The value of \[\left\{ 1-\frac{1}{2} \right\}\times \left\{ 1-\frac{1}{3} \right\}\times \left\{ 1-\frac{1}{4} \right\}\times ...\times \left\{ 1-\frac{1}{n} \right\}\] equal to
When simplified, the expression \[{{(0.001)}^{\frac{1}{3}}}-{{(0.0016)}^{\frac{1}{4}}}\times {{3}^{0}}+{{\left( \frac{5}{4} \right)}^{-1}}\]is equal to
A six digit number is formed by repeating a three digit number; for example, 256, 256 or 678, 678 etc. Any number of this form is always exactly divisible by
A man, a woman and, a boy can complete a job in 3, 4 and 12 days respectively. How many boy must assist 1 man and 1 woman to complete the job in \[\frac{1}{4}\]of a day?
A contractor undertakes to make a road in 40 days and employs 25 men. After 24 days, he finds that only one-third of the road is made. How many extra men should he employ so that he is able to complete the work 4 days earlier?
A cricketer whose bowling average is 24.85 runs per wicket, takes 5 wickets for 52 runs and there by decreases his average by 0.85. The number of wickets taken by him till the last match was
800 chocolates were distributed among the students of a class. Each student got twice as many chocolates as the number of students in the class. The number of students in the class was
A builder borrows Rs. 2550 to be paid back with compound interest at the rate of 4% per annum by the end of 2 yr in two equal yearly instalments. How much will each instalment be?
In a class 60% of the student pass in Hindi and 45% pass in Sanskrit. If 25% of them pass in at least one subject, what percentage of the students fail in both the subjects?
A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km/h and 11 km/h respectively. What is the distance between them after 6 min?
If a man reduces his speed to \[\frac{2}{3},\]he takes 1 h more a walking a certain distance. The time (in h) to cover the distance with his normal speed is
The arithmetic mean of the scores of a group students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25 mean score of 31. The mean score of remaining 55% is
The marked price of a watch was Rs. 720. A man bought the same for Rs. 550.80, after getting two successive discounts, the first at 10%. What was second discount rate?
A tap can empty a tank in 1 h. A second tap can empty it in 30 min. If both the taps operate simultaneously, how much time is needed to empty the tank?
ABC is a triangle with base AB. D is a point on AB such that AB = 5 and DB = 3. What is the ratio of the area of \[\Delta ADC\] to the area of\[\Delta ABC\]?
How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/h in the direction of the moving train if the speed of the train is 63 km/h?
A, B and C hired a field for Rs. 800 for the whole year. A puts in 50 cows for 2 months, B 80 cows for 5 months and C 60 cows and 30 calves for 4 months. How much should C pay if one cow eats as much as 2 calves?
Alok, Bhism and Chandra hired a meadow jointly for the whole year. Alok put in 80 buffaloes for 10 months, Bhism 100 buffaloes for 5 months and Chandra 150 buffaloes for 4 months. If Alok paid Rs. 320 as rent, what is the total rent for the meadow?
Milk and water in two vessels A and B are in the ratio 4 : 3 and 2 : 3 respectively. In what ratio the liquids in both the vessels should be mixed to obtain a new mixture in vessel C containing half milk and half water?
A steamer goes downstream from one port to another in 4 h. It covers the same distance upstream in 5 h. If the speed of the stream is 2 km/h, the distance between the two ports is
If \[{{\sin }^{2}}x+{{\sin }^{2}}y+{{\sin }^{2}}z=\,\,{{(\sin x+\sin y+\sin z)}^{2}},\]then which of the following expressions must necessarily vanish?
Two houses are collinear with the base of a tower and are at distance 3 m and 12 m from the base of the tower. The angles of elevation from these two houses of the top of the tower are complementary. What is the height of the tower?
In the given figure, ABC is a right angled triangle, right angled at B. BC = 21cm and AB = 28 cm. Width AC as diameter of a semi-circle and width BC as radius a quarter circle are drawn. What is the area of the shaded portion?
The area of an equilateral triangle, inscribed in a circle is\[4\sqrt{3}\,\,\text{c}{{\text{m}}^{2}}.\]The area of the circle in terms of \[\pi \] will be
Two medians drawn from acute angles of a right angled triangle intersect at an angle k/g. If the length of the hypotenuse of the triangle is 3 units, then area of the triangle (in sq units) is
A toy is in the form of a cone mounted on a hemisphere such that the diameter of the base the cone is equal to that of the hemisphere. If the diameter of the base of the cone is 6 cm and its height is 4 cm, what is the surface area of the toy (in sq cm)? (Take \[\pi =3.14\])
A cylinder having base of circumference 60 cm is rolling without sliding at a rate of 5 round per seconds. How much distance will the cylinder roll in 5 s?
The outer and inner diameters of a circular pipe are 6 cm and 4 cm, respectively. If its length is 10 cm, then what is the total surface area (in sq cm)?
A and B enter into a partnership. A contributes Rs. 5000 while B contributes Rs. 4000. After 1 month B withdraws \[\frac{1}{4}\]part of his contribution and after 3 months from the starting A puts Rs. 2000 more. When B withdraws his money at the same time C also joins them with Rs. 7000. If at the end of 1 yr there is a profit of Rs. 1218, what will be share of C in the profit?
Three different containers contain different qualities of mixtures of milk and water, whose measurements are 403 kg, 434 kg and 465 kg. What biggest measure must be there to measure all the different quantities exactly?
On a Rs. 10000 payment order a person has choice between three successive discounts of 10%, 10% and 30% and three successive discounts of 40%, 5% and 5%. By choosing the better one, he can save
My grandfather was 8 times older to me 16 yr ago. He would be 3 times of my age 8 yr from now.8 yr ago, what was the ratio of my age to that of my grandfather?
The marked price of an electric iron is Rs. 690. The shopkeeper allows a discount of 10% and gains 8%. If no discount is allowed, his gain per cent would be
A shopkeeper sold an air-conditioner for Rs. 25935 with a discount of 9% and earned a profit of 3.74%. What would have been the percentage of profit earned if no discount were offered?
A pen is listed for Rs. 12. A discount of 15% is given on it A second discount is given bringing the price down to Rs. 8.16. The rate of second discount is
A dealer buys an article marked at Rs. 25000 with 20% 2nd 5% off. He spends Rs. 1000 on its repairs and sells it for Rs. 25000. What is his gain or loss per cent?
In what ratio Darjeeling Tea costing Rs. 320 per kg be mixed with Assam Tea costing Rs. 250 per kg so that there is a gain of 20% by selling the mixture at Rs. 324 per kg?
A cistern is normally filled in 8 h, but takes 2 h more to fill because of a leak in its bottom. If the cistern is full, the leak will make it empty in