 7% is ₹12,000 – x. The total income is 6% of x + 7% of (₹12,000 – x) = ₹800. Solving for x gives x = ₹6000.

“A new method to treat the disease has been discovered by scientists” is the correct passive form. The present perfect tense ‘have discovered’ becomes ‘has been discovered’ in the passive voice. Example: “A breakthrough in medical research has been achieved recently.”

Total of 9 numbers = 9 * 50 = 450. Total of first 5 numbers = 5 * 54 = 270. Total of last 3 numbers = 3 * 52 = 156. The 6th number = Total – (Sum of first 5 and last 3) = 450 – (270 + 156) = 24.

At 3:15, the hour and minute hands are at a 90-degree angle. If the hour hand at 3 points East, the minute hand at 15 minutes (or 3 on the clock) will point North.

‘Transparent’ is the odd one out as the other words are synonyms for ‘not clear’ or ‘difficult to see through’.

Speed of the second train = 400 km / 4 hrs = 100 km/hr. Using the ratio of speeds, 3:4, speed of the first train = 3/4 × 100 = 75 km/hr.

A’s 1 day’s work = 1/15, B’s 1 day’s work = 1/10. Work done by A and B in 2 days = 2 * (1/15 + 1/10) = 1/3. Remaining work = 1 – 1/3 = 2/3. B completes 1/10 of work in 1 day, so for 2/3 work, B will take 2/3 * 10 = 6.67 days, which is approximately 7 days.

“I had finished my homework when she called.” is correct. The past perfect tense is used to show that one action was completed before another in the past. In this sentence, ‘had finished’ indicates that the homework was completed before ‘she called’.

Greenland is the world’s largest island, located between the Arctic and Atlantic oceans. It is an autonomous territory within the Kingdom of Denmark.

The error is in “have.” “Many a” is followed by a singular noun and verb, so it should be “has.” Correct sentence: “Many a student has failed the exam due to lack of study.”

A is the brother of B, who is the sister of C. C, being the father of D, makes A the uncle of D.

The passage indicates that virtual reality technology has practical applications in education and healthcare, making “Both B and C” the correct answer.

“My bicycle was stolen by someone yesterday” is the correct passive form. The past simple tense ‘stole’ becomes ‘was stolen’ in the passive voice. Example: “The package was delivered by the courier this morning.”

A ‘Mixed Economy’ combines elements of both capitalism and socialism, featuring a mix of public and private ownership and control. India is an example of a mixed economy.

The pattern is the first letter decreasing by 1, the number increasing by 3, 4, 5, etc., and the last letter increasing by 3. So, after W17L, it is V23O.

Both arguments present valid points. Argument 1 focuses on promoting equality, while Argument 2 emphasizes personal freedom and expression. Both are important considerations in the debate over school uniforms.

India’s first Greenfield smart city, the Gujarat International Finance Tec-City (GIFT City), is being developed in Gujarat. It’s planned as a global financial and IT services hub.

A ‘Dam’ controls the flow of a ‘River’; similarly, a ‘Traffic Light’ controls the flow of ‘Traffic’.

The most direct inference is that the concert cannot be held outdoors due to heavy rainfall. This is a logical reaction to the weather condition affecting the scheduled outdoor event. The other options are broader inferences that are not directly supported by the given information.

The implicit assumption is that the health app’s challenge to encourage walking 10,000 steps daily will reduce the risk of heart disease among its users. This is based on the belief that the study’s findings can be effectively applied through the app’s challenge.

The HCF of two numbers divides both numbers completely. Since 12 is the HCF of 36 and ‘n’, ‘n’ must be a multiple of 12. Among the options, 48 is a multiple of 12 and when divided by 36, leaves 12 as HCF.

