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If $(x^{2}+\frac{1}{x^{2}})=25$ and $x>0$ then the value of $(x^{7}+\frac{1}{x^{7}})$ is
Let p, q and r be three natural numbers such that their sum is 900, and r is a perfect square whose value lies between 150 and 500. If p is not less than 0.3q and not more than 0.7q, then the sum of the maximum and minimum possible values of p is
The average salary of 5 managers and 25 engineers in a company is 60000 rupees. If each of the managers received 20% salary increase while the salary of the engineers remained unchanged, the average salary of all 30 employees would have increased by 5%. The average salary, in rupees, of the engineers is
If $f(x)=(x^{2}+3x)(x^{2}+3x+2)$, then the sum of all real roots of the equation $\sqrt{f(x)+1}=9701,$ is
The rate of water flow through three pipes A, B and C are in the ratio 4: 9: 36. An empty tank can be filled up completely by pipe A in 15 hours. If all the three pipes are used simultaneously to fill up this empty tank, the time, in minutes, required to fill up the entire tank completely is nearest to
For real values of x, the range of the function $f(x)=\frac{2x-3}{2x^{2}+4x-6}$ is
If $12^{12x}\times4^{24x+12}\times5^{2y}=8^{4z}\times20^{12x}\times243^{3x-6}$ where x, y and z are natural numbers, then $x+y+z$ equals
In a school with 1500 students, each student chooses any one of the streams out of science, arts, and commerce, by paying a fee of Rs 1100, Rs 1000, and Rs 800, respectively. The total fee paid by all the students is Rs 15,50,000. If the number of science students is not more than the number of arts students, then the maximum possible number of science students in the school is
ABCD is a trapezium in which AB is parallel to DC, AD is perpendicular to AB, and $AB=3DC$. If a circle inscribed in the trapezium touching all the sides has a radius of 3 cm, then the area, in sq. cm, of the trapezium is
In an arithmetic progression, if the sum of fourth, seventh and tenth terms is 99, and the sum of the first fourteen terms is 497, then the sum of first five terms is