Mathematics Mock Test - 11

Ashok bought tables and chairs for a marriage hall. The cost of a table is $\text{₹}2500$ and a chair is $\text{₹}500$. He has a budget of $\text{₹}60000$ and space for at most $60$ items. If the profit is $\text{₹}75$ per table and $\text{₹}25$ per chair, find the maximum profit.

The system of linear equations$x+y+z=4$,$x+2y+3z=7$,$x+4y+\lambda z=\mu$ has a unique solution if:

If the difference between the greatest and the least value of the function $f(x)={\sin }^{2}x+\cos x$ on $[0,\pi ]$ is $\frac{a-4}{4}$, then $a$ equals:

Consider $f(x)=2x^3-9x^2+12x+6$. Then:

Let $m\in \mathbb{Z}$ and consider the relation $R_m$ defined by $a{R}_{m}b$ if and only if $a\equiv b(\mathrm{mod}m)$. Then $R_m$ is: