AP POLYCET 2021 Set B Question Paper with Answer Key PDFs (September 1)

Step 1: Concept

Determine \(\theta\) from the given sine value for an acute angle.

Step 2: Meaning

Since \(\sin\theta = 1/2\), then \(\theta = 30^\circ\).

Step 3: Analysis

Calculate \(\sin 2\theta = \sin(2 \times 30^\circ) = \sin 60^\circ\).

Step 4: Conclusion

The value of \(\sin 60^\circ\) is \(\sqrt{3}/2\).


Final Answer: (2) Quick Tip: \(\sin 2\theta = 2\sin\theta\cos\theta\). Since \(\sin\theta=1/2\), \(\cos\theta=\sqrt{3}/2\), so \(2(1/2)(\sqrt{3}/2) = \sqrt{3}/2\).

Step 1: Concept

Trigonometric identity where sine and cosine values are equal.

Step 2: Meaning

Divide both sides by \(\cos\alpha\) to get \(\tan\alpha = 1\).

Step 3: Analysis

The angle \(\alpha\) for which \(\tan\alpha = 1\) in the first quadrant is \(45^\circ\).

Step 4: Conclusion

Hence, \(\alpha = 45^\circ\).


Final Answer: (2) Quick Tip: At \(45^\circ\), both \(\sin\) and \(\cos\) are \(1/\sqrt{2}\).

Step 1: Concept

Use the tangent ratio: \(\tan\theta = Opposite / Adjacent\).

Step 2: Meaning
\(\tan\theta = h / (\sqrt{3}h)\).

Step 3: Analysis
\(\tan\theta = 1/\sqrt{3}\).

Step 4: Conclusion
\(\theta = \arctan(1/\sqrt{3}) = 30^\circ\).


Final Answer: (2) Quick Tip: Shadow longer than height (\(\sqrt{3} \approx 1.732\)) means the angle is less than \(45^\circ\).

Step 1: Concept

A non-leap year has 365 days.

Step 2: Meaning

365 days = 52 weeks + 1 extra day.

Step 3: Analysis

To have 53 Thursdays, the one extra day must be a Thursday. Total possible days for the extra day are 7.

Step 4: Conclusion

Probability = \(1/7\).


Final Answer: (2) Quick Tip: Non-leap year extra days = 1 (Prob = 1/7); Leap year extra days = 2 (Prob = 2/7).

Step 1: Concept

Probability \(P(E) = Favorable outcomes / Total outcomes\).

Step 2: Meaning

Total balls = 4 (Black) + 6 (Red) = 10.

Step 3: Analysis

Favorable outcomes (Red balls) = 6. Probability = \(6/10\).

Step 4: Conclusion

Simplified fraction = \(3/5\).


Final Answer: (2) Quick Tip: Always simplify the fraction: \(6/10 = 3/5\).

Step 1: Concept

Definition of mutually exclusive events.

Step 2: Meaning

Events that cannot happen at the same time.

Step 3: Analysis

If they cannot occur together, their intersection is the null set.

Step 4: Conclusion
\(E_1 \cap E_2 = \phi\).


Final Answer: (3) Quick Tip: Mutually exclusive \(\implies\) Intersection is empty (\(\phi\)).

Step 1: Concept

Total outcomes for \(n\) coins is \(2^n\).

Step 2: Meaning

Here \(n = 3\).

Step 3: Analysis
\(2^3 = 2 \times 2 \times 2 = 8\).

Step 4: Conclusion

Total outcomes are 8.


Final Answer: (4) Quick Tip: Outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

Step 1: Concept

Standard formula for Median in statistics.

Step 2: Meaning
\(L\) = Lower limit, \(N\) = Total frequency, \(F\) = Cumulative frequency of preceding class, \(f\) = frequency, \(C\) = Class width.

Step 3: Analysis

Option 1 matches the standard mathematical definition.

Step 4: Conclusion

Correct formula is \(L + \left(\frac{\frac{N}{2}-F}{f}\right) \times C\).


Final Answer: (1) Quick Tip: The sign is always '+' and we subtract the cumulative frequency '\(F\)'.

Step 1: Concept

Mode is the value that appears most frequently in a data set.

Step 2: Meaning

Observe the frequency of each number.

Step 3: Analysis

Each number (1, 2, 3, 8, 10, 11, 16) appears exactly once.

Step 4: Conclusion

Since no number repeats, there is no mode.


Final Answer: (4) Quick Tip: If all values occur with the same frequency, the data is "amodal" (no mode).

Step 1: Concept

Mean = Sum of terms / Number of terms.

Step 2: Meaning

Sum = \((a-3d) + (a-d) + (a+d) + (a+3d)\).

Step 3: Analysis

Sum = \(a + a + a + a - 3d - d + d + 3d = 4a\). Mean = \(4a / 4\).

Step 4: Conclusion

Arithmetic Mean = \(a\).


Final Answer: (1) Quick Tip: Symmetric terms around 'a' always result in a mean of 'a'.

Step 1: Concept

Measures of central tendency represent the center of a data set.

Step 2: Meaning

Mean, Median, and Mode are the three standard measures used to find the center.

Step 3: Analysis

Range is a measure of dispersion or spread, not central tendency.

Step 4: Conclusion

Hence, Range is the odd one out.


Final Answer: (3) Quick Tip: Central Tendency = Center; Dispersion (Range, SD) = Spread.

Step 1: Concept

Formula: \(Product of two numbers = HCF \times LCM\).

Step 2: Meaning
\(30 = 5 \times LCM\).

Step 3: Analysis
\(LCM = 30 / 5\).

Step 4: Conclusion
\(LCM = 6\).


Final Answer: (2) Quick Tip: \(LCM = \frac{Product}{HCF}\).

Step 1: Concept

Composite numbers have more than two factors.

Step 2: Meaning

Check odd numbers: 3 (Prime), 5 (Prime), 7 (Prime), 9 (Composite: 1, 3, 9).

Step 3: Analysis

9 is the first odd number that is not prime.

Step 4: Conclusion

The smallest odd composite number is 9.


Final Answer: (4) Quick Tip: 1 is neither prime nor composite. 2 is the only even prime.

Step 1: Concept

Rational numbers can be written as \(p/q\).

Step 2: Meaning
\(\sqrt{2}\) cannot be expressed as a simple fraction and has a non-terminating, non-repeating decimal.

Step 3: Analysis

Any square root of a non-square natural number is irrational.

Step 4: Conclusion
\(\sqrt{2}\) is irrational.


Final Answer: (2) Quick Tip: \(\pi\) and \(\sqrt{non-square}\) are always irrational.

Step 1: Concept

Convert log to exponential form: \(\log_{a}b = c \implies a^{c} = b\).

Step 2: Meaning
\(3^{2} = x^{2}\).

Step 3: Analysis
\(9 = x^{2}\).

Step 4: Conclusion
\(x = \sqrt{9} = 3\) (Note: base/argument constraints usually imply positive \(x\)).


Final Answer: (3) Quick Tip: \(\log_b a^n = n \log_b a\). So \(2 \log_3 x = 2 \implies \log_3 x = 1 \implies x=3\).

Step 1: Concept

Prime numbers are greater than 1 with exactly two factors.

Step 2: Meaning

List primes: 2, 3, 5, 7, 11...

Step 3: Analysis

2 is the only number in the list that is even.

Step 4: Conclusion

The set is \{2\.


Final Answer: (4) Quick Tip: 2 is the unique even prime number.

Step 1: Concept

Intersection (\(\cap\)) gives the common elements.

Step 2: Meaning

If the intersection of \(A\) and \(B\) is exactly \(B\), it means all elements of \(B\) are inside \(A\).

Step 3: Analysis

By definition, if every element of \(B\) is in \(A\), then \(B\) is a subset of \(A\).

Step 4: Conclusion
\(B \subset A\).


Final Answer: (2) Quick Tip: \(A \cap B = Smaller set\); \(A \cup B = Larger set\).

Step 1: Concept

A finite set has a countable/limited number of elements.

Step 2: Meaning

Natural numbers and prime numbers go on forever (infinite).

Step 3: Analysis

There are exactly 12 months in a year.

Step 4: Conclusion

Option 3 is finite.


Final Answer: (3) Quick Tip: If you can finish counting the elements, it's finite.

Step 1: Concept

A polynomial of degree \(n\) has at most \(n\) zeroes.

Step 2: Meaning

"Biquadratic" refers to a polynomial of degree 4.

Step 3: Analysis

Degree 4 \(\implies\) maximum 4 zeroes.

Step 4: Conclusion

Maximum zeroes = 4.


Final Answer: (4) Quick Tip: Linear (1), Quadratic (2), Cubic (3), Biquadratic (4).

Step 1: Concept

For \(ax^2 + bx + c\), product of zeroes = \(c/a\).

Step 2: Meaning

Rewrite the polynomial: \(2x^2 + 1x + 1\). Here \(a=2, b=1, c=1\).

Step 3: Analysis

Product = \(1/2\).

Step 4: Conclusion

The product is 1/2.


Final Answer: (4) Quick Tip: Always arrange in descending powers of \(x\) to identify '\(a\)' correctly.

Step 1: Concept

Find values of \(x\) that make the polynomial zero.

Step 2: Meaning

Set \(x^3 - x^2 = 0\).

Step 3: Analysis

Factorize: \(x^2(x - 1) = 0\). This gives \(x^2 = 0\) or \(x - 1 = 0\).

Step 4: Conclusion
\(x = 0, 0\) and \(x = 1\).


Final Answer: (1) Quick Tip: The degree is 3, so there must be 3 zeroes (including repetitions).

Step 1: Concept

Standard form of a quadratic equation using its roots.

Step 2: Meaning

A polynomial is formed as \(k[x^2 - (sum of zeroes)x + (product of zeroes)]\).

Step 3: Analysis

Sum = \(\alpha + \beta\); Product = \(\alpha\beta\).

Step 4: Conclusion

The expression is \(x^2 - (\alpha + \beta)x + \alpha\beta\).


Final Answer: (1) Quick Tip: Remember the minus sign before the sum of zeroes.

Step 1: Concept

Nature of solutions for a linear equation in two variables.

Step 2: Meaning

The equation represents a straight line on a graph.

Step 3: Analysis

For every value of \(x\), there is a corresponding value of \(y\).

Step 4: Conclusion

Since a line consists of infinite points, there are infinitely many solutions.


Final Answer: (4) Quick Tip: A single linear equation with two variables always has infinite solutions.

Step 1: Concept

Solving a linear equation in one variable.

Step 2: Meaning

Isolate the variable \(x\).

Step 3: Analysis
\(ax = -b\).

Step 4: Conclusion
\(x = -b/a\).


Final Answer: (4) Quick Tip: The zero of a linear polynomial \(ax+b\) is always \(-b/a\).

Step 1: Concept

A linear equation has variables with a maximum power (degree) of 1.

Step 2: Meaning

Check the degree of each equation.

Step 3: Analysis

In option 4, the term \(x^2\) appears, making it a quadratic equation.

Step 4: Conclusion

Option 4 is not linear.


Final Answer: (4) Quick Tip: Linear = Degree 1. Quadratic = Degree 2.

Step 1: Concept

Translating a word problem into an algebraic equation.

Step 2: Meaning

Let price of an apple be \(x\) and price of an orange be \(y\).

Step 3: Analysis

Siri's cost: \(5x + 6y\). Laxmi's cost: \(2x + 15y\).

Step 4: Conclusion

Since the total money is the same: \(5x + 6y = 2x + 15y\).


Final Answer: (1) Quick Tip: "Same amount" indicates the use of the '=' sign between the two costs.

Step 1: Concept

A quadratic equation must have the form \(ax^2 + bx + c = 0\) (\(a \neq 0\)).

Step 2: Meaning

Simplify each option to see if the \(x^2\) term remains.

Step 3: Analysis

(1) \(x^2 + 4x - 12 = 0\) (Quadratic). (2) \(x^2 + 4x = x^2 + 2x + 1 \implies 2x - 1 = 0\) (Linear).

Step 4: Conclusion

Only option 1 remains a second-degree equation.


Final Answer: (1) Quick Tip: Check if the \(x^2\) terms cancel out on both sides before deciding.

Step 1: Concept

Classification of equations based on degree.

Step 2: Meaning

A polynomial of degree 2 is known as a quadratic polynomial.

Step 3: Analysis

When set to zero, it forms a quadratic equation.

Step 4: Conclusion

The answer is quadratic equation.


Final Answer: (3) Quick Tip: Degree 1 = Linear; Degree 2 = Quadratic; Degree 3 = Cubic.

Step 1: Concept

Modeling integer relations.

Step 2: Meaning

Let \(x\) be the first integer. The consecutive integer is \(x + 1\).

Step 3: Analysis

Product = \(x(x + 1) = x^2 + x\). Setting product equal to 306 gives \(x^2 + x - 306 = 0\).

Step 4: Conclusion

This matches the provided equation.


Final Answer: (2) Quick Tip: \(x(x+1)\) expanded is \(x^2 + x\).

Step 1: Concept

The degree of an equation is the highest power of the variable after simplification.

Step 2: Meaning

Expand and simplify the equation.

Step 3: Analysis

LHS: \(x^4 + x^3 + x^2\). RHS: \(x^4 + x^3 - x^2 + 3x - 1\).

Subtracting \(x^4 + x^3\) from both sides: \(x^2 = -x^2 + 3x - 1 \implies 2x^2 - 3x + 1 = 0\).

Step 4: Conclusion

The highest power remaining is 2.


Final Answer: (2) Quick Tip: Don't assume the degree is the highest visible power; always simplify first!

