In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A) :A relation R on the set of complex number defined by Z_{1} R Z_{2} ⇔ Z_{1} − Z_{2} is real, is an equivalence relation.
Reason(R) :Reflexive and symmetric properties may not imply transitivity.
Straight line px+qy+r=0 touches the circle x^{2}+y^{2}=a^{2} if
The area contained between the curve x y = a^{2} , the vertical line x = a, x = 4a (a > 0) and x axis is
A circle passes through (0,0) and its centre lies on y=x. If it cuts the circle x^{2}+y^{2}4x6y+10=0 orthogonally, then its equation is
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Let n ≥ 3 and let the complex numbers α_{1} , α_{2} , . . . , α_{n} be the roots of x^{n} − 1 = 0 with α_{1} = 1 .
Assertion(A) :For any positive integer is again a positive integer.
Reason(R) :For any positive integer
If y=x^{2}(x2)^{2}, then the values of x for which y is increasing, are
When y = 3, which of the following is FALSE?
Remember what is TRUE: 3 is prime, odd and 2(3) is even.
Choice 1: T and T is TRUE
Choice 2: T or F is TRUE
Choice 3: F and T is FALSE
Choice 4: T and T is TRUE
Let the function f be defined by f(x) = 2x + 1/1 3x. Then f⁻^{1}(x) is
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): If f : R → R defined by f (x) = x^{3} then f is one one onto
Reason(R) : Function f is strictly decreasing on R.
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): y = sin (ax + b) is a general solution of y" + a^{2} y = 0 .
Reason(R) : y = sin (ax + b) is a trigonometric function.
If A is a square matrix such that A^{2} = I, then A⁻^{1} is equal to
If x+y+1=0 tocuhes the parabola y^{2}=λx,then λ is equal to
A polygon has 44 diagonals. The number of its sides is
If P(B)=(3/4), P(A∩B∩C̅) = (1/3) and P(A̅∩B∩C̅) = 1/3, then P(B∩C) is
Given n = 10, ∑x = 4, ∑y = 3, ∑x^{2} = 8, ∑y^{2} = 9 and ∑xy = 3, then coefficient of correlation is
The straight line x + y = a will be a tangent to the ellipse x^{2}/9 + y^{2}/16 = 1 if a =
Let then the value of a + b is:
Let f(x) = [2x^{3} – 5]; then number of points in (1, 2) where the function is discontinuous are where [.] → G.I.F.
The equation of the perpendicular bisectors of the sides AB and AC of a triangle ABC are y = x and y = –x, respectively. If the point A is (1, 2), then the area of ΔABC is :
Let f(x) be a function given by
f(x + y) = f(x) + f(y) for all x, y. Let f '(5) exist and is equal to 7, then ?
If the foci of the ellipse and the hyperbola coincide, then the value of b^{2} is:








