y = {x(x  3)}^{2} increases for all values of x lying in the interval
Since y = {x(x  3)}^{2}
∴ dy dx = 2x (x  3) (2x  3)
For increasing function dy/dx > 0
or 2x (x  3) (2x  3) > 0
or x(x  3) (x  3/2) > 0
∴ x∈(0, 3/2) ∪ (3, ∞)
The area bounded by the xaxis and the curve y = 4x  x^{2}  3, is
If the sum of the coefficients in the expansion of (x+y)^{n} is 1024, then the value of the greatest coefficient in the the expansion is
If the equation 3x^{2} + xy  y^{2}  3x + 6y + K = 0 represents pair of lines, then the value of K is
The equation of a circle with centre (4, 1) and having 3x + 4y 1 = 0 as tangent is
If (z1)/(zi) = 1, then the locus of z is
The focus of the parabola y^{2}x2y+2=0 is
If y=a cos (log x) + b sin (log x) where a,b are parametres, then x^{2}y+xy'
The derivative of
∫[(1)/(xx^{2})]dx=
4tan⁻^{1}(1/5)tan⁻^{1}(1/239)=
What is the value of
If f : ℝ → ℝ is defined by
then f is continuous on the set
If A is a nonsingular, then adj A is
Let f(x) = x^{3} + 3x^{2} + 3x + 2. Then, at x = 1
f(x) = (x+1)^{3} + 1 ∴ f'(x) = 3(x+1)^{2}.
f'(x) = 0 ⇒ x = 1.
Now, f" (1  ∈) = 3(∈)^{2} > 0, f'(1 + ∈)^{2} = 3∈^{2} > 0.
∴ f(x) has neither a maximum nor a minimum at x = 1.
Let f'(x) = φ ′ (x) = 3(x+1)^{2} ∴ φ ′ (x) = 6(x+1).
φ ′ (x) = 0 ⇒ x = 1
φ ′ (1∈) = 6(∈) < 0, φ ′ (1∈) = 6∈ > 0
∴ φ (x) has a minimum at x = 1
Can a quartile, a decile and a percentile be the median?
The gap between the highest and the lowest score is called
The number of 4digit even numbers that can be formed using 0, 1, 2, 3, 4, 5, 6 without repetition is
Each even number must have 0, 2, 4 or 6 in is units place
Here total number of digits = 7
When 0 occurs at units place there is no restriction on other places and when 2 or 4 occurs at units place there is restriction on thousands' place as 0 can not be put at thousands' place
Case I When 0 occurs at units place:
∴ The number of numbers formed in this case
Case II. When 0 does not occur at units place:
The units' place can be filled up by any one of the three digits 2, 4 and 6 in 3 ways
∴ The number of numbers formed in this case
∴ The required number = 120 + 300 = 420
The base of triangle is passing through a fixed point (a,b) and its sides are bisected at right angles by lines, y^{2}  4xy  5x^{2} = 0, then the locus of the vertex of triangle is
y^{2}  4xy  5x^{2} = 0
⇒ (y  5x) (y + x) = 0
y  5x, cuts AB at M at right angle
and y + x = 0 cuts AC at N at right angle
By collinearity of (x_{1}, y_{1}), (x_{2}, y_{2}), (a, b) we get h = x, k = y
2x^{2} + 2y^{2} + (3a + 2b)x + (2a  3b)y = 0
If two dice are rolled then the probability that their sum is a prime number is
The diameter of the circumcircle of the triangle whose sides 61, 60, 11 is
If α , β are the roots of x^{2}  2x + 4 = 0 then α^{5} + β^{5} =
If the roots of the equation x^{3}  12x^{2} + 39x  28 = 0 are in A.P., then their common difference will be
Which one of the following is (A  B) ∪ (B  A)?
Lines 2x+y1=0, ax+3y3=0 and 3x+2y2=0 are concurrent
The tangent to the curve x=at^{2}, y=2at is perpendicular to xaxis, then its point of contact is
A random variable X has the following distribution
The value of c is
If tan2θ tanθ=1, the general value of θ is
If 4 sinθ=3 cosθ, then sec^{2}θ/4[1tan^{2}θ] is
If a,b,c are the position vectors of vertices of a ∆ABC, the vectorial area of ∆ABC is
If the modulus of a and b are equal and angle between them is 120°, and a.b=8, then the value of a is
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