Step 1: Concept

In an Arithmetic Progression (AP), the middle term is the arithmetic mean of the surrounding terms.

Step 2: Meaning

For terms \(a, b, c\), the relation is \(b = (a + c) / 2\).

Step 3: Analysis
\(x = (18 + 36) / 2 = 54 / 2\).

Step 4: Conclusion
\(x = 27\).


Final Answer: (3) Quick Tip: Arithmetic Mean = Sum / 2.

Step 1: Concept

Definition of common difference in AP.

Step 2: Meaning
\(b - a = c - b\).

Step 3: Analysis

Rearranging the terms: \(b + b = a + c\).

Step 4: Conclusion
\(2b = a + c\).


Final Answer: (2) Quick Tip: The sum of extremes equals twice the mean.

Step 1: Concept

Common difference \(d = a_2 - a_1\).

Step 2: Meaning

Subtract the first term from the second term.

Step 3: Analysis
\(d = 806 - 781\).

Step 4: Conclusion
\(d = 25\).


Final Answer: (3) Quick Tip: \(d\) is constant throughout the sequence.

Step 1: Concept

Use the properties of mean and product.

Step 2: Meaning

Mean = 10 \(\implies\) Sum = 20. Product = 91.

Step 3: Analysis

We need two numbers that add to 20 and multiply to 91. \(13 + 7 = 20\) and \(13 \times 7 = 91\).

Step 4: Conclusion

The numbers are 13 and 7.


Final Answer: (3) Quick Tip: Check options: \(13 \times 7\) is the only one ending in 1.

Step 1: Concept

Properties of a triangle's centroid.

Step 2: Meaning

The centroid is the point of concurrency of medians.

Step 3: Analysis

The distance from the vertex to the centroid is twice the distance from the centroid to the midpoint.

Step 4: Conclusion

The ratio is 2 : 1.


Final Answer: (2) Quick Tip: Vertex to Centroid : Centroid to Side = 2 : 1.

Step 1: Concept

Centroid formula: \(((x_1+x_2+x_3)/3, (y_1+y_2+y_3)/3)\).

Step 2: Meaning
\((a+b+c)/3 = 0 \implies a+b+c = 0\).

Step 3: Analysis

Algebraic identity: If \(a+b+c = 0\), then \(a^3 + b^3 + c^3 = 3abc\).

Step 4: Conclusion

The value is 3abc.


Final Answer: (4) Quick Tip: If sum of three numbers is zero, the sum of their cubes is \(3 \times\) their product.

Step 1: Concept

Diagonals of a parallelogram bisect each other.

Step 2: Meaning

The intersection point is the midpoint of either diagonal.

Step 3: Analysis

Midpoint of diagonal joining (2, -3) and (-2, 1): \(((2-2)/2, (-3+1)/2) = (0, -1)\).

Step 4: Conclusion

The intersection point is (0, -1).


Final Answer: (1) Quick Tip: Intersection = Midpoint of \((x_1, y_1)\) and \((x_3, y_3)\).

Step 1: Concept

Distance formula: \(\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\).

Step 2: Meaning

Points are on the Y-axis.

Step 3: Analysis

Distance = \(|a - (-a)| = |2a|\).

Step 4: Conclusion

Distance is 2a.


Final Answer: (2) Quick Tip: Distance on an axis is the absolute difference of coordinates.

Step 1: Concept

Apply Pythagoras theorem.

Step 2: Meaning

Horizontal distance = 12 m. Vertical height difference = \(11 - 6 = 5\) m.

Step 3: Analysis
\(Distance^2 = 12^2 + 5^2 = 144 + 25 = 169\).

Step 4: Conclusion
\(\sqrt{169} = 13\) m.


Final Answer: (3) Quick Tip: (5, 12, 13) is a standard Pythagorean triplet.

Step 1: Concept

Corresponding angles of similar triangles are equal.

Step 2: Meaning
\(\angle P = \angle A = 50^\circ\).

Step 3: Analysis

In \(\triangle PQR\), sum of angles = \(180^\circ\). \(\angle P + \angle Q + \angle R = 180^\circ\).

Step 4: Conclusion
\(\angle Q + \angle R = 180^\circ - 50^\circ = 130^\circ\).


Final Answer: (1) Quick Tip: Sum of remaining two angles = \(180^\circ - given angle\).

Step 1: Concept

Definition of points of concurrency in a triangle.

Step 2: Meaning

The circumcentre is the center of the circle that passes through all vertices.

Step 3: Analysis

Since it is the center of the circumcircle, the distance to each vertex is the radius (\(R\)).

Step 4: Conclusion

Thus, the circumcentre is equidistant from all vertices.


Final Answer: (4) Quick Tip: Circumcentre \(\to\) Vertices; Incentre \(\to\) Sides.

Step 1: Concept

Properties of tangents to a circle.

Step 2: Meaning

A tangent touches the circle at exactly one point.

Step 3: Analysis

At any specific point on the circumference, only one line can be perpendicular to the radius at that point.

Step 4: Conclusion

Exactly one tangent can be drawn.


Final Answer: (1) Quick Tip: Point ON circle = 1 tangent; Point OUTSIDE = 2 tangents; Point INSIDE = 0 tangents.

Step 1: Concept

Mensuration formula for surface area.

Step 2: Meaning

A cuboid has 6 rectangular faces (3 pairs of equal faces).

Step 3: Analysis

Area = \(2 \times (base area) + 2 \times (side area) + 2 \times (front area)\).

Step 4: Conclusion
\(TSA = 2(lb + bh + hl)\).


Final Answer: (3) Quick Tip: \(lbh\) is the Volume; \(2h(l+b)\) is the Lateral Surface Area.

Step 1: Concept

Relation between radius, height, and slant height: \(l = \sqrt{r^2 + h^2}\).

Step 2: Meaning

Substitute \(r = 7\) and \(h = 10\).

Step 3: Analysis
\(l = \sqrt{7^2 + 10^2} = \sqrt{49 + 100} = \sqrt{149}\).

Step 4: Conclusion
\(\sqrt{149} \approx 12.206\) cm.


Final Answer: (4) Quick Tip: Since \(12^2=144\) and \(13^2=169\), \(\sqrt{149}\) must be very close to 12.

Step 1: Concept

Volume of sphere \(V = (4/3)\pi r^3\).

Step 2: Meaning

Diameter \(d = 2r\), so \(r = d/2\).

Step 3: Analysis
\(V = (4/3)\pi (d/2)^3 = (4/3)\pi (d^3/8)\).

Step 4: Conclusion
\(V = (4/24)\pi d^3 = (1/6)\pi d^3\).


Final Answer: (1) Quick Tip: Replace \(r\) with \(d/2\) in any volume/area formula to get it in terms of \(d\).

Step 1: Concept

Identifying geometric shapes in real-life objects.

Step 2: Meaning

A sharpened pencil tapers from a circular base to a point.

Step 3: Analysis

This structure consists of a curved surface meeting at a vertex.

