English Medium कक्षा १० - CBSE Question Bank Solutions

Points A(-1, y) and B(5,7) lie on the circle with centre O(2, -3y).Find the value of y.

If the point A(0,2) is equidistant from the points B(3,p) and C(p, 5), find p.

ABCD is a rectangle whose three vertices are A(4,0), C(4,3) and D(0,3). Find the length of one its diagonal.

If the point P(k - 1, 2) is equidistant from the points A(3, k) and B(k, 5), find the value of k.

Prove that the diagonals of a rectangle ABCD with vertices A(2,-1), B(5,-1) C(5,6) and D(2,6) are equal and bisect each other

If the point C(k,4) divides the join of A(2,6) and B(5,1) in the ratio 2:3 then find the value of k. 

Find the point on x-axis which is equidistant from points A(-1,0) and B(5,0)

Find the value of a, so that the point ( 3,a ) lies on the line represented by 2x - 3y =5 .

If the points  A(4,3)  and B( x,5) lie on the circle with center  O(2,3 ) find the value of x .

Find the centroid of ΔABC  whose vertices are A(2,2) , B (-4,-4) and C (5,-8).

In what ratio does the point C (4,5) divides the join of A (2,3)  and B (7,8) ?

 If the points  A (2,3),  B (4,k ) and C (6,-3) are collinear, find the value of k.

Find the coordinates of the points of trisection of the line segment joining the points (3, –2) and (–3, –4) ?

If the quadratic equation (c² – ab) x² – 2 (a² – bc) x + b² – ac = 0 in x, has equal roots, then show that either a = 0 or a³ + b³ + c³ = 3abc ?

Solve for x:

4x² + 4bx − (a² − b²) = 0

Find the ratio in which the point (−3, k) divides the line-segment joining the points (−5, −4) and (−2, 3). Also find the value of k ?

Solve the given quadratic equation for x : 9x² – 9(a + b)x + (2a² + 5ab + 2b²) = 0 ?

A cylindrical tub, whose diameter  is 12 cm and height 15 cm is full of ice-cream. The whole ice-cream is to be divided into 10 children in equal ice-cream cones, with conical base surmounted by hemispherical top. If the height of conical portion is twice the diameter of base, find the diameter of conical part of ice-cream cone ?

A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole has a radius of `3/2` cm and its depth is `8/9 `cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape.

In Figure 4, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the shaded region.\[[Use\pi = 3 . 14]\]