English Medium Class 9 - CBSE Question Bank Solutions

In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that: LN = MN. 

Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:

`g(x)=3x^2-2,`  `x=2/sqrt3     2/sqrt3`

In a ΔABC, if AB = AC and ∠B = 70°, find ∠A. 

Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:

`f ( x ) = 5x - pi , x = 4/5`

Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:

`f ( x) = x^2and x = 0`

Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:

`f(x) = lx + m , x = - m/1`

Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:

`f (x) = 2x +1, x = 1/2`

BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.  

In two right triangles one side an acute angle of one are equal to the corresponding side and angle of the othe Prove that the triangles are congruent.

If `x = −1/2` is a zero of the polynomial `p(x)=8x^3-ax^2 -+2` find the value of a.

The perimeter of a triangle is 300 m. If its sides are in the ratio 3 : 5 : 7. Find the area of the triangle ?

The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find the length of the perpendicular on the side of length 50 dm from the opposite vertex.

A triangle has sides 35 cm, 54 cm and 61 cm long. Find its area. Also, find the smallest of its altitudes ?

The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find the area of the triangle and the height corresponding to the longest side.

The perimeter of an isosceles triangle is 42 cm and its baše is (32) times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.

Find the area of the shaded region in the given figure.

A rhombus sheet, whose perimeter is 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of Rs 5 per m2. Find the cost of painting.

Find the area of a quadrilateral ABCD in which AB = 42 cm, BC = 21 cm, CD = 29 cm, DA =34 cm and diagonal BD =20 cm.

In the below figure, compute the area of quadrilateral ABCD.

In the below figure, PQRS is a square and T and U are respectively, the mid-points of PS
and QR. Find the area of ΔOTS if PQ = 8 cm.