RRB JE Mathematics Flashcards

24 sample cards from the Mathematics deck

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

1. State the Pythagoras theorem for a right-angled triangle.

   In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: c² = a² + b².

2. State the angle sum property of a triangle and the exterior angle property.

   The three interior angles of a triangle sum to 180°. An exterior angle equals the sum of the two opposite (remote) interior angles.

3. Give the formulas for the area of a triangle by base-height and by Heron's formula.

   Area = ½ × base × height. Heron's formula: Area = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2.

4. What does it mean for two triangles to be similar, and what is the ratio of their areas?

   Two triangles are similar if their corresponding angles are equal and corresponding sides are proportional. The ratio of their areas equals the square of the ratio of corresponding sides.

5. State the standard congruence criteria for triangles.

   SSS, SAS, ASA, AAS, and RHS (right angle–hypotenuse–side, for right triangles).

6. Give the formulas for the circumference and area of a circle of radius r.

   Circumference = 2πr; Area = πr².

7. What is the formula for the length of an arc and the area of a sector subtending angle θ (in degrees) at the centre?

   Arc length = (θ/360) × 2πr; Sector area = (θ/360) × πr².

8. State the relationship between the angle subtended by an arc at the centre and at any point on the remaining circle.

   The angle subtended at the centre is twice the angle subtended at any point on the remaining part of the circle (same arc).

9. What is the angle in a semicircle, and what is the property of the tangent to a circle at the point of contact?

   The angle in a semicircle is a right angle (90°). A tangent is perpendicular to the radius drawn to the point of contact.

10. Classify quadrilaterals: how do a parallelogram, rectangle, rhombus, and square differ?

    Parallelogram: opposite sides parallel and equal. Rectangle: parallelogram with all angles 90°. Rhombus: parallelogram with all sides equal. Square: rectangle with all sides equal (all angles 90° and all sides equal).

11. Give the area formulas for a parallelogram, rhombus (diagonals d₁, d₂), and trapezium.

    Parallelogram: base × height. Rhombus: ½ × d₁ × d₂. Trapezium: ½ × (sum of parallel sides) × height.

12. What is the sum of the interior angles of any quadrilateral?

    360°.

13. State the distance formula between two points (x₁, y₁) and (x₂, y₂).

    Distance = √[(x₂ − x₁)² + (y₂ − y₁)²].

14. State the midpoint formula and the section formula (internal division in ratio m:n).

    Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2). Section (ratio m:n) = ((mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n)).

15. What is the slope of a line through (x₁, y₁) and (x₂, y₂), and what is the slope-intercept form?

    Slope m = (y₂ − y₁)/(x₂ − x₁). Slope-intercept form: y = mx + c, where c is the y-intercept.

16. Define the six trigonometric ratios for an angle in a right triangle.

    sin = opposite/hypotenuse; cos = adjacent/hypotenuse; tan = opposite/adjacent; cosec = 1/sin; sec = 1/cos; cot = 1/tan.

17. Give the values of sin, cos, and tan for 0°, 30°, 45°, 60°, and 90°.

    sin: 0, 1/2, 1/√2, √3/2, 1. cos: 1, √3/2, 1/√2, 1/2, 0. tan: 0, 1/√3, 1, √3, undefined.

18. In a height and distance problem, define the angle of elevation and the angle of depression.

    Angle of elevation: angle above the horizontal when looking up at an object. Angle of depression: angle below the horizontal when looking down at an object. (They are equal for the same line of sight.)

19. State the three Pythagorean trigonometric identities.

    sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.

20. How are mean, median, and mode defined for a data set?

    Mean = sum of values ÷ number of values. Median = middle value when data is arranged in order (average of two middle values if even count). Mode = the most frequently occurring value.

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

    Mode = 3 × Median − 2 × Mean.

22. What is the formula for the probability of an event, and what is the range of probability values?

    P(event) = (number of favourable outcomes)/(total number of equally likely outcomes). Probability ranges from 0 (impossible) to 1 (certain).

23. What is the relationship between the probability of an event and its complement?

    P(not E) = 1 − P(E); i.e., P(E) + P(not E) = 1.

24. What does standard deviation measure, and what is its formula for a population of n values with mean x̄?

    Standard deviation measures the spread/dispersion of data about the mean. σ = √[ Σ(xᵢ − x̄)² / n ]; it is the square root of the variance.

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