Explanation:

In a parallelogram, adjacent angles are supplementary and opposite angles are equal. If one angle is 90°, then all angles become 90°, making it a rectangle. If all sides are equal, the parallelogram is a rhombus.

A quadrilateral that is both a rectangle (all angles 90°) and a rhombus (all sides equal) is a square. Therefore, the figure described is a square.

Explanation:

A line meets the x-axis where y = 0. Substitute y = 0 into 2x + 5y = 10: 2x = 10 ⇒ x = 5.

Hence, the x-intercept is (5, 0), which is Option 3. (0, 2) is the y-intercept; (2, 1) and (5/2, 2) do not satisfy the equation.

Explanation:

Option 2 is correct.
– Proximity: The propinquity effect shows we are more likely to choose to communicate with those who are physically or socially close because repeated contact increases familiarity and opportunity.
– Utility: Social exchange and predicted outcome value perspectives explain that we select partners expected to offer rewards (information, support, resources), i.e., high utility.
– Loneliness: The need to belong/affiliation motive drives people to seek interaction to reduce loneliness, shaping whom they approach.
Elimination of other options:
– Secrecy, dissonance, deception (Options 1 and 3) are interaction tactics or cognitive states, not primary determinants of initial partner choice.
– Dissimilarity and deviance (Option 4) generally deter selection; dissonance is not a standard selection criterion.
Therefore, Proximity, Utility, and Loneliness best capture recognized drivers of choosing communication partners.

Explanation:

Simple interest: SI = P*r*t/100 = 1200 with r = 5% and t = 3, so P = 1200*100/(5*3) = 8000.

Compound interest for 3 years at 5%: CI = P[(1 + 0.05)^3 – 1] = 8000[(1.157625) – 1] = 8000*0.157625 = 1261.

Alternatively, CI – SI for 3 years = P[3(r/100)^2 + (r/100)^3] = 8000[3*0.0025 + 0.000125] = 61; hence CI = 1200 + 61 = 1261.

Explanation:

Let the numbers be 3k and 5k. After increasing each by 10, the ratio becomes 5:7.

So, (3k + 10)/(5k + 10) = 5/7 ⇒ 7(3k + 10) = 5(5k + 10) ⇒ 21k + 70 = 25k + 50 ⇒ 20 = 4k ⇒ k = 5.

Thus, the numbers are 3k = 15 and 5k = 25, which matches Option 4.

Explanation:

Let the daughter’s present age be D years. Then the mother’s present age is 3D.
After 12 years: mother’s age = 3D + 12, daughter’s age = D + 12.
Given: 3D + 12 = 2(D + 12)
=> 3D + 12 = 2D + 24
=> D = 12.
Check: Mother now = 36; after 12 years, 48; daughter after 12 years, 24; 48 = 2 × 24. Hence, the daughter’s present age is 12 years.

Explanation:

A handshake involves an unordered pair of people. With 11 friends, the number of unique pairs is C(11,2) = 11*10/2 = 55.

Alternatively, if each person shakes hands with 10 others, the naive count 11*10 double-counts each handshake, so divide by 2 to get 55.

Explanation:

Let the total work be 1 trench. A’s rate = 1/12 trench/hour. Together (A+B) rate = 1/8 trench/hour.

Therefore, B’s rate = 1/8 − 1/12 = (3−2)/24 = 1/24 trench/hour.

Time taken by B alone = 1 ÷ (1/24) = 24 hours.

Explanation:

Let S = scientists and P = philosophers. The premise “No scientists are philosophers” means S ∩ P = ∅, equivalently All S are non-P.

Evaluate options:
– Option 2: “Some philosophers are scientists” asserts P ∩ S ≠ ∅, directly contradicting the premise. False.
– Option 4: “All scientists are philosophers” says S ⊆ P, the opposite of the premise (which says S ⊆ non-P). False.
– Option 3: “No non-philosophers are scientists” means non-P ∩ S = ∅, i.e., S ⊆ P (again, the exact opposite). False.
– Option 1: “Some non-philosophers are not non-scientists” simplifies to “Some non-P are S” (since not non-scientists = scientists), i.e., Some S are non-P. This is consistent with the premise (indeed, it follows if at least one scientist exists). It is the only option compatible with the given statement.

Therefore, Option 1 is true.

Explanation:

Let the speaker be M. He says, “I have no brother and sister,” meaning he has no siblings (only child). He also says, “the father of that man is the son of my father.” Since M has no siblings, “the son of my father” can only be M himself.

Therefore, the father of the man in the photograph is M, implying the photograph is of M’s son.