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What is a perfect square number among 156, 289, 300, and 420?

Given numbers are: 156, 289, 300, 420We know that the list of perfect square numbers between 100 and 500 is:121, 144, 169, 196, 225, 256, 289,... View Article

How do you determine a perfect square?

We can determine whether the given number is a perfect square by finding its square root. We know that the square root value of a perfect square... View Article

Find the square root of 6400.

The value of the square root of 6400 is 80. This can be calculated by the division method as follows. Therefore, √6400 = 80.... View Article

What is mean median mode?

Mean, median and mode are the measures of central tendency in statistics. These terms can be defined as follows:Mean: Mean is the average of the... View Article

How do you write 6 in binary?

To convert the decimal to a binary number, divide the given number by 2 till we get the quotient 0.6/2 = 3; remainder =03/2 = 1; remainder = 11/2... View Article

Find the coordinates of the points at which line joining (2,3) and (3,2) meets the x-axis and y-axis respectively

Given coordinates are (2, 3) and (3, 2) As, we know the coordinates of any point on the x-axis is (x, 0) and the coordinates of any point on the... View Article

The equation of the straight line passing through (3,−4) and parallel to x− axis is

We know that the equation of the x-axis is y = 0. Given that, the equation of the straight line is parallel to the x-axis means, y = a, Where... View Article

The density of a cube is measured by measuring its mass and length of its side. If the maximum errors in the measurement of its mass and length are 3% and 2% respectively, the maximum error in the measurement of density would be:

We know that, Density = Mass / volume = m/l3 (Where, l3 is the volume of cube). [(Δρ/ρ)×100]max = ((Δm/m)×100)+... View Article

A1x + B1y +C1 = 0, A2x + B2y+ C2 = 0 are a system of two simultaneous linear equations, if (a1/a2) = (b1/b2) = (c1/c2), then the system has ________ solution.

Here, A1x + B1y +C1 = 0, A2x + B2y+ C2 = 0 are the system of two simultaneous linear equations. The system of equations is consistent and... View Article

xy square k is equals to (4xy + 3y)whole square – (4 xy – 3y) square. Find the value of k.

Given: xy2k = (4xy + 3y)2 - (4xy - 3y)2 As we know, (a+b)2 = a2 + b2 + 2ab (a-b)2 = a2 +b2 - 2ab xy2k = (16x2y2+24xy2 +9y2) - (16x2y2-24xy2... View Article

Find the least number which when divided by 10, 15, 30 and 60 leaves remainder 9 in each case

To find the least number which when divided by 10, 15, 30 and 60 leaves the remainder 9 in each case, we have to find the LCM of 10, 15, 30, 60... View Article

Integral sin⁴x.

Solution: Let I = ∫ sin4x dx = ∫ (sin2x)2 dx We know sin2x = (1 - cos 2x)/2 Therefore (sin2x)2 = [(1 - cos 2x)/2]2 I = ¼... View Article

Prove: (cot A + tan B)/(cot B + tan A) = cot A tan B

Solution: (cot A + tan B)/(cot B + tan A) = [(1/tan A) + tan B]/[(1/tan B) + tan A)] = (1+tan A tan B)/tan A ÷ [(1+ tan A tan B)/tan... View Article

If the tangent to the curve y = x³ + ax + b at (1, -6) is parallel to the line x-y+5 = 0, find a and b.

Solution: Given y = x3 + ax + b ..(i) Tangent to the curve, dy/dx = 3x2 + a Tangent to the curve at point (1, -6) = dy/dx at (1, -6) =... View Article

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