What must be subtracted from \[34a-22{{a}^{3}}-12{{a}^{4}}-10{{a}^{2}}-75\] so that the resulting polynomial is exactly divisible by \[-\,4{{a}^{3}}+2{{a}^{2}}-8a+30\]?
In a class 40% of the students enrolled for Maths and 60% enrolled for English. If 25% of the students enrolled for both Maths and English, what % of the students of the class did not enroll for either of the two subjects?
Three cubes of metal with edges 3 cm, 4 cm and 5 cm, respectively are melted to form a single cube. Find the lateral surface area of the new cube so formed.
There are four points P, Q, R and S marked on the side of the square ABCD so that each side is divided in the ratio \[3:2\]and PQRS also forms a square. The ratio of area of PQRS and the area of ABCD is given by:
The area of the base of a right cone is \[1386\,\,c{{m}^{2}}\]and its curved surface area is \[2310\,\,c{{m}^{2}}\]. Find the height of the cone.\[\left( Use\,\pi =\frac{22}{7} \right)\]
Thomas asked Harry to think of the two numbers such that 20% of the greater number is equal to the 30% of the smaller number. If Harry said that the sum of two numbers is 75, then the greater number he thinks of is:
Four friends Prem, Arun, Sanjay and Rajesh work in the same organisation. Salary of Arun is 20% less than that of Prem and Sanjay gets 20% more salary than Arun and Rajesh gets 20% less salary than Sanjay. If the salary of Prem is Rs. 16000, then find the salary of Rajesh.
Jacob scored 8 marks more than what he did in the previous examination in which he had obtained 20 marks. Martin scored 16 marks more than he did in the previous examination in which he had scored 80 marks. Who had shown more improvement and by how much from other?
Alam and Vinod work on a job together for four days and complete 40% of it. Alam takes leave and Vinod works for nine more days to complete the job. How long would Alam take to complete the entire job alone?
Direction : The pie-chart given here shows expenditure incurred by a family on various items and their savings. Study the chart and answer the questions based on it.
If the monthly income is Rs. 45000, then yearly savings is _______.
Direction : The pie-chart given here shows expenditure incurred by a family on various items and their savings. Study the chart and answer the questions based on it.
If the expenditure on education is Rs. 1800 more than that of rent then the expenditure on others is _________.
Direction : The pie-chart given here shows expenditure incurred by a family on various items and their savings. Study the chart and answer the questions based on it.
If the expenditure on cloth is Rs. 1680, then savings is _______.
Amit chooses three numbers x, y and z in such a way that x is twice of y and thrice of z, if the average of all the three numbers is 88, then the smallest number is:
A borrowed a sum of Rs. 6000 from B at the rate of 12% p.a. under simple interest. Immediately A gave this money to C at the same rate under compound interest compounded quarterly. Find the profit of A in doing so after 6 months.
If \[A+B\] means \['A'\] is the brother of \['B'\], \[A\,\times B\] means \['A'\] is the mother of \['B'\], \[A\div B\]means is the sister of \['B'\], then which of the following would mean\['P'\] is the maternal uncle of \['S'\]?
A man faces towards North. Turning to his right, he walks 25 metres. He then turns to his left and walks 30 meters. Next, he moves 25 meters to his right. He then turns to his right again and walks 55 meters. Finally, he turns to the right and moves 40 meters. In which direction is he from his starting point?
If 'ish Ito inm' stands for 'neat and tidy', 'upr inm sen' stands for 'small but neat', 'hsm sen rso' stands for 'good but erratic', what would 'but' stand for?
If p, q, r and s are four different positive integers selected from 1 to 50, then find the highest possible value of\[\frac{(p+q)+(r+s)}{(p+q)+(r-s)}\].
A cube of side 6 cm is painted on all its side. If it is cut into 1 cubic centimeter cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?
James exchanges a friendship band with his friends. For every band he gives someone, he gets 5 bands back. Suppose he starts the exchange with just one band. How many bands will he have after 60 exchanges?