Your Answer : (Not Answered)

Correct Answer : C

The selling price is ₹ 378. After the discount of \(x\)% and then 15%: \[ \begin{aligned} 450\times\left(1-\tfrac{x}{100}\right) &= \frac{351.90}{0.85} \\ &= 414 \end{aligned} \] \[ 1-\frac{x}{100} = \frac{351.90}{382.50} = 0.92 \] so \(x = 8\). A single discount of \(2x = 16\)% on the marked price gives \[ 450\times 0.84 = 378 \] ₹ 360 would be a 20% discount, ₹ 382.50 is only the 15% discount without the other, and ₹ 387.50 is not a whole-number discount of 450; only 378 matches.

Your Answer : (Not Answered)

Correct Answer : B

The mean is a linear function of the data, so multiplying every observation by 3 multiplies the mean by 3.

\[ \frac{\sum 3x_{i}}{n} = 3 \times \frac{\sum x_{i}}{n} \]

The variance, by contrast, would be multiplied by 9.

Your Answer : (Not Answered)

Correct Answer : B

This is a fundamental Pythagorean identity, derived by dividing \(\sin^2 A + \cos^2 A = 1\) by \(\sin^2 A\).

\(\frac{\sin^2 A}{\sin^2 A} + \frac{\cos^2 A}{\sin^2 A} = \frac{1}{\sin^2 A}\)

\(1 + \cot^2 A = \csc^2 A\).

Your Answer : (Not Answered)

Correct Answer : B

Correct answer: ₹30.60

The banker’s gain is the simple interest on the true discount, which gives the standard relation \[ \text{BG} = \frac{\text{TD}^{2}}{\text{PW}}. \] Substituting, \[ \text{BG} = \frac{30^{2}}{1500} = \frac{900}{1500} = 0.60. \] The banker’s discount then follows from \( \text{BD} = \text{TD} + \text{BG} \): \[ \text{BD} = 30 + 0.60 = 30.60. \] The relationships worth holding together are these. True discount is the interest on the present worth; banker’s discount is the interest on the face value, which is larger; and the banker’s gain is the difference between them, which is why BD always exceeds TD. The trap is to treat BD as equal to TD, which the small size of BG makes tempting on figures like these.

Your Answer : (Not Answered)

Correct Answer : C

Simple interest is reckoned on the amount, true discount on the present worth. Both use the same \( \dfrac{RT}{100} \), so

\[ \text{SI} = A \times \frac{RT}{100}, \qquad \text{TD} = \text{PW} \times \frac{RT}{100} = (A - \text{TD}) \times \frac{RT}{100} \]

Dividing one by the other:

\[ \frac{\text{SI}}{\text{TD}} = \frac{A}{A - \text{TD}} \quad\Longrightarrow\quad \frac{85}{80} = \frac{A}{A - 80} \]

\[ 85A - 6800 = 80A \quad\Longrightarrow\quad 5A = 6800 \quad\Longrightarrow\quad A = 1360 \]

The shortcut worth remembering is

\[ \text{Sum} = \frac{\text{SI} \times \text{TD}}{\text{SI} - \text{TD}} = \frac{85 \times 80}{5} = 1360 \]

Your Answer : (Not Answered)

Correct Answer : A

Each coin can land in 2 ways, and the ten coins are independent.

\[ 2^{10} = 1024 \]

The rule is \( 2^{n} \) for \( n \) coins - not \( 2n \), which would give only 20.

Your Answer : (Not Answered)

Correct Answer : C

The person exactly between T and Q is S.

Placing the seven gives the line, from left to right, W T S Q P V R. Put T in place p; then W is p − 1, Q is p + 2 and V is p + 4. V cannot be at an end, so p + 4 is at most 6, and W needs p of at least 2, so p = 2: W 1, T 2, Q 4, V 6. R is not next to Q, so R is not in 3 or 5 and takes 7. S is not next to V, so S is not in 5 or 7 and takes 3. P takes 5.

T is in place 2 and Q is in place 4, so the one between them is in place 3, which is S. W, R and P are not in place 3.

Your Answer : (Not Answered)

Correct Answer : E

Clearly, treatment of addiction requires personal attention as the first step. So, I is implicit. Also, since intimacy and personal attention are required to treat addicts, it implies that addiction arises out of frustration due to strained relationships. So, II is also implicit.

