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The equations $3x^{2}-5x+p=0$ and $2x^{2}-2x+q=0$ have one common root. The sum of the other roots of these two equations is
In a $\Delta ABC$, points D and E are on the sides BC and AC, respectively. BE and AD intersect at point T such that $AD: AT=4:3,$ and $BE: BT=5:4$. Point F lies on AC such that DF is parallel to BE. Then, $BD: CD$ is
A mixture of coffee and cocoa, 16% of which is coffee, costs Rs 240 per kg. Another mixture of coffee and cocoa, of which 36% is coffee, costs Rs 320 per kg. If a new mixture of coffee and cocoa costs Rs 376 per kg, then the quantity, in kg, of coffee in 10 kg of this new mixture is
If a, b, c and d are integers such that their sum is 46, then the minimum possible value of $(a-b)^{2}+(a-c)^{2}+(a-d)^{2}$ is
Let $a_{n}$ be the $n^{th}$ term of a decreasing infinite geometric progression. If $a_{1}+a_{2}+a_{3}=52$ and $a_{1}a_{2}+a_{2}a_{3}+a_{3}a_{1}=624$, then the sum of this geometric progression is
Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after 20 days. If the job got completed in 60 days, the number of days needed by Chandan to complete the job alone, is
The number of divisors of $(2^{6}\times3^{5}\times5^{3}\times7^{2})$ which are of the form $(3r+1)$ where r is a non-negative integer, is
Let $f(x)=\frac{x}{(2x-1)}$ and $g(x)=\frac{x}{(x-1)}$. Then, the domain of the function $h(x)=f(g(x))+g(f(x))$ is all real numbers except
If $\log_{64}x^{2}+\log_{8}\sqrt{y}+3\log_{512}(\sqrt{y}z)=4$ where x, y and z are positive real numbers, then the minimum possible value of $(x+y+z)$ is
The average number of copies of a book sold per day by a shopkeeper is 60 in the initial seven days and 63 in the initial eight days, after the book launch. On the ninth day, she sells 11 copies less than the eighth day, and the average number of copies sold per day from second day to ninth day becomes 66. The number of copies sold on the first day of the book launch is