JKSSB Math MCQs

Explanation

• Formula: $(n - 2) \times 180^\circ$

  • Any polygon with $n$ sides can be divided into exactly $(n - 2)$ triangles by drawing diagonals from a single vertex.

  • Since the sum of angles in a single triangle is $180^\circ$, the total sum for the polygon is the number of triangles multiplied by $180^\circ$.

• Examples:

  1. Triangle ($n=3$): $(3 - 2) \times 180^\circ = 180^\circ$.

  2. Quadrilateral ($n=4$): $(4 - 2) \times 180^\circ = 360^\circ$.

  3. Pentagon ($n=5$): $(5 - 2) \times 180^\circ = 540^\circ$.

  4. Hexagon ($n=6$): $(6 - 2) \times 180^\circ = 720^\circ$.

Explanation

• A Regular Polygon is defined by two specific conditions:

  1. Equiangular: All interior angles are equal.

  2. Equilateral: All sides are of equal length.

• Examples:

  • An Equilateral Triangle (3 sides, all angles 60°).

  • A Square (4 sides, all angles 90°).

  • A Regular Pentagon (5 sides, all angles 108°).

• In contrast, an Irregular Polygon has sides or angles that are not all equal.

Explanation

• Step 1: Use the formula for the circumference of a circle.

  $$\text{Circumference} = 2 \pi r$$

• Step 2: Substitute the given value (88 m) into the formula.

  $$88 = 2 \times \frac{22}{7} \times r$$

• Step 3: Simplify the equation.

  $$88 = \frac{44}{7} \times r$$

• Step 4: Solve for $r$.

  $$r = \frac{88 \times 7}{44}$$

  $$r = 2 \times 7 = 14 \text{ m}$$

Explanation

• Step 1: Find the side of the square.

  $$\text{Area of Square} = \text{side}^2 = 484 \text{ cm}^2$$

  $$\text{side} = \sqrt{484} = 22 \text{ cm}$$

• Step 2: Find the length of the wire (Perimeter of the square).

  Since the wire forms the boundary, its length is the perimeter:

  $$\text{Perimeter} = 4 \times \text{side} = 4 \times 22 = 88 \text{ cm}$$

• Step 3: Find the radius of the circle.

  The same wire (88 cm) is reshaped into a circle. Thus, the Circumference = 88 cm.

  $$2 \pi r = 88$$

  $$2 \times \frac{22}{7} \times r = 88$$

  $$\frac{44}{7} \times r = 88 \implies r = \frac{88 \times 7}{44} = 14 \text{ cm}$$

• Step 4: Calculate the area of the circle.

  $$\text{Area} = \pi r^2 = \frac{22}{7} \times 14 \times 14$$

  $$\text{Area} = 22 \times 2 \times 14 = 616 \text{ cm}^2$$

Explanation

• Step 1: Identify the Sample Space ($S$).

  When two coins are tossed, the possible outcomes are:

  1. Head, Head (HH)

  2. Head, Tail (HT)

  3. Tail, Head (TH)

  4. Tail, Tail (TT)

  • Total outcomes $n(S)$ = 4

• Step 2: Identify the Favorable Outcomes ($E$).

  The condition is getting exactly one head and one tail:

  • Favorable outcomes = {HT, TH}

  • Number of favorable outcomes $n(E)$ = 2

• Step 3: Apply the probability formula.

  $$\text{P(1 Head and 1 Tail)} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$

  $$\text{P} = \frac{2}{4} = \frac{1}{2}$$

Explanation

• Step 1: Identify the total number of possible outcomes.

  When a fair die is rolled, the sample space ($S$) is:

  $$S = \{1, 2, 3, 4, 5, 6\}$$

  $$\text{Total outcomes } n(S) = 6$$

• Step 2: Identify the favorable outcomes.

  The condition is an even number greater than 2.

