if the pair of lines ax^{2} + 2hxy + by^{2} + 2gx + 2fy + c = 0
The circle x^{2} + y^{2}  8x + 4y + 4 = 0 touches
The foci of the ellipse 25(x+1)^{2} + 9(y+2)^{2} = 225 are
The product of all roots of is
The differential equation of the family of lines passing through the origin is
If f: R → R and g : R → R defined by f(x) = 2x + 3 and g(x) = x^{2} + 7, then the value of x for which f(g(x)) = 25 are
The area bounded by the curve y = x^{2}  4x, xaxis and line x = 2 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): f (x) = log x^{3} and g (x) = 3 log x are equal .
Reason(R) : Two functions f and g are said to be equal if their domains, ranges are equal and f (x) = g (x) ∀ x in the domain .
Which of the following statements are true ?
(1) The amplitude of the product of complex numbers is equal to the product of their amplitudes.
(2) For any polynomial f(x) =0 with real coefficients, imaginary roots occurs in conjugate paris.
(3) Order relation exists in complex numbers whereas it does not exist in real numbers.
(4) The value of ω used as a cube root of unity and as a fourth root of unity are different.
A tangent is drawn at the point (3√3 cos θ, sin θ) 0 < θ < (π/2) of an ellipse (x^{2}/27) + (y^{2}/1) = 1 the least value of the sum of the intercepts on the coordinate axes by this tangent is attained at θ =
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):
Reason (R): The non zero vectors are always linearly independent
How many numbers between 99 and 1000 can be formed from the digits 2,3,7,0,8,6 so that in each number each digit may occur once only?
If two dice are thrown, find the probability of getting an odd number of on one and multiple of 3 on the other is
Odd no. on the first die
1, 3, 5
multiple of 3 on the other die
3, 6
now let's see the combination of these two events happening simultaneously
as the question says
(1,3) , (1,6) , (3,3) , (3,6) , (5,6) , (5,3)
total no of favourable events = 6
total no of events throwing two dice simultaneously = 6² = 36
so probability = 6/36 = 1/6
The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved is
We have, probability that A can solve the problem = P(A) = 1/2 ,
And in this way P(B) = 1/3 and P(C) = 1/4.
P(A cannot solve the problem) = 1 – P(A) = 1/2 ,
P(B cannot solve the problem) = 1 – P(B) = 1 – 1/3 = 2/3,
P(C cannot solve the problem) = 1 – P(C) = 1 – 1/4 = 3/4.
P(A, B, and C cannot solve the problem) = 1/2 x 2/3 x 3/4 = 1/4.
Therefore , P(Problem will be solve) = 1 – P(Problem is not solved by any of them)
= 1 – 1/4 = 3/4
If the roots of ax^{2} + bx + c = 0 are α,β and roots of Ax^{2} + Bx + C = 0 are α + K, β + K, then B^{2}  4AC/b^{2}  4ac is equal to
Let f(x) be a polynominal function of second degree,If f(1) = f(1) and a,b,c are in A.P., then f'(a),f'(b) and f'(c) are in
The total expenditure incurred by an industry under different heads is best presented as a
A house of height 100 m subtends a right angle at the window of an opposite house. If the height of the window be 64 m, then the distance between the two houses is
The value of is :
The area (in sq. units) of the region A = is :
A line makes α/2, β/2, γ/2 angles with positive direction of coordinate axes then cosα + cosβ + cosγ equals
If a, b and c are perpendicular to b + c, c + a and a + b respectively and if a + b = 6, b + c = 8 and c + a = 10 then a + b + c =
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