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If P(1, 0), Q(– 1, 0) and R(2, 0) are three given points, then the locus of point S, which satisfies the relation (SQ)2 + (SR)2 = 2(SP)2, is (where SQ, SR and SP are line segments)
Let the point be (h, k)
So, SQ2 = (h + 1)2 + k2
SR2 = (h - 2)2 + k2
SP2 = (h - 1)2 + k2
Substituting in the given equation and replacing the values of h and k by x and y, we get
x = - 3/2 (A straight line parallel to y-axis).
The orthocenter of the triangle with vertices
The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is
The triangle formed by the given lines is a right angle triangle right angled at (0, 0). Hence, it is the orthocenter.
The diagonals of a parallelogram PQRS are along the lines x + 3y = 4 and 6x - 2y = 7. Then PQRS must be a
The slope of the first line: - 1/3
Slope of second line is: 3
Hence the diagonals are perpendicular, which is the property of a Rhombus.
If the vertices P, Q, R of a triangle PQR are rational points, then which of the following points of the triangle PQR is not always a rational point?
Incentre of is not ΔPQR always a rational point.
If f(x) = xa + ax and g(x) = xa – ax, find the value of f(x) + g(x).
f(x) + g(x) = 2xa
Find the period of the given function:
f(x) = tan(x/3) + sin(2x)
Given, f(x) = tan(x/3) + sin(2x).
Here, tan(x/3) is periodic with period 3π and sin2x is periodic with period π.Hence, f(x) will be periodic with period 3π.
We know that amount = P(1+ r/100)n. Substituting r = 12 and n = 3 in it, we get A = P[1.12]3 or A/P = 1.404.
If
L(X, Y) = Square of the larger number,
S(X, Y) = Square of the smaller number,
MODD (X, Y) = Absolute value of the difference (X - Y) and
X * Y = Product of X and Y,
then the value of MODD [{L (1, 2) * S(1, - 3)}, {S(0, 2) * MODD (3, - 4)}] *MODD[{S(3, -1) * L(1, - 2)}, { MODD (1, 2) * L(1, 2)}] will be
If f(x) = log (1 + x) - log (1 - x) and log (g(x)) = log (3x + x3) - log (1 + 3x2), then what is the value of f(g(x))?
Directions: Refer to the following functions:
A(x, y, z) = Max {max (x, y), min (y, z), min (x, z)}
B(x, y, z) = Max {max (x, y), min (y, z), max (x, z)}
C(x, y, z) = Max {min (x, y), min (y, z), min (x, z)}
D(x, y, z) = Min {max (x, y), max (y, z), max (x, z)}
Max (x, y, z) = Maximum of x, y and z.
Min (x, y, z) = Minimum of x, y and z.
Assume x, y and z as distinct integers.
For what condition, will A(x, y, z) be equal to Max (x, y, z)?
Let us assign some values to x, y and z.
Put x = 1, y = 2, z = 3.
Now, A(x, y, z) = Max (2, 2, 1) = 1.
B (x, y, z) = Max (2, 2, 2) = 2
C (x, y, z) = Max (1, 2, 1) = 1
D (x, y, z) = Min (2, 3, 1) = 3
Max (x, y, z) = Min (1, 2, 3) = 1
Min (x, y, z) = Max (1, 2, 3) = 3
They will be equal only when z has the minimum value among the three, and x or y has the maximum value.
1. You might have checked by options and option 1 satisfies, but option 2 also satisfies.
2. You might have checked by options and option 2 satisfies, but option 1 also satisfies.
3. We can simply ignore this option as for x = 1, y = 2 , z = 3, it does not satisfy.
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