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What is the greatest number by which 1037 and 1159 can both be divided exactly?

As we know, 1037 = 17×61 1159 = 19×61 Hence, the HCF of 1037 and 1159 is 61. Therefore, the greatest number by which 1037 and... View Article

what is the square root of 353?

The square root of 353 is approximately equal to 18.788. As we know, the square root of 353 is a number, which when multiplied by itself results... View Article

Convert 0.05 into fraction.

0.05 in fraction is 1/20. Explanation: First, write the given number as a fraction. (i.e.) 0.05/1. Since, the number 0.05 has two digits after... View Article

Convert 75 into binary.

75 in binary is 10010112 Explanation: To convert 75 into binary, follow the below steps: Step 1: Divide 75 by 2, and use the quotient obtained... View Article

Rahul bought a sweater and saved Rs. 20 when a discount of 25% was given. What was the price of the sweater before the discount?

Let the price of the sweater before the discount be “x”. Hence, 25% of x = 20 (25/100) of x = 20 x = (20×100)/25 x =... View Article

If the HCF of 85 and 153 is expressible in the form of 85m -153, the value of m is

(a) 1 (b) 2 (c) 3 (d) 4 Solution: Correct Answer: Option (b) 2 Explanation: HCF of 85 and 153 is 17. Now equate 17 and 85m -153, to find... View Article

If nth order square matrix A is a orthogonal, then ∣adj(adjA)∣ is

(a)always -1 if n is even (b) always 1 if n is odd (c) always 1 (d) none of these Solution: Correct Answer: Option (b)... View Article

What is the value of 3 power -2?

The value of 3 power -2 is 0.1111. We know that 3 power -2 means 3-2. 3-2 is written as 1/32, which is equal to 1/9 If 1 is divided by 9, we... View Article

The number of all possible triplets (a1, a2, a3) such that a1 + a2 cos (2x) + a3 sin^2 (x) = 0 for all x is

(a) Zero (b) One (c) Three (d) Infinite Solution: Correct Answer: Option (d) Infinite Explanation: Given: a1 + a2 cos (2x) + a3 sin2(x) =... View Article

What is a homogeneous differential equation?

The homogeneous differential equation is a differential equation, which is formed using the homogeneous function. That is, the differential... View Article

Let y = (A + Bx)e^(3x) is a solution of the differential equation(d^2y)/dx^2 + m(dy/dx) + ny = 0; m, n ∈ I, then find m and n.

Given,y = (A + Bx)e3xDifferentiating w.r.t x on both sides,dy/dx = 3(A + Bx)e3x + Be3xAdding my on both sides,(dy/dx) + my = 3(A + Bx)e3x + Be3x... View Article

Solve: 2(sin x – cos 2x) – sin 2x(1 + 2 sin x) + 2 cos x = 0

2(sin x − cos 2x) − sin 2x(1 + 2 sin x) + 2 cos x = 0 ⇒ 2 sin x − sin 2x − 2 cos 2x − 2 sin x sin 2x + 2 cos x = 0 We know that, sin 2x = 2 sin x... View Article

If am = bl, then find whether the pair of linear equation ax + by = c and lx + my = n has no solution, a unique solution or infinitely many solutions.

Given, am = bl a/l = b/m....(i) And the given pair of linear equations are: ax + by = c lx + my = n Comparing with the standard form of pair of... View Article

In the figure given below, AD = 4 cm, BD = 3 cm and CB = 12 cm, then cot θ equals

(a) 3/4 (b) 5/12 (c) 4/3 (d) 12/5 Correct answer: (d) 12/5 Solution: Given, AD = 4 cm BD = 3 cm CB = 12 cm In right ∆ABC, AB2 = AD2 + BD2 AB2 =... View Article

What is the square root of 106?

The value of the square root of 106 is 10.295630141.... The square root of 106 can be estimated using the long division methods as given below:... View Article

What is a quadratic equation formula?

We know that the standard form of a quadratic equation is ax2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0. If α, β are the root of a... View Article

What are the types of linear equations?

There are three types of linear equations as given below: 1. Conditional equation: This is the most commonly used linear equation. Also, the... View Article

The minute hand of a clock overtakes the hour hand at intervals of 65 minutes. How much in a day does the clock gain or lose?

Solution: The minute hand gains 55 min. spaces over the hour hand in 60 minutes (in a correct clock). To be together again, the minute hand... View Article

At what time between 4 and 5, will the hands of a clock coincide?

(a) 15.81 min (b) 21.81 min (c) 23.81 min (d) 33.48 min Solution: Angle divisions of a clock A close observation of a clock reveals that an... View Article

If the product of perpendiculars from the foci upon the polar of P be constant and equal to c², prove that the locus of P is the ellipse b⁴x²(c² + a²e²) + c²a⁴y² = a⁴b⁴.

Solution: Let the equation of the ellipse is (x2/a2) + (y2/b2) = 1 The coordinates of foci are (ae, 0) and (-ae, 0). Let the coordinates of... View Article