Step 4: Conclusion

It represents a cone.


Final Answer: (2) Quick Tip: An unsharpened pencil is a cylinder; the tip is a cone.

Step 1: Concept

Algebraic identity: \((a+b)^2 = a^2 + b^2 + 2ab\).

Step 2: Meaning

Square both sides: \((\tan\theta + \cot\theta)^2 = 2^2\).

Step 3: Analysis
\(\tan^2\theta + \cot^2\theta + 2\tan\theta\cot\theta = 4\). Since \(\tan\theta\cot\theta = 1\).

Step 4: Conclusion
\(\tan^2\theta + \cot^2\theta + 2(1) = 4 \implies \tan^2\theta + \cot^2\theta = 2\).


Final Answer: (2) Quick Tip: If \(x + 1/x = 2\), then \(x^n + 1/x^n\) is always 2.

Step 1: Concept

Identify the angle from the tangent value.

Step 2: Meaning
\(\tan\theta = 1/\sqrt{3} \implies \theta = 30^\circ\).

Step 3: Analysis

We need \(\cos 30^\circ\).

Step 4: Conclusion
\(\cos 30^\circ = \sqrt{3}/2\).


Final Answer: (2) Quick Tip: Standard values: \(\tan 30^\circ = 1/\sqrt{3}\), \(\cos 30^\circ = \sqrt{3}/2\).

Step 1: Concept

Use Pythagorean triplet: \(Opposite^2 + Adjacent^2 = Hypotenuse^2\).

Step 2: Meaning
\(Opp = 12\), \(Hyp = 13\). \(Adj = \sqrt{13^2 - 12^2} = \sqrt{169 - 144} = 5\).

Step 3: Analysis
\(\tan\theta = Opp / Adj\).

Step 4: Conclusion
\(\tan\theta = 12/5\).


Final Answer: (4) Quick Tip: (5, 12, 13) is a common triplet. \(\tan = 12/5\).

Step 1: Concept

Complementary angle formula: \(\sin\theta = \cos(90^\circ - \theta)\).

Step 2: Meaning
\(\sin 18^\circ = \cos(90^\circ - 18^\circ)\).

Step 3: Analysis
\(\sin 18^\circ = \cos 72^\circ\).

Step 4: Conclusion
\(\cos 72^\circ / \cos 72^\circ = 1\).


Final Answer: (1) Quick Tip: If \(\theta_1 + \theta_2 = 90^\circ\), then \(\sin\theta_1 / \cos\theta_2 = 1\).

Step 1: Concept

Identify the physical quantity measured in Dioptres.

Step 2: Meaning

Power of a lens (\(P\)) is the reciprocal of its focal length (\(f\)) in metres.

Step 3: Analysis
\(P = 1/f\). The SI unit for this reciprocal length is \(m^{-1}\).

Step 4: Conclusion

This unit is specifically named Dioptre (\(D\)).


Final Answer: (4) Quick Tip: \(P = 1/f(m)\). If \(f\) is in cm, \(P = 100/f\).

Step 1: Concept

Understand the variation of the least distance of distinct vision with age.

Step 2: Meaning

The least distance of distinct vision is the closest distance at which an eye can see clearly.

Step 3: Analysis

For a standard adult, this is 25 cm, but for young children, the eye lens is more flexible.

Step 4: Conclusion

In children below 10, this distance is significantly shorter, approximately 7-8 cm.


Final Answer: (1) Quick Tip: The value increases as you age because the ciliary muscles and lens lose flexibility.

Step 1: Concept

Identify properties of magnetic field lines.

Step 2: Meaning

Field lines represent the direction and strength of a magnetic field in space.

Step 3: Analysis

Magnetic fields exist in all directions around a magnet, making the field structure 3D.

Step 4: Conclusion

Stating they are 2D is false.


Final Answer: (2) Quick Tip: Field lines are 3-dimensional imaginary curves forming continuous closed loops.

Step 1: Concept

Recall SI units for magnetic quantities.

Step 2: Meaning

Magnetic flux (\(\Phi\)) measures total field lines; Flux density (\(B\)) measures lines per unit area.

Step 3: Analysis
\(\Phi\) unit is Weber (Wb). \(B\) unit is Weber/\(m^2\), also known as Tesla (T).

Step 4: Conclusion

The correct pair is Weber and Tesla.


Final Answer: (3) Quick Tip: \(1 Tesla = 1 Weber/meter^2\).

Step 1: Concept

Link electromagnetism to specific inventions.

Step 2: Meaning

Electromagnetism involves the production of magnetic fields from current or electricity from motion.

Step 3: Analysis

Bulbs and geysers use heating effects. Batteries use chemical effects.

Step 4: Conclusion

A dynamo uses electromagnetic induction to convert mechanical energy into electricity.


Final Answer: (4) Quick Tip: Dynamo = Electromagnetic Induction (Faraday's Law).

Step 1: Concept

Define magnetic field strength quantities.

Step 2: Meaning

Flux (\(\Phi\)) over Area (\(A\)) gives density.

Step 3: Analysis

Mathematically, \(B = \Phi / A\) (when perpendicular).

Step 4: Conclusion

This quantity is termed magnetic flux density.


Final Answer: (1) Quick Tip: Flux density is also known as Magnetic Induction.

Step 1: Concept

Understand the behavior of a magnet in Earth's magnetic field.

Step 2: Meaning

A compass needle is a small bar magnet.

Step 3: Analysis

Earth acts as a giant magnet, aligning external magnets with its field lines.

Step 4: Conclusion

It naturally aligns with the Earth's geographic North-South axis.


Final Answer: (4) Quick Tip: The North pole of the needle points toward the Geographic North.

Step 1: Concept

Apply the principle of calorimetry (heat exchange).

Step 2: Meaning

When hot and cold bodies mix, the final temperature reaches equilibrium.

Step 3: Analysis

The final temperature (\(z\)) must be lower than the hot sample (\(x\)) and higher than the cold sample (\(y\)).

Step 4: Conclusion

The relationship is \(x > z > y\).


Final Answer: (3) Quick Tip: Equilibrium temperature always lies between the initial temperatures of the components.

Step 1: Concept

Recall the laws of refraction.

Step 2: Meaning

Snell's law defines the relationship between angles of incidence and refraction.

Step 3: Analysis

The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media.

Step 4: Conclusion

Equation is \(\frac{\sin i}{\sin r} = n\) (Constant).


Final Answer: (4) Quick Tip: The constant is called the relative refractive index of the second medium with respect to the first.

Step 1: Concept

Define the physical requirements for a lens.

Step 2: Meaning

A lens must allow light to pass through and undergo refraction.

Step 3: Analysis

Opaque materials block light, while transparent materials allow light transmission.

Step 4: Conclusion

Lenses are made of transparent materials like glass or plastic.


Final Answer: (1) Quick Tip: A lens must have at least one curved surface and be transparent.

