In a AABC, if C = 90°, r and R are the inradius and circumradius of the ABC respectively, then 2(r + R) is equal to
b + c
c + a
a + b
a + b + c
Let be two distinct roots of where a, b, c are three real constants and . Then, is also a root of the same equation, if
a + b = c
b + c = a
c + a = b
c = a
If are solutions of the differential equation
where a0, a1 and a2 are real constants, then which of the following is/are always true?
is a solution, where A and B are real constants
is a solution, where A is a real constant
is a solution, where A is a real constant
is a souton, where A and B are real constants
Let 16x2 - 3y - 32x - 12y = 44 represents a hyperbola. Then,
length of the transverse axis is
length of each latusrectum is
eccentricity is
equation of a directrix is x =
For the function f(x) = . where [x] denotes the greatest integer less than or equal to x, which of the following statements are true?
The domain is
The range is
The domain is
The range is
Which of the following is /are always false?
A quadratic equation with rational coefficients has zero or two irrational roots
A quadratic equation with real coefficients has zero or two non-real roots
A quadratic equation with irrational coefficients has zero or two irrational roots
A quadratic equation with integer coefficients has zero or two irrational roots
If the straight line (a - 1)x - by + 4 = 0 is normal to the hyperbola xy = 1, then which of the following does not hold?
a > 1, b > 0
a > 1, b < 0
a < 1, b < 0
a < 1, b > 0
Let f: be a continuous function which satisfies f(x) = . Then, the value of is
0
2
5
3
A.
0
Given, f(x) = ...(i)
Using Leibnitz theorem, we get
f'(x) = f(x)
On putting x = 0 in Eq. (i), we get
Let f: [2, 2] R be a continuous function such that f(x) assumes only irrational values. If , then
f(0) = 0