English Medium Class 10 - CBSE Question Bank Solutions

If the sum of the roots of the equation \[x^2 - \left( k + 6 \right)x + 2\left( 2k - 1 \right) = 0\] is equal to half of their product, then k =

If a and b are roots of the equation x² + ax + b = 0, then a + b =

A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.

If one of the equation ax² + bx + c = 0 is three times times the other, then b² : ac =

If one root the equation 2x² + kx + 4 = 0 is 2, then the other root is

If one of the equation x² + ax + 3 = 0 is 1, then its other root is

If one root of the equation 4x² − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ =

If y = 1 is a common root of the equations \[a y^2 + ay + 3 = 0 \text { and } y^2 + y + b = 0\], then ab equals

The values of k for which the quadratic equation  \[16 x^2 + 4kx + 9 = 0\]  has real and equal roots are

Find the number of metallic circular discs with a 1.5 cm base diameter and of height  0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.

How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimension  6cm \[\times\] 42cm \[\times\] 21 cm.

A solid cuboid of iron with dimensions 53 cm ⨯ 40 cm ⨯ 15 cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe.

The largest cone is curved out from one face of solid cube of side 21 cm. Find the volume of the remaining solid. 

Three solid spheres of radii 3, 4 and 5 cm respectively are melted and converted into a single solid sphere. Find the radius of this sphere.

The inner and outer radii of a hollow cylinder are 15 cm and 20 cm, respectively. The cylinder is melted and recast into a solid cylinder of the same height. Find the radius of the base of new cylinder.

A cylindrical bucket 28 cm in diameter and 72 cm high is full of water. The water is emptied into a rectangular tank 66 cm long and 28 cm wide. Find the height of the water level in the tank.

A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter  4 \[\frac{2}{3}\] cm and height 3 cm. Find the number of cones so formed.

Show that the points (−4, −1), (−2, −4) (4, 0) and (2, 3) are the vertices points of a rectangle.

 Prove hat the points A (2, 3) B(−2,2) C(−1,−2), and D(3, −1) are the vertices of a square ABCD.