For every real number x,
let f(x) = Then, the equation f(x) = 0 has
no real solution
exactly one real solution
exactly two real solutions
infinite number of real solutions
Let [x] denote the greatest integer less than or equal to x for any real number x. Then,
is equal to
0
2
1
Let z, be a fixed point on the circle of radius 1 centered at the origin in the Argand plane and . Consider an equilateral triangle inscribed in the circle with z1, z2, z3 as the vertices taken in the counterclockwise direction. Then, z1z2z3 is equal to
z12
z13
z14
z1
Suppose that z1, z2, z3 are three vertices of an equilateral triangle in the Argand plane. Let be a non-zero complex number. The points will be
the vertices of an equilateral triangle
the vertices of an isosceles triangle
collinear
the vertices of a scalene triangle
In the Argand plane, the distinct roots of 1 + z + z3 + z4 = 0 (z is a complex number) represent vertices of
a square
an equilateral triangle
a rhombus
a rectangle
In a , a, b, c are the sides of the triangle opposite to the angles A, B, C, respectively. Then, the value of a3sin(B - C) + b3sin(C - A) + c3sin(A - B) is equal to
0
1
3
2
A.
0
A fair six-faced die is rolled 12 times. The probability that each face turns up twice is equal to
If are the roots of the quadratic equation x2 + px + q = 0, then the values of are respectively
- p(3q - p2) and (p2 - q)(p2 + 3q)
pq - 4 and p4 - q4
3pq - p3 and (p2 - q)(p2 - 3q)