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If the perimeter and the area of a circle are numerically equal, then the radius of the circle is

(a) 2 units (b) π units (c) 4 units (d) 7 units Solution: Let r be the radius of a circle. Then Area = πr2... View Article

How to find the breadth of a rectangle if length and perimeter are given.

Solution: Let L be the length and B be the breadth. Perimeter of a rectangle, P = 2L+2B 2B = P-2L B = (P-2L)/2 We can find the breadth... View Article

Find the number of integers between 100 and 1000 that are

(i) divisible by 7 (ii) not divisible by 7 Solution: (i) We have to find out the number of integers between 100 and 1000 that are... View Article

The point (a², a+1) lies in the angle between the lines 3x-y+1 = 0 and x+2y-5 = 0 containing the origin then

(a) a ∈ (-3, 0) ⋃ (⅓, 1) (b) a ∈ (-∞, 3) ⋃ (⅓, 1) (c) a ∈ (-3, ⅓) (d) a ∈ (⅓ , ∞) Solution: Let L1:... View Article

Let M and N be two 3×3 non-singular skew-symmetric matrices such that MN = NM. If P^Tdenotes the transpose of P, then M²N²(M^TN)^-1(MN^-1)^T is equal to

(a) M2 (b) -N2 (c) -M2 (d) MN Solution: Given that M and N are non-singular skew-symmetric matrices. => MT = -M NT = -N MN =... View Article

Sam purchased 20 dozen toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?

Solution: Rate of one dozen toys = 375 Total cost price = 20×375 = 7500 Selling price of 20 dozen toys = 20×12×33 =... View Article

On the portion of the straight line, x + 2y = 4 intercepted between the axes, a square is constructed on the side of the line away from the origin. Then the point of intersection of its diagonals has co-ordinates

(a) (2, 3) (b) (3, 2) (c) (3, 3) (d) (2, 2) Solution: Let A(0, 2) and B(4, 0) be the point where the line x + 2y = 4 intercepted between the... View Article

If A = [latex]begin{bmatrix}0 & 1\ 1& 0\end{bmatrix}[/latex], then A⁴ =

Solution: Given A = A2 = A×A = A4 = A2×A2 =... View Article

A right triangle has hypotenuse of length p cm and one side of length q cm. If p – q = 1, find the length of third side of the triangle :

(a) √(2p +3) (b) √(2p +4) (c) √(2q -1) (d) √(2q +1) Solution: Given hypotenuse = p cm Length of... View Article

LCM of 3, 4, 5, 6.

Solution: LCM stands for least common multiple. LCM is the smallest possible multiple of two or more numbers. LCM of two numbers is divisible... View Article

Factors of 2876

Solution: Factors of a number are defined as the numbers that divide the original number evenly. 2876 has 6 factors. The factors of 2876 are 1,... View Article

How to turn a fraction into a decimal?

Solution: Following are the steps to convert a fraction into a decimal. Step 1: Find a number you can multiply by the denominator of the... View Article

7 x 11 x 13 x 15 15 is a Prime number. Is this True or False?

Given, 7×11×13×15+15 We can take, 15 common from the above expression; 15 ( 7×11×13+1) = 15 (1002) Now,... View Article

Find the smallest number which when divided by 15 and 27, respectively, leaves a remainder 7, in each case.

The smallest number which when divided by 15 and 27, respectively, leaves a remainder 7, is 142. Explanation: Given, the numbers are 15 and 27.... View Article

The least number which is a perfect square and is divisible by each of 16, 20 and 24 is:

The least number which is a perfect square and is divisible by each of 16, 20 and 24 is 3600. Explanation: Prime factorisation of 16 = 2 x 2 x... View Article

The number of angular nodes for 4d orbital is:

(A) 1 (B) 2 (C) 3 (D) 4 The Correct Answer is (B) 2 Solution: The number of angular nodes of 4d orbital is 2, respectively. Number... View Article

When a lead storage battery is discharged, then:

(A) Pb is formed (B) SO2 is evolved (C) H2SO4 is consumed (D) PbSO4 is consumed The Correct Answer is (C) H2SO4 is consumed. Solution:... View Article

What is the oxidation number of manganese (Mn) in potassium permanganate(KMnO4)?

(A) +5 (B) +7 (C) +8 (D) +9 The Correct Answer is (B) +7 Solution: The oxidation number of Potassium(K) in Potassium... View Article

Osmotic pressure of a solution is

(A) Equal to the pure solvent. (B) Lesser than the pure solvent. (C) Greater than the pure solvent. (D) Both (B) and (C) The Correct Answer... View Article

Extraction of zinc from zinc blende is achieved by:

(A) Electrolytic reduction (B) Roasting followed by self reduction (C) Roasting followed by reduction with carbon (D) Roasting followed by... View Article