In an examination, a student was asked to find\[\frac{3}{14}\]of a certain number, by mistake, he found\[\frac{3}{4}\]of it. His answer was 150 more than the correct answer. The given number is
The value of\[\frac{{{(1.5)}^{3}}+{{(4.7)}^{3}}+{{(3.8)}^{3}}-3\times 1.5\times 4.7\times 3.8}{{{(1.5)}^{2}}+{{(4.7)}^{2}}+{{(3.8)}^{2}}-1.5\times 4.7-4.7\times 3.8-3.8\times 1.5}\]
A cube of 9 cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of base are 15 cm and 12 cm. Then, the rise in water level in the vessel is
A rectangular block measuring \[\text{18}\,\,\text{cm }\!\!\times\!\!\text{ 15}\,\,\text{cm }\!\!\times\!\!\text{ 12}\,\,\text{cm}\] is cut into exact number of cubes, the least possible number of cubes will be
The simplification of \[\left( 1-\frac{1}{2} \right)\left( 1-\frac{1}{3} \right)\left( 1-\frac{1}{4} \right)...\left( 1-\frac{1}{100} \right)\]results in
Three women started a business by sharing equal amount of the total investment. After some calculations they found that if they get two more equal investors, each of the five will have to pay Rs. 15000 less. What was the total investment?
A man travels 35 km partly at 4 km/h and at 5 km/h. If he covers former distance at 5 km/h and later at 4 km/h, he could cover 2 km more in the same time. The time taken to cover the whole distance at original rate is
Satish travelled 1200 km by air which formed (2/5) of his trip. One-third of the whole trip, he travelled by car and the rest of the journey he performed by train. The distance travelled by train was
A square has its side equal to the radius of a sphere. The square revolves round a side to generate a surface of total area S. If A be the surface area of the sphere, which one of the following is correct?
The diameter of a solid metallic right circular cylinder is equal to its height. After cutting out the largest possible solid sphere S from this cylinder the remaining material is recast to form a solid sphere\[{{S}_{1}}.\] What is the ratio of the radius of sphere S to that of sphere \[{{S}_{1}}?\]
In a school, the average age of students is 6 yr the average age of 12 teachers is 40 yr. If the average age of the combined group of all the teachers and students is 7 yr, then the number of students
A fan is listed at Rs. 1500 and a discount of 20% is offered on the list price. What additional discount must be offered to the customer to bring the net price to Rs. 1104?
A cistern has two pipes. One can fill it with water 8 h and other can empty it in 5 h. In how many hours will the cistern be emptied if both the pipes are opened together when 3/4 of the cistern is already full of water?
20 boys and 32 girls form a group for some social cause work. During their membership drive same number of boys and girls joined the group. How many members the group have had, if the ratio between boys and girls is 3 : 4 respectively?
A man and a boy received Rs. 800 as wages for 5 days for the work they did together. The man's efficiency in the work was three times that of the boy. What are the daily wages of the boy?
A train running at \[\frac{7}{11}\]of its normal speed reached place in 22 h. How much time could be save the train would have run at its normal speed?
The curved surface of a cylindrical pillar is \[264\,\,{{\text{m}}^{2}}\] and its volume is \[924\,\,{{\text{m}}^{3}}.\] The ratio of its diameter to its height is \[\left[ \text{use}\,\,\pi =\frac{22}{7} \right]\]
A began business with Rs. 45000 and was joined after wards by B with Rs. 54000. After how many months did B join if the profits at the end of the year were divided in the ratio 2 : 1?
The areas of a square and a rectangle are equal. The length of the rectangle is greater than the length of a side of the square by 5 cm and the breadth is less than the length of the side of the square by 3 cm. The perimeter of the rectangle is
The ratio of incomes of two persons is 5 : 3 and that of their expenditures is 9 : 5. If they save Rs. 2600 and Rs. 1800 respectively, their incomes are
A sum of Rs. 1500 is lent out in two parts in such a way that the simple interest on one part at 10% per annum for 5 yr is equal to that on another part at 12.5% per annum for 4 yr. The sum lent out at 12.5% is
Find the ratio in which the point P\[\left( \frac{3}{4},\frac{5}{12} \right)\] the line segment joining the points A\[\left( \frac{1}{2},\frac{3}{2} \right)\]
There is a small island in the middle of a 100 m wide river. There is tall tree on the island. Points P and Q are points directly opposite to each other on the two banks and in line with the tree. If the angles of elevation of the top of the tree at P and Q are \[30{}^\circ \]and \[45{}^\circ .\]Then, the height of tree is
If ABC is a triangle, then which of the following statements are correct? I. \[\sin A+B=\sin C\] II. \[\sin \left( \frac{A+B}{2} \right)=\cos \frac{C}{2}\] III. \[\tan \frac{(A+B+C)}{2}=\cot C\] IV. \[\tan \frac{(A-B-C)}{2}=-\cot A\]
What is the value of x in the equation \[x\frac{\text{cose}{{\text{c}}^{2}}30{}^\circ {{\sec }^{2}}45{}^\circ }{8\,\,{{\cos }^{2}}45{}^\circ {{\sin }^{2}}60{}^\circ }={{\tan }^{2}}60{}^\circ -{{\tan }^{2}}30{}^\circ ?\]
ABCD is a square, P, Q, R and 5 are points on the sides AB, BC, CD and DA, respectively such that AP = BQ = CR = DS. What is the value of\[\angle SPQ\]?
Find the values of a and b so that the polynomials \[p\,\,(x)\]and \[q\,\,(x)\]have \[(x+1)(x+3)\]as their HCF \[p\,\,(x)=({{x}^{2}}+3x+2)({{x}^{2}}+2x+a)\] \[q\,\,(x)=({{x}^{2}}+7x+12)({{x}^{2}}+7x+b)\]
X, Y and Z three friends started a business, investment is 2 times of Y's investment and investment is 5 times of Z's investment. What would be the profit of Y if, total profit is Rs. 25600?
Directions: Study the following graph carefully and answer the questions given below it. Target and actual production of cement (in 1000 gunny bags) of a factory for a period of six years
If the combined targeted production of two adjacent years in compared to the combined actual production (of these two years) then in which of the following pairs of years will it have a complete match?
Directions: Study the following graph carefully and answer the questions given below it. Target and actual production of cement (in 1000 gunny bags) of a factory for a period of six years
What was the difference between the target set and the actual production for year 2000-01 (unit gunny bags)?
Directions: Study the following graph carefully and answer the questions given below it. Target and actual production of cement (in 1000 gunny bags) of a factory for a period of six years
In which of the following years was the actual production as percentage of target production
Directions: Study the following graph carefully and answer the questions given below it. Target and actual production of cement (in 1000 gunny bags) of a factory for a period of six years
The actual production of cement for 1997-98 was how many times that of the target set for that year