CUET Mathematics Mock Test - 1

The system of equations $kx+y+z=1$, $x+ky+z=k$, and $x+y+kz=k^2$ has no solution if $k$ equals:

Consider the following statements regarding index numbers:(i) Simple average of price relative is a weighted index numbering method.(ii) The index number for the base year is always 100.(iii) If the price index is 25, then the prices have increased by 25%.(iv) If the price index is 75, then the prices have decreased by 25%.Which of the statements are correct?

A manufacturing firm sets the price per unit as $p(x)=400-\alpha x^2$, where $\alpha$ is a constant and $x$ is the units demanded. If the marginal revenue when 10 units were in demand was zero, then the value of $\alpha$ is:

Calculate the index number using the simple average of price relative method for the data below, taking 2010 as the base year:ItemPrice in 2010Price in 2015A100140B80120C160200D220385E112112

What is ${\sin }^{-1}(\sin \frac{3\pi }{5})$ equal to?