Step 1: Concept

Define basic terminologies associated with a lens.

Step 2: Meaning

The optic centre is the geometric centre of the lens, and the focal point is where light rays converge.

Step 3: Analysis

The linear distance between these two specific points on the principal axis is a fundamental property of the lens.

Step 4: Conclusion

This distance is defined as the focal length.


Final Answer: (2) Quick Tip: Focal length is usually denoted by '\(f\)' and is half the radius of curvature (\(R\)) for thin spherical mirrors.

Step 1: Concept

Identify the sensory function of the human eye.

Step 2: Meaning

The eye is a biological organ that reacts to light and pressure.

Step 3: Analysis

While ears are for hearing and the tongue is for taste, the eyes process light to create images.

Step 4: Conclusion

The principle function is the sensation of vision.


Final Answer: (1) Quick Tip: The retina acts as a light-sensitive screen where the image is formed.

Step 1: Concept

Define the rate of flow of electric charge.

Step 2: Meaning

Charge (\(Q\)) passing through time (\(t\)) is represented as \(I = Q/t\).

Step 3: Analysis

When \(t = 1\) second, the current \(I\) equals the amount of charge \(Q\).

Step 4: Conclusion

This physical quantity is electric current.


Final Answer: (2) Quick Tip: SI unit of current is Ampere (A). \(1 A = 1 Coulomb / 1 Second\).

Step 1: Concept

Distinguish between Ohmic and Non-Ohmic conductors.

Step 2: Meaning

Ohmic materials maintain a constant resistance regardless of voltage.

Step 3: Analysis

Silicon and Germanium are semiconductors (non-ohmic), and LEDs are diodes (non-ohmic).

Step 4: Conclusion

Aluminium, being a metal, acts as an Ohmic conductor under standard conditions.


Final Answer: (3) Quick Tip: Most metals are Ohmic conductors at constant temperature.

Step 1: Concept

Analyze properties of metallic conductors in relation to Ohm's law.

Step 2: Meaning

Metallic conductors are Ohmic, meaning \(V = IR\), where \(R\) is constant.

Step 3: Analysis

Since \(V \propto I\), the graph of \(V\) vs \(I\) must be a straight line passing through the origin (linear).

Step 4: Conclusion

The statement that the graph is "non-linear" is false.


Final Answer: (3) Quick Tip: A linear V-I graph indicates that resistance is independent of voltage.

Step 1: Concept

Identify instruments used to measure electrical quantities.

Step 2: Meaning

Potential difference (Voltage) is the work done per unit charge.

Step 3: Analysis

An ammeter measures current, a calorimeter measures heat, and a barometer measures pressure.

Step 4: Conclusion

The voltmeter is specifically designed to measure potential difference.


Final Answer: (2) Quick Tip: A voltmeter is always connected in parallel across the component to be measured.

Step 1: Concept

Define units of heat energy.

Step 2: Meaning

Specific heat capacity is the basis for this unit definition.

Step 3: Analysis

Joule is the SI unit, but the specific definition involving 1g of water and \(1^\circ\)C describes the calorie.

Step 4: Conclusion

The quantity is 1 calorie.


Final Answer: (3) Quick Tip: \(1 calorie \approx 4.184 Joules\).

Step 1: Concept

Convert temperatures to a common scale for comparison.

Step 2: Meaning

The relationship between Kelvin and Celsius is \(K = C + 273\).

Step 3: Analysis

Convert A to Kelvin: \(-100 + 273 = 173\) K. Body B is already \(173\) K.

Step 4: Conclusion

Since \(173 K = 173 K\), both are at the same temperature.


Final Answer: (3) Quick Tip: Absolute zero is \(0 K\) or \(-273.15^\circ C\).

Step 1: Concept

Identify specific heat values for various substances.

Step 2: Meaning

Specific heat is the heat required to raise the temperature of unit mass by \(1^\circ\)C.

Step 3: Analysis

Specific heat of ice \(\approx 0.5 cal/g^\circC\) and kerosene is also \(\approx 0.5 cal/g^\circC\). Water is \(1.0\), much higher than ice.

Step 4: Conclusion

Ice and kerosene oil have approximately the same specific heat.


Final Answer: (4) Quick Tip: Water has the highest specific heat among common substances.

Step 1: Concept

Understand thermal conductivity and perception of cold.

Step 2: Meaning

Metal is a better conductor of heat than wood.

Step 3: Analysis

When you touch metal, it quickly drains heat from your finger, making it "feel" colder even if both objects are at the same room temperature.

Step 4: Conclusion

The sensation of extreme cold is due to the rapid heat transfer specifically to the metal.


Final Answer: (1) Quick Tip: Cold is not something that "flows"; it is simply the absence or removal of heat.

Step 1: Concept

Specific heat determines how much heat an object can store per unit mass.

Step 2: Meaning

High specific heat means a substance takes a long time to heat up and a long time to cool down.

Step 3: Analysis

The outer crust of a samosa has low specific heat and cools quickly. The internal curry, often containing water and oils, has high specific heat.

Step 4: Conclusion

The high specific heat of the ingredients allows the inside to retain heat for much longer.


Final Answer: (2) Quick Tip: Water has a very high specific heat, which is why wet food stays hot longer than dry food.

Step 1: Concept

Distinguish between the phenomena of refraction and reflection.

Step 2: Meaning

Refraction is the bending of light as it passes between media. Reflection is light bouncing off a surface.

Step 3: Analysis

Options 1, 2, and 3 involve light traveling from water to air (refraction).

Step 4: Conclusion

An image in a plane mirror is formed strictly by the reflection of light.


Final Answer: (4) Quick Tip: Refraction = Bending through; Reflection = Bouncing back.

Step 1: Concept

Formula for refractive index: \(n = c/v\).

Step 2: Meaning
\(c\) = speed in vacuum (\(3 \times 10^8\) m/s); \(v\) = speed in medium (\(2 \times 10^8\) m/s).

Step 3: Analysis
\(n = (3 \times 10^8) / (2 \times 10^8) = 3/2\).

Step 4: Conclusion

The refractive index is 1.5.


Final Answer: (3) Quick Tip: Refractive index is always \(\ge 1\) because light is fastest in a vacuum.

Step 1: Concept

Understand the behavior of light moving from a rarer to a denser medium.

Step 2: Meaning

Air is rarer; glass is denser.

Step 3: Analysis

When light enters a denser medium, it bends toward the normal, meaning the angle of refraction (\(r\)) is smaller than the angle of incidence (\(i\)).

Step 4: Conclusion

Since \(i = 45^\circ\), the only possible smaller angle in the options is \(30^\circ\).


Final Answer: (4) Quick Tip: Rarer to Denser \(\implies\) Angle decreases (\(i > r\)).

Step 1: Concept

Recall the first law of refraction.

Step 2: Meaning

The law describes the geometric relationship of the rays at the point of incidence.

Step 3: Analysis

The incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane.

