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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... 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... 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... 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... View Article

Integral sin⁴x.

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

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

Solution: Given A = \(\begin{array}{l}\begin{bmatrix}0 & 1\\ 1& 0\\\end{bmatrix}\end{array} \) A2 = A×A = \(\begin{array}{l}\begin{bmatrix}0 & 1\\ 1& 0\\\end{bmatrix}\begin{bmatrix}0 &... 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

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