1
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If A, B and C are the angles of a triangle and $$\left| {\matrix{ 1 & 1 & 1 \cr {1 + \sin A} & {1 + \sin B} & {1 + \sin C} \cr {\sin A + {{\sin }^2}A} & {\sin B + {{\sin }^2}B} & {\sin C + {{\sin }^2}C} \cr } } \right| = 0$$, then which one of the following is correct?
A
The triangle ABC is isosceles
B
The triangle ABC is equilateral
C
The triangle ABC is scalene
D
No conclusion can be drawn with regard to the nature of the triangle
2
NDA 2019 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If x + a + b + c = 0, then what is the value of $$\left| {\matrix{ {x + a} & b & c \cr a & {x + b} & c \cr a & b & {x + c} \cr } } \right|$$ ?
A
0
B
(a + b + c)2
C
a2 + b2 + c2
D
a + b + c $$-$$ 2
3
NDA 2019 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
What are the values of x that satisfy the equation $$\left| {\matrix{ x & 0 & 2 \cr {2x} & 2 & 1 \cr 1 & 1 & 1 \cr } } \right| + \left| {\matrix{ {3x} & 0 & 2 \cr {{x^2}} & 2 & 1 \cr 0 & 1 & 1 \cr } } \right| = 0$$ ?
A
$$ - 2\, \pm \,\sqrt 3 $$
B
$$ - 1\, \pm \,\sqrt 3 $$
C
$$ - 1\, \pm \,\sqrt 6 $$
D
$$ - 2\, \pm \,\sqrt 6 $$
4
NDA 2019 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
What is the value of the determinant $$\left| {\matrix{ {1!} & {2!} & {3!} \cr {2!} & {3!} & {4!} \cr {3!} & {4!} & {5!} \cr } } \right|$$ ?
A
0
B
12
C
24
D
36
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