1
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
A value of $$\theta \in \left( {0,{\pi \over 3}} \right)$$, for which
$$\left| {\matrix{ {1 + {{\cos }^2}\theta } & {{{\sin }^2}\theta } & {4\cos 6\theta } \cr {{{\cos }^2}\theta } & {1 + {{\sin }^2}\theta } & {4\cos 6\theta } \cr {{{\cos }^2}\theta } & {{{\sin }^2}\theta } & {1 + 4\cos 6\theta } \cr } } \right| = 0$$, is :
A
$${\pi \over {18}}$$
B
$${\pi \over {9}}$$
C
$${{7\pi } \over {24}}$$
D
$${{7\pi } \over {36}}$$
2
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = $$\left[ {\matrix{ 2 & 3 \cr 5 & { - 1} \cr } } \right]$$, then AB is equal to :
A
$$\left[ {\matrix{ 4 & { - 2} \cr 1 & { - 4} \cr } } \right]$$
B
$$\left[ {\matrix{ { - 4} & { - 2} \cr { - 1} & 4 \cr } } \right]$$
C
$$\left[ {\matrix{ { - 4} & 2 \cr 1 & 4 \cr } } \right]$$
D
$$\left[ {\matrix{ 4 & { - 2} \cr { - 1} & { - 4} \cr } } \right]$$
3
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
If $$B = \left[ {\matrix{ 5 & {2\alpha } & 1 \cr 0 & 2 & 1 \cr \alpha & 3 & { - 1} \cr } } \right]$$ is the inverse of a 3 × 3 matrix A, then the sum of all values of $$\alpha$$ for which det(A) + 1 = 0, is :
A
2
B
- 1
C
0
D
1
4
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
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