Class 10 Maths Solved Past Paper 2019

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Section B


(i) Solve the equation ax2+4x-a=0 by completing square method. (a≠0)

(ii) Find ‘k’, if the roots of the equation (2k-1)x2+3kx+3=0   are equal.

(iii) If α and β are the roots of the equation 2x2-3x-5=0. Form a quadratic equation whose roots are 2α+1 and 2β+1.

(iv) Use synthetic division to find ‘l’ and ‘m’ if (x-1) and (x+1) are factors of polynomial x3+3lx2+mx-1.

(v) The product of two positive consecutive numbers is 182. Find the numbers.

(vi) Find x in the following proportion: 

(vii) Using componendo-dividendo theorem, solve the equation. 

(viii)  The surface area S of the sphere varies directly as the square of radius r and S=16π when r=2. Find r when S=36π

(ix) Resolved into partial fractions.

(x)  If U = {1,2,3,4,5,6,7,8,9,10}, A = {1,3,5,7,9}, B = {1,4,7,10} then verify that (A∩B)’ = A’ ∪ B’

(xi)  Find a and b if ( 2a + 5, 3 ) = ( 7, b – 4 ).

(xii)  A student has obtained following marks 82, 93, 86, 92 and 79 in 5 test of mathematics. Find the median.

(xiii)   Find area of the sector of a circle of radius 16 cm, if the angle at the centre is 60°.

(xiv)   Verify the identity: (tanΘ+cotΘ)tanΘ = sec2Θ

Section C

Q3. Prove that in an obtuse triangle, the square on the side opposite to the obtuse angle is equal to the sum of the squares on the sides containing that obtuse angle together with twice the rectangle contained by one of the sides and the projection on it of the other.

Q4. Prove that two tangents drawn to a circle from a point outside it, are equal in length.

Q5. Prove that any two angles in the same segment of a circle are equal. 

Q6. Inscribe a circle in an equilateral triangle ABC with each side of length 5cm.

Q7. A flag pole 17.9 meter high casts a 7 meter shadow. Find angle of elevation of the sun.

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