List of top Mathematics Questions asked in CBSE CLASS XII

The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is
If the radius of a sphere is measured as 9 m with an error of 0.03 m, then find the approximate error in calculating in surface area.
If the radius of a sphere is measured as 7 m with an error of 0.02m, then find the approximate error in calculating its volume.
Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1%

Find the approximate change in volume V of a cube of side x meters caused by increasing side by 1%.

 

Find the approximate value of f (5.001), where f (x) = x3 − 7x2 + 15

Find the approximate value of f (2.01), where f (x) = 4x2+5x + 2

Using differentials, find the approximate value of each of the following up to 3 places of decimal (i) 25.3 (ii)49.5 (iii)0.6(iv)(0.009)1/3(v)(0.999)1/10(vi)(15)1/4(vii)(26)1/3(viii)(225)1/4(ix)(82)1/4(x)(401)1/2(xi)(0.0037)1/2(xii)(26.57)1/3(xiii)(81.5)1/4(xiv)(3.968)1/2(xv)(32.15)1/5

The anti derivative of \(\bigg(\sqrt x+\frac{1}{\sqrt x}\bigg)\) equals

The line y = x + 1 is a tangent to the curve y2 = 4x at the point

Find the equation of the normals to the curve y = x3 + 2x + 6 which are parallel to the line x + 14y + 4 = 0.

 The slope of the normal to the curve y = 2x2 + 3 sin x at x = 0 is

Find the equation of the tangent to the curve which is parallel to the line 4x − 2y + 5 = 0

Find the equations of the tangent and normal to the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}\)=1at the point (x0,y0).

Prove that the curves x = y2 and xy = k cut at right angles if 8k2 = 1. [Hint: Two curves intersect at right angle if the tangents to the curves at the point of intersection are perpendicular to each other.]

A square piece of tin of side 18 cm is to made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible?
The points on the curve \(9y^2 = x^3\) , where the normal to the curve makes equal intercepts with the axes are
Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum
The normal to the curve \(x^2 = 4y\) passing \((1, 2)\) is
The normal at the point \((1, 1)\) on the curve \(2y + x^2 = 3\) is
The line \(y = mx + 1\) is a tangent to the curve \(y^2 = 4x\) if the value of \(m\) is
The slope of the tangent to the curve \(x=t^2+3t-8,y=2t^2-5\) at the point \((2, −1)\) is

Find two positive numbers \(x \space and\space  y\) such that their sum is \(35\) and the product \(x^{2} y^{5}\) is a maximum

Find the points on the curve y = x3 at which the slope of the tangent is equal to the Y-coordinate of the point.

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height \(h\) and semi vertical angle \(α\) is one-third that of the cone and the greatest volume of cylinder is \(\frac{4}{27}πh^3 \,tan^2α\)