Your Answer : (Not Answered)

Correct Answer : E

The correct order is :

So, The lecture on Leadership is on Thursday.

Your Answer : (Not Answered)

Correct Answer : A

A mirror always reflects.

A mirror is a smooth, highly polished surface whose essential property is to reflect light, so that images are formed. Every mirror, plane, concave or convex, works by reflection.

Refraction, the bending of light as it passes from one medium into another, is how lenses work. Distortion happens only with curved or uneven mirrors, not always, and 'retracts' has nothing to do with light.

Your Answer : (Not Answered)

Correct Answer : D

If D is Male, the answer is Nephew.

If D is Female, the answer is Niece.

As the sex of D is not known, hence, the relation between D and A cannot be determined.

Note: Niece - A daughter of one's brother or sister, or of one's brother-in-law or sister-in-law. Nephew - A son of one's brother or sister, or of one's brother-in-law or sister-in-law.

Your Answer : (Not Answered)

Correct Answer : C

Vivek Sagar Prasad is associated with Hockey.

Vivek Sagar Prasad, from Itarsi in Narmadapuram (Hoshangabad) district, is a midfielder in the Indian men's hockey team. He was part of the team that won the bronze medal at the Tokyo Olympics in 2021, and he trained at the Madhya Pradesh Hockey Academy.

Shooting, archery and cricket are not his sport, so those options are wrong.

Your Answer : (Not Answered)

Correct Answer : B

The Chartered Accountants Act was enacted in 1949.

It established the Institute of Chartered Accountants of India as a statutory body to regulate the profession, hold examinations, maintain the register and enforce professional discipline.

Your Answer : (Not Answered)

Correct Answer : B

The wrong statement is that in oomycetes the female gamete is smaller and motile while the male is larger and non-motile - it is exactly the other way round.

In oogamy, which the oomycetes show, the female gamete is the larger and non-motile one and the male the small motile one.

Your Answer : (Not Answered)

Correct Answer : C

The Child Marriage Restraint Act was enacted in 1929.

Known as the Sarda Act after its sponsor Harbilas Sarda, it set the minimum age of marriage at 14 for girls and 18 for boys. Those ages were later raised to 18 and 21, and the Act was replaced in 2006.

Your Answer : (Not Answered)

Correct Answer : C

Formaldehyde among the ozonolysis products confirms a vinyl group.

Ozonolysis cleaves a double bond and gives a carbonyl compound from each end. A terminal \(\mathrm{=CH_2}\) is the only fragment that can yield \(\mathrm{HCHO}\), so the compound must contain \(\mathrm{CH_2{=}CH-}\).

Your Answer : (Not Answered)

Correct Answer : C

Newton stated three laws of motion.

The first defines inertia, the second gives \(F = ma\) as the rate of change of momentum, and the third states that action and reaction are equal and opposite. Together they are the foundation of classical mechanics.

Your Answer : (Not Answered)

Correct Answer : A

Venus Williams won her fifth Olympic tennis medal at Rio in 2016, taking silver in the mixed doubles.

She had won four golds before that - singles and doubles at Sydney in 2000, and doubles at Beijing and London. The total equals the record for the sport.

Your Answer : (Not Answered)

Correct Answer : A

Hillary Clinton was appointed Secretary of State by Barack Obama.

She served from 2009 to 2013, having been a Senator from New York and Obama's rival for the Democratic nomination in 2008. Condoleezza Rice was her predecessor under George W. Bush.

Your Answer : (Not Answered)

Correct Answer : D

Correct answer: 1986

The Nilgiri Biosphere Reserve was established in 1986, the first in India, and covers parts of Tamil Nadu, Kerala and Karnataka. It includes Bandipur, Nagarhole, Mudumalai and Wayanad, along with Silent Valley and Mukurthi National Parks. A biosphere reserve under the UNESCO Man and the Biosphere Programme is zoned rather than uniformly protected: a strictly guarded core, a buffer permitting research and limited use, and a transition area where communities live and work. The design is intended to reconcile conservation with human use rather than exclude one for the other. The reserve holds the largest population of Asian elephants in India, along with tigers, gaur and the endemic Nilgiri tahr and lion-tailed macaque. India now has a substantial number of biosphere reserves, of which several are also recognised internationally by UNESCO. The distinction from a national park or wildlife sanctuary is that those are legal categories under Indian wildlife law, whereas a biosphere reserve is a management designation that may contain them.