Step 4: Conclusion

Option 2 correctly lists all three components.


Final Answer: (2) Quick Tip: This is similar to the first law of reflection.

Step 1: Concept

Define the orientation of the focal plane in optics.

Step 2: Meaning

The focal plane is the plane where parallel rays (not parallel to the principal axis) converge.

Step 3: Analysis

This plane passes through the principal focus (\(F\)).

Step 4: Conclusion

By definition, this plane is perpendicular to the principal axis.


Final Answer: (2) Quick Tip: Every lens has two focal planes, one on each side.

Step 1: Concept

Identify lenses based on their converging/diverging properties.

Step 2: Meaning

A magnifying glass requires a lens that can form an enlarged, virtual image.

Step 3: Analysis

Converging lenses (convex) are capable of magnification when the object is placed within the focal length.

Step 4: Conclusion

A double convex lens is the standard choice for magnification.


Final Answer: (1) Quick Tip: Magnifying Glass = Simple Microscope = Convex Lens.

Step 1: Concept

Recall image formation rules for a convex lens.

Step 2: Meaning

The size of the image changes based on the object's distance (\(u\)).

Step 3: Analysis

When an object is at \(2F_1\) (the centre of curvature), the image is formed at \(2F_2\) on the other side.

Step 4: Conclusion

In this specific position, the image is real, inverted, and exactly the same size as the object.


Final Answer: (4) Quick Tip: At \(C\) (\(2F\)), Magnification (\(m\)) = -1.

Step 1: Concept

Define the structural requirements of different lens types.

Step 2: Meaning

Statement (a): A lens is defined by having at least one curved boundary. Statement (b): "Plano" means flat.

Step 3: Analysis

A plano-concave lens has one flat (plane) surface and one inward-curved (concave) surface.

Step 4: Conclusion

(a) is correct; (b) is incorrect because it only has one curved surface.


Final Answer: (1) Quick Tip: Plano = 0 curvature (Flat); Concave/Convex = 1 curvature.

Step 1: Concept

Identify materials with high resistivity and high melting points.

Step 2: Meaning

Heating elements must convert electrical energy to heat without melting or oxidizing.

Step 3: Analysis

Copper and silver are excellent conductors (low resistance). Germanium is a semiconductor.

Step 4: Conclusion

Nichrome (an alloy of nickel and chromium) has high resistivity and does not oxidize easily at high temperatures.


Final Answer: (2) Quick Tip: Alloys are generally preferred over pure metals for heating elements.

Step 1: Concept

Identify the standard SI units for the given electrical quantities.

Step 2: Meaning

Electric current is the flow of charge; Electric charge is a physical property of matter; Electric potential is the work done per unit charge.

Step 3: Analysis

- Current: Ampere (c)

- Charge: Coulomb (a)

- Potential: Volt (b)

Step 4: Conclusion

The matching sequence is (i)-(c), (ii)-(a), (iii)-(b).


Final Answer: (1) Quick Tip: Remember: \(I\) (Ampere), \(Q\) (Coulomb), \(V\) (Volt).

Step 1: Concept

Categorize materials based on their electrical resistivity (\(\rho\)).

Step 2: Meaning

High resistivity means the material strongly opposes the flow of electric current.

Step 3: Analysis

Conductors have very low \(\rho\) (\(10^{-8}\) \(\Omega\)-m); Semiconductors are intermediate. Values like \(10^{14}\) are extremely high.

Step 4: Conclusion

These materials are classified as insulators.


Final Answer: (1) Quick Tip: Insulators = High Resistance; Conductors = Low Resistance.

Step 1: Concept

Understand the graphical representation of Ohm's Law.

Step 2: Meaning
\(V \propto I\) for an Ohmic conductor.

Step 3: Analysis

If \(V = 0\), then \(I = 0\). This relationship is linear and starts from \((0,0)\).

Step 4: Conclusion

The graph is a straight line passing through the origin.


Final Answer: (3) Quick Tip: The slope of a \(V-I\) graph represents Resistance (\(R\)).

Step 1: Concept

Recall the definition of Electric Potential (\(V\)).

Step 2: Meaning
\(V = W / Q\), where \(W\) is work (Joules) and \(Q\) is charge (Coulombs).

Step 3: Analysis
\(1 Volt = 1 Joule / 1 Coulomb\).

Step 4: Conclusion

The result is 1 volt.


Final Answer: (1) Quick Tip: \(V = J/C\).

Step 1: Concept

Distinguish between Resistance and Resistivity.

Step 2: Meaning

Resistance (\(R\)) depends on dimensions; Resistivity (\(\rho\)) is a material property.

Step 3: Analysis

Resistance unit is Ohm (\(\Omega\)); Resistivity unit is Ohm-metre (\(\Omega\)-m).

Step 4: Conclusion

Statement 3 is false because their units are different.


Final Answer: (3) Quick Tip: \(R = \rho(L/A) \implies \rho = R(A/L)\).

Step 1: Concept

Apply Ohm's Law: \(V = IR\).

Step 2: Meaning
\(I = 1.5 A\), \(R = 20 \Omega\).

Step 3: Analysis
\(V = 1.5 \times 20\).

Step 4: Conclusion
\(V = 30 V\).


Final Answer: (2) Quick Tip: \(1.5 \times 20\) is the same as \(15 \times 2\).

Step 1: Concept

Identify the material class for electronic components.

Step 2: Meaning

Electronics require materials whose conductivity can be controlled.

Step 3: Analysis

Silicon and Germanium are the primary materials used for these devices.

Step 4: Conclusion

These are classified as semiconductors.


Final Answer: (3) Quick Tip: The "Silicon" in Silicon Valley refers to these semiconductors.

Step 1: Concept

Identify types of vision defects.

Step 2: Meaning

Myopia (nearsightedness) allows near vision but makes distant objects blurry.

Step 3: Analysis

In this condition, the far point is not at infinity but closer to the eye.

Step 4: Conclusion

The defect is myopia.


Final Answer: (3) Quick Tip: Myopia = Near sighted; Hypermetropia = Far sighted.

Step 1: Concept

Recall the focal length range of the human eye lens.

Step 2: Meaning

Accommodation is the eye's ability to change its focal length to see objects at various distances.

Step 3: Analysis

The distance between the lens and retina is fixed (\(\approx 2.5 cm\)). Focal length varies to keep images on the retina.

Step 4: Conclusion

The focal length typically ranges from \(2.5 cm\) (relaxed) to \(2.27 cm\) (strained).


Final Answer: (4) Quick Tip: The eye lens is thickest when viewing near objects (\(f = 2.27 cm\)).

Step 1: Concept

Identify correction methods for Hypermetropia.

Step 2: Meaning

Hypermetropia (farsightedness) means the near point is further away than 25 cm.

Step 3: Analysis

The eye lens lacks sufficient converging power, causing the image to form behind the retina.

Step 4: Conclusion

A converging (convex) lens is required for correction.


