The sum of the present ages of the father and the son is 60 yrs. Six yrs ago, the father was 5 times as old as his son. The age of the son after 6 yrs will be
The digits of a three-digit number A are written in the reverse order to form another three digit number B. If B > A and B - A is perfectly divisible by 7, then which of the following is necessarily true ?
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A telecom service provider engages male and female operators for answering 1000 calls per day. A male operator can handle 40 calls per day whereas a female operator can handle 50 calls per day. The male and the female operators get a fixed wage of Rs. 250 and Rs. 300 per day respectively. In addition, a male opeartor gets Rs. 15 per call he answers and a female operator gets Rs. 10 per call she answers. To minimize the total cost, how many male operators should the service provider employ assuming he has to employ assuming he has to employ more than 7 of the 12 female operators avilable for the job ?
In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer.
I. x2 + 28 = 11 x
II. 2y2 + 18 = 12y
Three circles A, B and C have a common center O. A is the inner circle, B middle circle and C is outer circle. The radius of the outer circle C, OP cuts the inner circle at X and middle circle at Y such that OX = XY = YP. The ratio of the area of the region between the inner and middle circles to the area of the region between the middle and outer circle is
A plot of land is in the shape of a trapezium whose dimensions are given in the figure below :
Hence the perimeter of the field is
Consider a sequence of seven consecutive integers. The average of the first five integers is n. The average of all the seven integers is :
In the figure given below, ABOP is a rectangle and O is the centre of the circle. It is also given that AB = BC and the measure of the angle ∠ABC is 60. Find the measure of the angle ∠OPN.
In ΔABC, ∠B is a right angle, AC = 6 cm, and D is the mid-point of AC. The length of BD is :
Consider the following two curves in the x-y plane
y = x3 + x2 + 5
y = x2 + x + 5
Which of the following statements is true for −2 ≤ x ≤ 2?
A father left a will of Rs.35 lakhs between his two daughters aged 8.5 and 16 such that they may get equal amounts when each of them reach the age of 21 years. The original amount of Rs.35 lakhs has been instructed to be invested at 10% p.a. simple interest. How much did the elder daughter get at the time of the will?
There are 3 containers : A, B and C which contain water, milk and acid respectively in equal quantities. 10% of the content of A is taken out and poured into B. Then the same amount from B is transferred to C, from which again the same amount is transferred to A. What is the proportion of milk in container A at the end of the process?
Let a, b, c be distinct digits. Consider a two-digit number 'ab' and a three-digit number 'ccb', both defined under the usual decimal number system, if ab2 = ccb > 300, then the value of b is
A positive whole number M less than 100 is represented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then M equals
If a1 = 1 and an+1−3an+2 = 4n for every positive integer n, then a100 equals
A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6:7:8:9:10. In all papers together, the candidate obtained 60% of the total marks then, the number of papers in which he got more than 50% marks is :
Number of triangles formed in a decagon by joining its vertices is
If S(n) is the set of all factors of n , then what is the probability that a randomly chosen element of S(1050) is a multiple of 5 ?
The cost of 13 kgs of sugar is Rs 195. The cost of 17 kg of rice is Rs 544 and the cost of 21 kgs of wheat is Rs 336. What is the total cost of 21 kgs of sugar, 26 kgs of rice and 19 kgs of wheat?
if α, β are the roots of the equation ax² + bx + c = 0, then the value of α³ + β³ is
A circular running path is 726 mts in circumference. Two men start from the same point and walk in opposite directions at 3.75 km/hr and 4.5 km/hr respectively. When will they meet for the first time?
A group of workers can do a piece of work in 24 days. However as 7 of them were absent it took 30 days to complete the work. How many people actually worked on the job to complete it?
Let S denote the infinite sum 2 + 5x + 9x2 + 14x3 + 20x4 + ...., where |x| < 1 and the coefficient of xn - 1 is
Let function f : R → R be defined by f (x) = 2x + sin x for x ∈ R. Then F is
f(x)= 2x3 + px2 + qx - 4 and f(2)= 0 , find the value of p + q , where p and q are non zero. If f(x)= 0 has three real roots, all of them being integers and further two of three roots are equal.
Rakesh traveled from city A to city B covering as much distance in the second part as he did in the first part of this journey. His speed during the second part was twice as that of the speed during the first part of the journey. What is his average speed of journey during the entire travel?