  • Even numbers on a die are: $\{2, 4, 6\}$

  • Even numbers greater than 2 are: $\{4, 6\}$

    $$\text{Favorable outcomes } n(E) = 2$$

• Step 3: Apply the probability formula.

  $$\text{P(Event)} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$

  $$\text{P(Even > 2)} = \frac{2}{6} = \frac{1}{3}$$

Explanation

• Step 1: Find the total number of possible outcomes.

  $$\text{Total balls} = 3 \text{ (Red)} + 2 \text{ (Blue)} + 5 \text{ (Green)} = 10$$

• Step 2: Identify the number of favorable outcomes.

  $$\text{Number of red balls} = 3$$

• Step 3: Apply the probability formula.

  $$\text{Probability (P)} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$

  $$\text{P(Red)} = \frac{3}{10}$$

Explanation

To find where a graph cuts the y-axis, you must set the value of $x$ to 0, because every point on the y-axis has an x-coordinate of zero.

1. Start with the equation:

   $$x + 2y = 2$$

2. Substitute $x = 0$:

   $$0 + 2y = 2$$

3. Solve for $y$:

   $$2y = 2$$

   $$y = 1$$

Explanation

To find $k$, substitute the coordinates of the point $(x, y) = (3, 4)$ into the given equation:

1. Substitute the values:

   $$3(4) = k(3) + 7$$

2. Simplify the terms:

   $$12 = 3k + 7$$

3. Isolate the term with $k$:

   $$12 - 7 = 3k$$

   $$5 = 3k$$

4. Solve for $k$:

   $$k = \frac{5}{3}$$

Explanation

The linear equation $3x - 11y = 10$ has infinitely many solutions.

In coordinate geometry, a linear equation with two variables (like $x$ and $y$) represents a straight line on a graph.

• Continuous Line: Every point located on that line is a solution to the equation.

• Infinite Points: Since a line extends infinitely in both directions, there are an infinite number of $(x, y)$ coordinate pairs that satisfy the equation.

Explanation

1. Find the Circumference ($C$):

Using the formula $C = 2\pi r$, where $r = 84 \text{ cm}$ and $\pi \approx \frac{22}{7}$:

$$C = 2 \times \frac{22}{7} \times 84$$

$$C = 2 \times 22 \times 12$$

$$C = 528 \text{ cm}$$

2. Multiply by Revolutions ($n$):

Total Distance = $C \times n$, where $n = 4$:

$$\text{Distance} = 528 \times 4$$

$$\text{Distance} = 2112 \text{ cm}$$

Explanation

The circumference ($C$) of a circle is related to its diameter ($d$) by the formula:

$$C = \pi \times d$$

Given the circumference is 22 km and using the common approximation for $\pi \approx \frac{22}{7}$:

1. Substitute the values: $22 = \frac{22}{7} \times d$

2. Solve for $d$: $d = 22 \div \frac{22}{7}$

3. Multiply by the reciprocal: $d = 22 \times \frac{7}{22}$

4. Simplify: $d = 7$

Explanation

The area of a rhombus ($A$) is calculated using the product of its diagonals ($d_1$ and $d_2$) divided by two:

$$A = \frac{1}{2} \times d_1 \times d_2$$

1. Multiply the diagonals: $10 \times 8.2 = 82$

2. Divide by 2: $82 \div 2 = 41$

Result: $41 \text{ cm}^2$

Explanation

The volume of a cuboid is calculated by multiplying its three dimensions: length ($l$), width ($b$), and height ($h$).

$$V = l \times b \times h$$

Explanation

the price rises and demand is elastic

Explanation

y = C e^ + x*

Explanation

(3x² - y)dx + (3y² - x²)dy = 0

Explanation

 Bernoulli equation

Explanation

–cot³x/3 – cosec⁵x/5

Explanation

π/2 – 1

Explanation

{nπ∣n∈Z}

Explanation

 –cosec²(x) + cosec(x)cot(x)

Explanation

The graph of f(x) is concave downward for all x > 0

Explanation

x = 7

Explanation

Square

Explanation

10, 13

Explanation

 k = 1/3 or k = 7

Explanation

30

Explanation

n(A ∪ B) = n(A − B) − n(A) + n(A ∩ B) is NOT universally valid.

Explanation

Relative speed = 75 km/hr = 75?(5/18)=20.83 m/s. Distance=500m. Time=500/20.83?24 sec.