# Category: 10th mathematics exercise questions with answers

• ## Circles Exercise 10.5 – Class 10

Circles Exercise 10.5 – Questions: Draw a circle of radius 6 cm and construct tangents to it from an external point 10 cm away from the centre. Measure and verify the length of the tangents. Construct a pair of tangents to a circle of radius 3.5 cm from a point 3.5 cm away from the […]

• ## Circles Exercise 10.4 – Chapter Circles – Class 10

1.In the figure PQ, PR and BC are the tangents to the circle BC touches the circles at X. If PQ = 7cm find the perimeter of ∆PBC Solution: The perimeter of ∆PBC = PC + PB + BC = PC + PB + BX + CX But Cx = CR and BX = BQ […]

• ## Circles Exercise 10.3 – Chapter Circles – Class 10

Circles Exercise 10.3 – Questions: Draw a circle of radius 4 cm  and construct a tangent at any point on the circle. Draw a circle of diameter 7 cm ad constrict tangents at the ends of a diameter. In a circle of radius 3.5 cm draw two mutually perpendicular diameters. construct tangents at the ends […]

• ## Circles Exercise 10.2 Solutions – Chapter Circles – Class 10

Property related to the chords of a circle – Circle Equal chords of a circle are equidistant from the centre If the chords of a circle are at equal distance from the centre, then they are equal in length If the length of the chord increases, its perpendicular distance from the centre decreases. If the […]

• ## Quadratic Equations Exercise 9.9 – Class X

Quadratic Equations – Exercise 9.9 – Question: Draw the graphs of the following quadratic equations: (i) y = – x2 (ii) y = 3×2 (iii) y = 1/2 x2 – 2 (iv) y = x2 – 2x (v) y = x2 – 8x + 7 (vi) y = (x + 2)(2 – x) (vii) y […]

• ## Quadratic Equation Exercise 9.8 – Class X

Quadratic Equations – Exercise 9.8 – Questions: Form the quadratic equation whose roots are i) 3, 5 ii) 6, -5 iii) -3, 3/2 iv) 2/3 , 3/2 v) (2 + √3), (2 – √3) vi) (-3 + 2√5)(-3 – 2√5) B. If m and n are the roots of the equation x2 – 6x + […]

• ## Quadratic Equations – Exercise 9.7 – Class X

Find the sum and product of the roots of the quadratic equation: x2 – 5x + 8 = 0 3a2 – 10a – 5 = 0 8m2 – m = 2 6k2 – 3 = 0 pr2 = r – 5 x2 + (ab)x + (a + b) = 0 Quadratic Equation – Exercise 9.7 […]

• ## Quadratic Equation – Exercise 9.6 – Class X

So far we have learnt to find the roots of given quadratic equations by different methods. We see that the roots are all real numbers. Is it possible to determine the nature of roots of a given quadratic equation, without actually finding them? Now, let us learn about this. Nature of the roots of quadratic […]

• ## Quadratic Equations – Exercise 9.5 – Class X

We know that, in mathematics calculations and solving problems are made easier by using formulae. In the same way, quadratic equation can be easily solved by using a formula. The quadratic formula, which is very useful for finding its roots can be derived using the method of completing the square. Let us derive the quadratic […]

• ## Quadratic Equations – Exercise 9.4 – Class X

Solving Quadratic Equations by Completing the Square Method: Let us consider the quadratic equation by completing the square equation, x2 + 5x + 5 = 0. Here in the middle tem 5x cannot split into terms such that m + n = 5 and mn = 5. This means we cannot resolve the equation as […]