Stocks A, B and C are priced at rupees 120, 90 and 150 per share, respectively. A trader holds a portfolio consisting of 10 shares of stock A, and 20 shares of stocks B and C put together. If the total value of her portfolio is rupees 3300, then the number of shares of stock B that she holds, is:
Let $3 \leq x \leq 6$ and $[x^2] = [x]^2$, where $[x]$ is the greatest integer not exceeding $x$. If set $S$ represents all feasible values of $x$, then a possible subset of $S$ is .
The number of distinct pairs of integers $(x, y)$ satisfying the inequalities $x$ >$ y \geq 3$ and $x + y $<$ 14$ is .
A value of $c$ for which the minimum value of $f(x) = x^2 - 4cx + 8c$ is greater than the maximum value of $g(x) = -x^2 + 3cx - 2c$, is .
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
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 m and n are integers such that $(m+2n)(2m+n)=27$, then the maximum possible value of $2m-3n$ is
Suppose a, b, c are three distinct natural numbers, such that $3ac = 8(a+b)$. Then, the smallest possible value of $3a+2b+c$ is
If $9^{x^{2}+2x-3}-4(3)^{x^{2}+2x-2}+27=0$ then the product of all possible values of x is
The set of all real values of x for which $(x^{2}-|x+9|+x)$ > 0, is
If $(x^{2}+\frac{1}{x^{2}})=25$ and $x>0$ then the value of $(x^{7}+\frac{1}{x^{7}})$ 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
For real values of x, the range of the function $f(x)=\frac{2x-3}{2x^{2}+4x-6}$ is
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
