IIT-JEE 1980Question 46
For what values of $m$ does the system of equations $$3x+my=m,\qquad 2x-5y=20$$ have a solution satisfying the conditions $x>0$, $y>0$?
Determinant
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IIT-JEE 1980Question 47
Find the solution set of the system $$x+2y+z=1;\quad 2x-3y-w=2;\quad x\ge0;\ y\ge0;\ z\ge0;\ w\ge0.$$
Determinant
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IIT-JEE 1982Question 48
Find all values of $\lambda$ such that $(x,y,z)\neq(0,0,0)$ and $$\left(\hat i+\hat j+3\hat k\right)x+\left(3\hat i-3\hat j+\hat k\right)y+\left(-4\hat i+5\hat j\right)z=\lambda\left(x\hat i+y\hat j+z\hat k\right)$$ where $\hat i,\hat j,\hat k$ are unit vectors along the coordinate axes.
Vector Algebra
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IIT-JEE 1983Question 49
A vector $\vec A$ has components $A_1,A_2,A_3$ in a right-handed rectangular Cartesian coordinate system $oxyz$. The coordinate system is rotated about the $x$-axis through an angle $\dfrac{\pi}{2}$. Find the components of $\vec A$ in the new coordinate system in terms of $A_1,A_2,A_3$.
Vector Algebra
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IIT-JEE 1978Question 50
Balls are drawn one-by-one without replacement from a box containing $2$ black, $4$ white and $3$ red balls till all the balls are drawn. Find the probability that the balls drawn are in the order $2$ black, $4$ white and $3$ red.
Probability
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