1
JEE Main 2019 (Online) 10th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Let $$\lambda $$ be a real number for which the system of linear equations x + y + z = 6, 4x + $$\lambda $$y – $$\lambda $$z = $$\lambda $$ – 2, 3x + 2y – 4z = – 5 has infinitely many solutions. Then $$\lambda $$ is a root of the quadratic equation:
A
$$\lambda $$2 + $$\lambda $$ - 6 = 0
B
$$\lambda $$2 - $$\lambda $$ - 6 = 0
C
$$\lambda $$2 - 3$$\lambda $$ - 4 = 0
D
$$\lambda $$2 + 3$$\lambda $$ - 4 = 0
2
JEE Main 2019 (Online) 10th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
The sum of the real roots of the equation
$$\left| {\matrix{ x & { - 6} & { - 1} \cr 2 & { - 3x} & {x - 3} \cr { - 3} & {2x} & {x + 2} \cr } } \right| = 0$$, is equal to :
A
- 4
B
0
C
1
D
6
3
JEE Main 2019 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
If $${\Delta _1} = \left| {\matrix{ x & {\sin \theta } & {\cos \theta } \cr { - \sin \theta } & { - x} & 1 \cr {\cos \theta } & 1 & x \cr } } \right|$$ and
$${\Delta _2} = \left| {\matrix{ x & {\sin 2\theta } & {\cos 2\theta } \cr { - \sin 2\theta } & { - x} & 1 \cr {\cos 2\theta } & 1 & x \cr } } \right|$$, $$x \ne 0$$ ;

then for all $$\theta \in \left( {0,{\pi \over 2}} \right)$$ :
A
$${\Delta _1} - {\Delta _2}$$ = x (cos 2$$\theta $$ – cos 4$$\theta $$)
B
$${\Delta _1} + {\Delta _2}$$ = - 2x3
C
$${\Delta _1} + {\Delta _2}$$ = – 2(x3 + x –1)
D
$${\Delta _1} - {\Delta _2}$$ = - 2x3
4
JEE Main 2019 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
If the system of linear equations
x + y + z = 5
x + 2y + 2z = 6
x + 3y + $$\lambda $$z = $$\mu $$, ($$\lambda $$, $$\mu $$ $$ \in $$ R), has infinitely many solutions, then the value of $$\lambda $$ + $$\mu $$ is :
A
10
B
9
C
7
D
12
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