The ordered pair (a, b), for which the system of linear equations 3x $$-$$ 2y + z = b 5x $$-$$ 8y + 9z = 3 2x + y + az = $$-$$1 has no solution, is :
JEE · Math · previous-year question
- A.$$\left( {3,{1 \over 3}} \right)$$
- B.$$\left( { - 3,{1 \over 3}} \right)$$
- C.$$\left( { - 3, - {1 \over 3}} \right)$$correct
- D.$$\left( {3, - {1 \over 3}} \right)$$
Answer
C. $$\left( { - 3, - {1 \over 3}} \right)$$
Explanation
$$\left| {\begin{matrix} 3 & { - 2} & 1 \\ 5 & { - 8} & 9 \\ 2 & 1 & a \\ \end{matrix} } \right| = 0 \Rightarrow - 14a - 42 = 0 \Rightarrow a = - 3$$ Now 3 (equation (1)) $$-$$ (equation (2)) $$-$$ 2 (equation (3)) is $$3(3x - 2y + z - b) - (5x - 8y + 9z - 3) - 2(2x + y + az + 1) = 0$$ $$ \Rightarrow - 3b + 3 - 2 = 0 \Rightarrow b = {1 \over 3}$$ So for no solution $$a = - 3$$ and $$b \ne {1 \over 3}$$
Practice more JEE questions
Answer thousands more real JEE previous-year questions free, get graded instantly, and climb the global ranked leaderboard.
Practice JEE free →More JEE Math questions
- What is the total number of distinct x \in \mathbb{R} for which \left|\begin{array}{ccc}x …
- Let m be the smallest positive integer such that the coefficient of x^{2} in the expansion…
- What is the total number of distinct x \in[0,1] for which \int_{0}^{x} \frac{t^{2}}{1+t^{4…
- Let \alpha, \beta \in \mathbb{R} be such that \lim _{x \rightarrow 0} \frac{x^{2} \sin (\b…
- Let z=\frac{-1+\sqrt{3} i}{2}, where i=\sqrt{-1}, and r, s \in\{1,2,3\}. Let P=\left[\begi…
- For how many values of p, the circle x^{2}+y^{2}+2 x+4 y-p=0 and the coordinate axes have …
- Let f: \mathbb{R} \rightarrow \mathbb{R} be a differentiable function such that f(0)=0, f\…
- For a real number \alpha, if the system \[ \left[\begin{array}{ccc} 1 & \alpha & \alpha^{2…