1
JEE Main 2019 (Online) 10th April Evening Slot
+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
+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
+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
+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
EXAM MAP
Medical
NEET