A to Z Exams

The angle A ofABC is found by measurement to be 630 an the area is calculated by the formula 1/2bc sin A. the percentage error in the calculated value of the area due to an error of 15 minutes in the measured value of A is

The point on y=x2+7x+2 which is closest to the line y=3x-3 is

The two curves 2x2+y2=20, x2-4y2+8=0

The approximate value of log (2.01), given that log 2=0.6934 is

The equation of the tangent to the  curve y2=4x+5 and which is parallel to0 y=2x+7 is

The radius and height of a cylinder are measured as 5 cm and 10 cm respectively and there is an error of 0.02 cm in both the measurements. The approximate error in the volume of the cone is

The base radius of a cylindrical vessel full of oil is 30 cm. Oil is drawn at the rate of 27000 cubic cm per minute. The rate at which the level of oil is falling in the vessel is

The equation of the tangent to the curve y2=4ax at (at2, 2at) is

The radius of a sphere is 3 cm. If an error of 0.03 cm is made in measuring the radius of the sphere, then the percentage error in its surface area is

If θ is the angle between the curves y2=4ax, ay=2x2 at (a, 2a) then tan θ=

The slant height of a cone is fixed as 7 cm. if the rate of increase I its height is 0.3 cm/sec, then the rate of increase of volume when height 4 cm is

At a given instant the legs of a right angled triangle are 8 inch and 6 inch respectively. The first leg decreases at 1 inch per minute and second increases at 2 inch per minute. The rate of increasing of the area after 2 minutes is

A straight line through the point (3, 4) in the first quadrant meets the axes at A and B. the minimum area of the triangle OAB is

If the normal to the curve x3-y2 =0 at (m2, -m3) is y=mx-2m3, then the value of m2  is

The function tan-1(sin x) increases in

Equation of the tangent line at y=a/4 to the curve y(x2+a2)=ax2 is

The length of the tangent of the curves x=a cos 3θ, y= a sin3θ (a>0) is

The distance between the origin and the normal to the curve y=e2x+x2 at x=0 is

If x is real, the maximum value of 3x2+9x+17/3x2-9x+17 is

A stone is dropped into a quiet pond and waves move in circles outward from the place where it strikes, at a speed of 30 cm per second. At the instant when the radius of the wave ring is 50mt, the rate of increase in the area of the wave ring is

The equation of the normal to the curve 3y2=4x+1 at (1, 2) is

The slope of the tangent to the curve x2+y2 =4 at (√2, √2) is

The length of the normal of the curve y2=x3/2a-x at (a, a) is

If θ is the angle between the curves xy=2, x2 +4y=0 then tan θ=

The least value of (x-a) (x-b) occurs at x=

In measuring the circumfence of a circle, there in an error of 0.05 cm. if with this error the circufence of the circle is measured of the circle is measured as c cm, then the percentage error in area is

The function f(x) =√25-4x2 is decreasing in

Tangent at any point of the curve (x/a)2/3+(y/b)2/3=1 makes intercepts x1and y1 on the axes. Then

f(x)= x-1/x is

A particle is moving in a straight line with the relation between the time and the distance in such a way that s=t3-9t2+24t-18. The value of its velocity when the acceleration is zero is