Final Answer: (2) Quick Tip: Convex = Converging; Concave = Diverging.

Step 1: Concept

Define terms used in metallurgy for non-metallic impurities.

Step 2: Meaning

Ores are extracted from the earth and are naturally contaminated.

Step 3: Analysis

Slag is a byproduct of smelting, flux is a substance added to remove impurities, and minerals are naturally occurring inorganic solids.

Step 4: Conclusion

The specific term for unwanted earthy impurities like sand and soil is gangue.


Final Answer: (4) Quick Tip: Ore - Gangue = Concentrated Ore.

Step 1: Concept

Understand the electrochemical theory of rusting (corrosion).

Step 2: Meaning

Corrosion is a redox reaction where metal is oxidized.

Step 3: Analysis

Oxidation (loss of electrons) always occurs at the anode. For iron: \(Fe \to Fe^{2+} + 2e^{-}\).

Step 4: Conclusion

The site of corrosion acts as the anode.


Final Answer: (2) Quick Tip: Anode = Oxidation (Loss of \(e^-\)); Cathode = Reduction (Gain of \(e^-\)).

Step 1: Concept

Identify ores/minerals and their chemical compositions.

Step 2: Meaning

Galena is Lead (Pb), Cinnabar is Mercury (Hg), and Horn Silver is Silver (Ag).

Step 3: Analysis

Pyrolusite is chemically Manganese Dioxide (\(MnO_2\)).

Step 4: Conclusion

Pyrolusite is the mineral containing manganese.


Final Answer: (3) Quick Tip: Pyrolusite (\(MnO_2\)) is the most important ore of Manganese.

Step 1: Concept

Identify various techniques used to protect metals from environmental oxidation.

Step 2: Meaning

Prevention involves creating a barrier or providing an alternative oxidation site.

Step 3: Analysis

Painting and electroplating create barriers. Sacrificial electrodes (like zinc) corrode instead of the main metal.

Step 4: Conclusion

All listed methods are valid prevention techniques.


Final Answer: (4) Quick Tip: Galvanization is a specific type of sacrificial protection using Zinc.

Step 1: Concept

Define properties of Carbon and similar elements in Organic Chemistry.

Step 2: Meaning

Self-linking is a unique property that allows for a vast variety of molecules.

Step 3: Analysis

Allotropy is different forms of an element; Hybridization is orbital mixing; Isomerism is same formula but different structure.

Step 4: Conclusion

The self-linking property is called catenation.


Final Answer: (3) Quick Tip: Carbon has the maximum power of catenation in the periodic table.

Step 1: Concept

Classify hydrocarbons based on the types of carbon-carbon bonds.

Step 2: Meaning

Saturated hydrocarbons have maximum hydrogen atoms and only single bonds.

Step 3: Analysis

Alkenes have double bonds, and Alkynes have triple bonds.

Step 4: Conclusion

Single-bonded hydrocarbons are known as alkanes.


Final Answer: (1) Quick Tip: Alkanes formula: \(C_nH_{2n+2}\).

Step 1: Concept

Understand the relationship between molecular mass and physical properties.

Step 2: Meaning

Increasing molecular formula size means a larger molecule with more atoms.

Step 3: Analysis

Larger molecules have stronger Van der Waals forces between them, requiring more energy to separate.

Step 4: Conclusion

Therefore, the melting point increases as the molecular size increases.


Final Answer: (1) Quick Tip: Heavier hydrocarbons are solids, lighter ones are liquids or gases.

Step 1: Concept

Understand the tetravalency of Carbon.

Step 2: Meaning

Carbon must always form a total of four covalent bonds to be stable.

Step 3: Analysis

Carbon can achieve this through various combinations: 4 singles (\(CH_4\)), 2 doubles (\(CO_2\)), or 1 single and 1 triple (\(HC \equiv CH\)).

Step 4: Conclusion

All the listed combinations are possible ways for carbon to bond.


Final Answer: (4) Quick Tip: Always count to four bonds for every Carbon atom!

Step 1: Concept

Identify organic functional groups.

Step 2: Meaning

Acids contain -COOH, Amines contain -NH\(_2\), and Esters contain -COOR.

Step 3: Analysis

The -CONH\(_2\) group consists of a carbonyl group (\(C=O\)) directly attached to an amino group (\(NH_2\)).

Step 4: Conclusion

This functional group defines the Amide class.


Final Answer: (2) Quick Tip: Amine is just \(-NH_2\); Amide has the extra 'O' from the Carbonyl.

Step 1: Concept

Identify the standard behavior of pH indicators.

Step 2: Meaning

Litmus is a natural dye used to detect acidity or alkalinity.

Step 3: Analysis

Bases turn red litmus blue. Acids have the opposite effect on blue litmus.

Step 4: Conclusion

Acids turn blue litmus paper red.


Final Answer: (3) Quick Tip: ABR: Acid turns Blue to Red.

Step 1: Concept

Identify the defining characteristic of olfactory indicators.

Step 2: Meaning

The term "olfactory" relates to the sense of smell.

Step 3: Analysis

Unlike visual indicators that change color, olfactory indicators change their smell in acidic or basic media.

Step 4: Conclusion

Odour is the property used.


Final Answer: (2) Quick Tip: Onion and vanilla essence are common olfactory indicators.

Step 1: Concept

Reaction of metal carbonates with acids.

Step 2: Meaning

Sodium carbonate (Na\(_2\)CO\(_3\)) is a metal carbonate.

Step 3: Analysis
\(Metal Carbonate + Acid \rightarrow Salt + Water + Carbon Dioxide\).

Step 4: Conclusion

The evolved gas is Carbon Dioxide (CO\(_2\)).


Final Answer: (4) Quick Tip: Carbonates always release \(CO_2\) when reacting with acids.

Step 1: Concept

Understand the function of antacids in treating acidity.

Step 2: Meaning

Acidity is caused by excess HCl in the stomach.

Step 3: Analysis

To neutralize an acid, a mild base is required.

Step 4: Conclusion

Therefore, an antacid is a base.


Final Answer: (3) Quick Tip: Milk of Magnesia (Magnesium Hydroxide) is a common antacid base.

Step 1: Concept

Chemical nature of oxides.

Step 2: Meaning

Non-metals are elements like Carbon or Sulphur.

Step 3: Analysis

Non-metal oxides (like \(CO_2\) or \(SO_2\)) react with water to form acids.

Step 4: Conclusion

They are acidic in nature.


Final Answer: (1) Quick Tip: Metal oxides are Basic; Non-metal oxides are Acidic.

Step 1: Concept

Representation of electron shells.

Step 2: Meaning

The principal quantum number \(n\) denotes the main shell.

Step 3: Analysis

While \(n\) takes numerical values 1, 2, 3, these shells are lettered alphabetically starting from K.

Step 4: Conclusion

Represented by K, L, M, etc.


