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The selling price of plot is directly proportional to the square of area of plot in m2. If the cost price of square shaped plot is Rs. 50000 and the profit percent of a dealer is 25% on selling square shaped plot then find the cost price of rectangular shaped plot if the dealer gains 50% on selling of rectangular plot where the length and breadth of rectangular plot is 30 m and 20 m while the side length of square plot is 20 m.
A rectangular plot has a concrete path running in the middle of the plot parallel to the breadth of the plot. The rest of the plot is used as a lawn which has an area of 420 sq. m. If the width of the path is 4 m and the length of the plot is greater than its breadth by 36 m, what is the area of the rectangular plot? 
PAB is a tangent which is common to two circles which touches each other at point X. The tangent touches the smaller circle at A and larger circle at B. If PA = 20 cm and the radius of smaller circle is 15 cm, then find the radius of larger circle.
A tangent is drawn from a point p outside the circle, which touches the circle at point A and B, another tangent is drawn from a point E on the circumference on the circle, which touches the line PA and PB at C and D, if PC measures 8 cm, PD measures 9 cm and CD measures 7 cm, then find the radius of circle.
At equilibrium condition, the chemical potential of a material in different phases in contact with each other is equal. The chemical potential for a real gas (μ) is given by (where, μ = standard chemical potential at unit fugacity (f° = 1 atm.) and the gas behaves ideally.)
A big rectangular plot of area 4320 m2 is divided into 3 square-shaped smaller plots by fencing parallel to the smaller side of the plot. However some area of land was still left as a square could not be formed. So, 3 more square-shaped plots were formed by fencing parallel to the longer side of the original plot such that no area of the plot was left surplus. What are the dimensions of the original plot ?
Consider the four statements given below about the function f(x) = x4 - x2 in the range $$ - \infty P. The plot of f(x) versus x has two maxima and two minima.
Q. The plot of f(x) versus x cuts the x axis at four points.
R. The plot of f(x) versus x has three extrema.
S. No part of the plot f(x) versus x lies in the fourth quadrant.
Pick the right combination of correct choices from those given below.
Which of the following is/are correct about a strictly binary tree? A. A binary tree is called strictly binary tree if every non-­leaf node of it has non empty left and right sub tree B. In strictly binary tree can have two children or no child C. A strictly binary tree with n leaves always contact 2n­-1 nodes
Two circles touch each other at point X. A common tangent touches them at two distinct points Y and Z. If another tangent passing through X cut YZ at A and XA = 16 cm, then what is the value (in cm) of YZ?
Centre of two concentric circles is O. The area of two circles is 616 cm2 and 154 cm2 respectively. A tangent is drawn through point A on the larger circle to the smaller circle. This tangent touches small circle at B and intersects larger circle at C. What is the length (in cm) of AC?