Perimeter of the circle = 2πr = 2 * 22/7 * 14 = 88 cm. Let the breadth of the rectangle be x cm. Then, length = 2x cm. Perimeter of rectangle = 2(x + 2x) = 6x cm. Equating, 6x = 88, x = 14.67 cm. Area = length * breadth = 2x * x ≈ 616 cm².

Since P is Q’s father and R’s son, and T is S’s (R’s husband) daughter, T is P’s sister, making Q her nephew.

“Heart of stone” is a metaphor as it equates one thing (heart) to another (stone) to imply hardness or lack of emotion.

The assumption is that CCTV cameras act as a deterrent to crime. The argument is based on the premise that the presence of CCTV cameras will reduce criminal activity.

“She decided to worry about the problem later, choosing to cross that bridge when she comes to it” is the correct usage. ‘Cross that bridge when you come to it’ means to deal with a problem if and when it becomes necessary, not before. Example: “We’ll figure out how to handle the negotiations when the time comes; we’ll cross that bridge when we come to it.”

Let the speed of the boat in still water be b km/hr and the speed of the stream be s km/hr. Upstream speed = b – s, Downstream speed = b + s. From the given equations, solve the two equations 30/(b-s) + 44/(b+s) = 10 and 40/(b-s) + 55/(b+s) = 13 to find b = 7 km/hr.

The Montreal Protocol was signed in 1987 and came into effect in 1989. It is an international treaty designed to protect the ozone layer by phasing out the production of substances believed to be responsible for ozone depletion, such as chlorofluorocarbons (CFCs). The protocol has been hailed as one of the most successful environmental agreements to date.

Let the numbers be x and y with x > y. x + y = 45 and x – y = 15. Adding these two equations, 2x = 60, giving x = 30. Therefore, y = 45 – 30 = 15. So, the numbers are 30 and 15.

The error is in “shows.” “Data” is a plural noun, so the verb should be “show.” Correct sentence: “The data from the experiments show that the hypothesis is correct.”

Each letter in ‘TRAIN’ is moved one position forward in the alphabet. Applying the same rule, ‘PLANE’ becomes ‘QMBOF’.

The sum of the numbers in the diagonal from the top left to the bottom right in any 3×3 grid with distinct numbers from 1 to 9 will always be 15 (for example, 1 + 5 + 9). This is because the middle number (5) is always included in this diagonal, and the remaining two numbers will always sum to 10.

Given 8% of x = 4% of y, or 0.08x = 0.04y. Solving for y, y = 2x. Hence, y is 50% of x.

The Right to Education Act (RTE) was enacted in 2009, making education a fundamental right for children aged 6 to 14 years. It mandates free and compulsory education for all children in this age group.

The Reserve Bank of India (RBI) was established on April 1, 1935, in accordance with the provisions of the Reserve Bank of India Act, 1934. It serves as the nation’s central bank and regulates the monetary policy of the Indian rupee.

The passage indicates that the internet has had multiple impacts: making information more accessible, transforming communication, and changing social interactions. Hence, “All of the above” is the correct option.

Speed = 80 km/hr = 80 * (1000/3600) m/s = 22.22 m/s. Distance covered in 9 seconds (length of train) = Speed * Time = 22.22 m/s * 9 s ≈ 200 meters.

Roll number B (5678) starts with ‘5’, fitting the criteria.

At 3:00, the hour hand is at 3 and the minute hand is at 12. In 15 minutes, the minute hand moves to 3, but the hour hand also moves 1/4 of the way between 3 and 4. The angle covered in one hour is 30°, so in 15 minutes, it’s 7.5°.

The ‘Ramsar Convention’, an international treaty for the conservation and sustainable use of wetlands, was established in 1971. This convention aims to protect and conserve wetlands of international importance, recognizing their value for biodiversity, flood control, water purification, and as habitats for a variety of flora and fauna. Signatory countries commit to maintaining the ecological character of their designated wetlands and to planning for their wise use and management.

The correct passive form is “The problem will be solved by someone,” maintaining the future tense and passive voice structure.