Final Answer: (2) Quick Tip: \(n=1\) is K, \(n=2\) is L, \(n=3\) is M, and so on.

Step 1: Concept

Successes of the Bohr model.

Step 2: Meaning

Line spectra refer to discrete wavelengths emitted by hydrogen.

Step 3: Analysis

Bohr successfully explained the origin of hydrogen lines but failed to explain the "fine structure" (closely spaced lines).

Step 4: Conclusion

Only line spectra were explained.


Final Answer: (1) Quick Tip: Sommerfeld's model was later proposed to explain the fine spectra.

Step 1: Concept

Electron capacity of subshells.

Step 2: Meaning

The p-subshell consists of three orbitals (\(p_x, p_y, p_z\)).

Step 3: Analysis

Each orbital can hold 2 electrons. \(3 \times 2 = 6\).

Step 4: Conclusion

Maximum capacity is 6.


Final Answer: (3) Quick Tip: s-shell (2), p-shell (6), d-shell (10), f-shell (14).

Step 1: Concept

Rules for filling electrons in orbitals.

Step 2: Meaning

Aufbau (order), Hund (pairing), and Pauli (spin).

Step 3: Analysis

All three rules must be followed simultaneously to write a correct configuration.

Step 4: Conclusion

The answer is All of the above.


Final Answer: (4) Quick Tip: Aufbau means "building up" in German.

Step 1: Concept

Allowed values for quantum numbers.

Step 2: Meaning
\(n\) (Principal), \(l\) (Azimuthal), \(m\) (Magnetic).

Step 3: Analysis
\(l\) can be 0 (s-orbital), \(m\) can be 0. However, \(n\) must be a positive integer (\(1, 2, 3...\)).

Step 4: Conclusion
\(n\) cannot be zero.


Final Answer: (1) Quick Tip: \(n\) starts from 1; \(l\) starts from 0.

Step 1: Concept

Basis of classification in different periodic tables.

Step 2: Meaning

Early models used atomic mass.

Step 3: Analysis

Dobereiner, Newland, and Mendeleev all used atomic mass. Moseley's modern table used atomic number.

Step 4: Conclusion

Modern periodic table is the correct choice.


Final Answer: (3) Quick Tip: Henry Moseley showed that atomic number is the fundamental property.

Step 1: Concept

Understand the relationship between periodic table position and quantum numbers.

Step 2: Meaning

Moving down a group means moving from one period to the next.

Step 3: Analysis

Each new period represents a new electron shell being added to the atom.

Step 4: Conclusion

The Principal quantum number (\(n\)), which denotes the shell, increases by 1 for each row down a group.


Final Answer: (1) Quick Tip: Period number = Principal quantum number of the valence shell.

Step 1: Concept

Identify the location of specific element series in the periodic table.

Step 2: Meaning

Lanthanoids are the series of 14 elements following Lanthanum.

Step 3: Analysis

These elements involve the filling of the \(4f\) subshell.

Step 4: Conclusion

Therefore, they are classified as f-block elements.


Final Answer: (4) Quick Tip: Lanthanoids and Actinoids together make up the f-block (inner transition elements).

Step 1: Concept

Recall the number of elements in each period of the modern periodic table.

Step 2: Meaning

The 3rd period starts with Sodium (Na) and ends with Argon (Ar).

Step 3: Analysis

It involves the filling of \(3s\) and \(3p\) orbitals. \(2 (s) + 6 (p) = 8\) electrons/elements.

Step 4: Conclusion

There are exactly 8 elements in the 3rd period.


Final Answer: (2) Quick Tip: Period 1 (2), Period 2 (8), Period 3 (8), Period 4 (18).

Step 1: Concept

Calculate valency based on group number.

Step 2: Meaning

Group VA (or Group 15) elements have 5 valence electrons.

Step 3: Analysis

To complete an octet, these atoms need to gain or share 3 more electrons.

Step 4: Conclusion

Valency = \(8 - 5 = 3\).


Final Answer: (2) Quick Tip: For groups 15-17, Valency = 8 - (number of valence electrons).

Step 1: Concept

Understand the mechanism of ionic bonding.

Step 2: Meaning

Ionic bonding occurs between metals and non-metals.

Step 3: Analysis

It begins with the transfer of electrons (1), which creates ions. These ions are then held together by electrostatic forces (2).

Step 4: Conclusion

Both statements describe parts of the ionic bond formation process.


Final Answer: (4) Quick Tip: Transfer of electrons \(\to\) Ions \(\to\) Attraction = Ionic Bond.

Step 1: Concept

Identify elements belonging to Group 18 (Noble Gases).

Step 2: Meaning

Noble gases are chemically inert and have complete valence shells.

Step 3: Analysis

Fluorine, Chlorine, and Iodine are Halogens (Group 17).

Step 4: Conclusion

Argon (Ar) is a noble gas.


Final Answer: (4) Quick Tip: He, Ne, Ar, Kr, Xe, Rn are the noble gases.

Step 1: Concept

Understand electron movement during ionic bond formation.

Step 2: Meaning

Metals have low ionization energy and 1-3 valence electrons.

Step 3: Analysis

To achieve stability, metals give away their valence electrons to non-metals.

Step 4: Conclusion

The metal atom loses electrons to become a positively charged cation.


Final Answer: (2) Quick Tip: Metals = Electron Donors; Non-metals = Electron Acceptors.

Step 1: Concept

Use the criss-cross method to determine chemical formulas.

Step 2: Meaning

Write symbols and their respective valencies: Na (1) and O (2).

Step 3: Analysis

Cross the valencies: The 2 from Oxygen goes to Sodium, and the 1 from Sodium goes to Oxygen.

Step 4: Conclusion

The resulting formula is Na\(_2\)O.


Final Answer: (3) Quick Tip: The total positive charge must equal the total negative charge (\(2 \times +1 = -2\)).

Step 1: Concept

Composition of multiple covalent bonds.

Step 2: Meaning

A single bond is always a sigma (\(\sigma\)) bond. Additional bonds are pi (\(\pi\)) bonds.

Step 3: Analysis

In a triple bond (\(N \equiv N\)), the first bond formed is a \(\sigma\) bond, and the remaining two are \(\pi\) bonds.

Step 4: Conclusion

The triple bond contains 1 sigma and 2 pi bonds.


Final Answer: (1) Quick Tip: Single (1\(\sigma\)), Double (1\(\sigma\), 1\(\pi\)), Triple (1\(\sigma\), 2\(\pi\)).

Step 1: Concept

Understand the relationship between metal reactivity and natural occurrence.

Step 2: Meaning

"Free state" means the metal is found as an element, not a compound.

Step 3: Analysis

Highly reactive metals react with oxygen or moisture to form compounds. Gold is at the bottom of the reactivity series.

Step 4: Conclusion

Due to its very low reactivity, gold does not easily form compounds and remains in its elemental form.


Final Answer: (1) Quick Tip: Noble metals like Gold and Platinum are found in the native state.