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... View Article
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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... 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... 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)... View Article
Locus of all point P (x, y) satisfying x3 + y3 + 3xy = 1 consists of union of
(a) A line and an isolated point (b) A line pair and an isolated point (c) A line and a... View Article
There is a boy who has six brothers. Each of them has 6 brothers and one sister. The boy’s father’s name is Mr. Patrick. How many children does Mr. Patrick has?
Solution: The boy has 6 brothers. Given that each of them has 6 brothers and one sister. So total number... View Article
What is absolute value?
The absolute value of a number is the distance of a number from the origin of a number line. It... View Article
What is solid angle formula?
The formula of solid angle(Ω) is, Ω = (Area of part of the spherical surface subtended)/(radius of the area of the... View Article
In a 3-digit number, unit’s digit is one more than the hundred’s digit and ten’s digit is one less than that hundred’s digit. If the sum of the original 3-digit number and numbers obtained by changing the order of digits cyclically is 2664. What is the number?
Let hundred digit = b ten digit = b−1 unit digit = b+1 First form of Number =100×b+100(b−1)+b+1 = 111b... View Article
Write 14/9 as mixed fraction.
Given, 14/9 is an improper fraction Dividing 14 by 9 we get; quotient = 1 remainder = 5 Therefore, the... View Article
The following table gives the distribution of students of two sections according to the marks obtained by them. Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.
Given, Section A Section B Marks Frequency Marks Frequency 0-10 3 0-10 5 10-20 9 10-20 19 20-30 17 20-30... View Article
Find the domain and range of 5 sin(x – π/6 ).
The domain and range of 5 sin(x – π/6 ). Domain: ( − ∞ , ∞ ) , { x... View Article
The number of different ways in which the letters of the word “YOGESH” can be placed in 8 boxes.
Given, the word YOGESH The total number of ways in which the rows can be filled = 8C6 =28 ways... View Article
A random variable x follows binomial distribution with mean 3 and variance 3/2, and P(x ≤5) = (63/2^x). Find the value of x.
Let n and p be the parameters of the binomial distribution. Mean = np=3 Variance = npq = 3/2 (npq/np)... View Article
A problem in statistics is given to five students A, B, C and D. Their chances of solving it are 1/3, 1/4, 1/5 and 1/6 respectively. What is the probability that the problem will be solved?
Probability of A solving = 1/3 P (A not solving) = 1 – 1/3 = 2/3 Similarly, P (B not... View Article
If two tangents drawn from a point P to the parabola y^2=4x are at right angles, then the locus of P is (a) 2x+1=0 (b) x=-1 (c) 2x-1=0 (d) x=1
Answer: (b) x=-1 If tangents are perpendicular from point P then point P lies on directrix of parabola Locus of P... View Article
The graph of which of the following equations passes through the origin? (i) y = 2x + c (ii) y = 2x – c (iii) y = 2x
Answer: (iii) y = 2x If x = 0, then y = 2(0) = 0
Two varieties of oil are mixed in the ratio 4:3 to produce first quality and if they are mixed in the ratio 2:3, Second quality is obtained. How many kg of the first quality be mixed with 10 kg of the second quality so that a third quality having the 2 varieties in the ratio 5:4 may be produced?
Let the common ratio of the first quality oil be x. Given, the ratio is 4:3 Therefore, the total quantity... View Article
Find the range of eccentricity of the ellipse (x^2/a^2) + (y^2/b^2) = 1 (a>b) such that the line segment joining the foci does not subtend a right angle at any point on the ellipse
Let the point on ellipse be P (a cosθ, b sinθ) Let A and B are the diameter of the ellipse... View Article
A watch loses 3% time during the first week and then gains 2% time during the next one week. If the watch was set right at 12 noon on a Sunday, what will be the time that the watch will show exactly 14 days from the time it was set right ?
Number of hours in a week = 7 x 24 = 168 hours The watch loses 3% time during the... View Article
