10th Class Math Quiz: First 4 Chapters
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Questions and Answers

In a circle of radius 5 cm, an arc subtends an angle of 60 degrees at the centre. Find the length of the arc.

Use the formula, length of arc = (θ/360) × 2 × π × r, θ in degrees.

Prove that the points $(a, b + c), (a, b), (a + c, b)$ and $(a + c, b + c)$ are the vertices of a parallelogram.

Draw a diagram and show that opposite sides are equal using distance formula.

Prove that $(1 + cot A)/ (cosec A) = sin A$.

Use trigonometric identities and simplify the given expression.

Find the value of $sin^{-1} (1/2) + cos^{-1} (1/2)$.

<p>Use the property, $sin^{-1} x + cos^{-1} x = π/2$, and simplify.</p> Signup and view all the answers

Find the coordinates of the point which divides the line segment joining the points $(2, 4)$ and $(8, 10)$ in the ratio 3:2.

<p>Use the section formula, $((mx_2 + nx_1)/(m + n), (my_2 + ny_1)/(m + n))$.</p> Signup and view all the answers

Study Notes

Properties of Shapes

  • The points $(a, b + c), (a, b), (a + c, b)$ and $(a + c, b + c)$ are the vertices of a parallelogram.

Circle Properties

  • In a circle of radius 5 cm, an arc subtends an angle of 60 degrees at the centre, implying the arc length is a portion of the circle's circumference.

Trigonometric Identities

  • $(1 + cot A)/ (cosec A) = sin A$ is a trigonometric identity.

Trigonometric Functions

  • The value of $sin^{-1} (1/2) + cos^{-1} (1/2)$ can be found by evaluating the inverse sine and cosine of 1/2.

Coordinate Geometry

  • The coordinates of the point dividing the line segment joining $(2, 4)$ and $(8, 10)$ in the ratio 3:2 can be found using the section formula.

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Test your understanding of the first four chapters of class 10 mathematics with these 50 marks questions covering topics such as coordinate geometry, circle, and trigonometry.

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