SSC CHSL (Combined Higher Secondary Level) Tier II - Module-Specific Topics Flashcards

24 sample cards from the Tier II - Module-Specific Topics deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. State the volume and curved surface area of a cone with radius $r$, height $h$, slant height $l$.

   Volume $= \frac{1}{3}\pi r^{2} h$; CSA $= \pi r l$, where $l = \sqrt{r^{2} + h^{2}}$.

2. State the Pythagorean theorem for a right triangle.

   In a right triangle, $\text{hypotenuse}^{2} = \text{base}^{2} + \text{height}^{2}$, i.e. $c^{2} = a^{2} + b^{2}$.

3. Define $\sin\theta$, $\cos\theta$ and $\tan\theta$ in a right triangle.

   $\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta = \frac{\text{opposite}}{\text{adjacent}}$.

4. State the fundamental Pythagorean trigonometric identity.

   $\sin^{2}\theta + \cos^{2}\theta = 1$.

5. Give the values of $\sin\theta$ for $\theta = 0^{\circ}, 30^{\circ}, 45^{\circ}, 60^{\circ}, 90^{\circ}$.

   $0,\ \frac{1}{2},\ \frac{1}{\sqrt{2}},\ \frac{\sqrt{3}}{2},\ 1$ respectively.

6. What is the sum of the interior angles of a triangle, and of the exterior angle property?

   Interior angles sum to $180^{\circ}$. An exterior angle equals the sum of the two opposite interior angles.

7. State the angle sum of a polygon with $n$ sides.

   Sum of interior angles $= (n-2) \times 180^{\circ}$.

8. What is the relationship between a tangent to a circle and the radius at the point of contact?

   The tangent is perpendicular to the radius drawn to the point of contact (angle $= 90^{\circ}$).

9. State the theorem about the angle subtended by a diameter on the circle.

   The angle in a semicircle (subtended by a diameter at any point on the circle) is a right angle, $90^{\circ}$.

10. What is the tangent-secant length property for two tangents drawn from an external point?

    The lengths of two tangents drawn from an external point to a circle are equal.

11. In a heights and distances problem, define angle of elevation and angle of depression.

    Angle of elevation is the angle above the horizontal to an object higher than the observer; angle of depression is the angle below the horizontal to an object lower than the observer.

12. If a tower of height $h$ subtends an angle of elevation $\theta$ from a point at distance $d$, what is the relation?

    $\tan\theta = \frac{h}{d}$, so $h = d\tan\theta$.

13. Define mean (arithmetic average) for a set of $n$ values.

    $$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$ — the sum of all values divided by the number of values.

14. How do you find the median of a data set?

    Arrange data in ascending order; the median is the middle value. For $n$ odd it is the $\frac{n+1}{2}$th term; for $n$ even it is the average of the $\frac{n}{2}$th and $\left(\frac{n}{2}+1\right)$th terms.

15. What is the mode of a data set?

    The mode is the value that occurs most frequently in the data set. A set may have no mode, one mode, or several modes.

16. State the empirical relationship between mean, median and mode.

    $\text{Mode} = 3\,\text{Median} - 2\,\text{Mean}$.

17. In a frequency distribution, what is the class mark (mid-value) of a class interval?

    $\text{Class mark} = \frac{\text{lower limit} + \text{upper limit}}{2}$.

18. What is the classical (theoretical) definition of probability of an event?

    $$P(E) = \frac{\text{number of favourable outcomes}}{\text{total number of equally likely outcomes}}$$ where $0 \leq P(E) \leq 1$.

19. State the probability of the complement of an event $E$.

    $P(\text{not } E) = 1 - P(E)$.

20. In reasoning, what is a semantic analogy and how does it differ from a number/figural analogy?

    A semantic analogy relates words by meaning (e.g. doctor : hospital). A number analogy relates by numerical pattern, and a figural analogy relates by shape/position patterns rather than meaning.

21. In symbolic operations reasoning, if symbols like $@, \#, \$$ replace $+, -, \times$, what is the first step to solve such problems?

    Substitute each given symbol with its defined arithmetic operation, then evaluate using the BODMAS/order-of-operations rule.

22. What is coding-decoding in reasoning, and name a common type based on letter positions?

    Coding-decoding is encrypting a word/number by a rule and decoding it back. A common type is letter-shifting, e.g. each letter moved forward by a fixed number of positions in the alphabet (Caesar-style shift).

23. Identify the rule and next term of the series $2, 6, 12, 20, 30, \ldots$

    Differences increase by $2$: $4,6,8,10,\ldots$ (i.e. $n(n+1)$). The next term is $30 + 12 = 42$.

24. In problem solving and critical thinking, what does it mean to 'draw an inference' from given statements?

    To draw an inference is to derive a logically valid conclusion that necessarily follows from the given premises, without adding outside assumptions or information not stated.

What this deck covers

Tier II - Module-Specific Topics flashcards FAQ