The maximum value of the function f(x) = sin(x + π/6) + cos (x + π/6) in the interval (0, π/2) occurs at :
The area bounded by the curve y^{2} = 9x and the lines x = 1, x = 4 and y = 0 in the first quadrant is
Let f(x) = x  x  x^{2}, x ∈[1, 1]. Then the number of points at which f(x) is discontinuous is
f(x)= x  x. 1x. We know that x, x, 1x are continuous everywhere. As the product and algebraic sum of continuous functions are continuous, f(x) is continuous everywhere.
If two circles of equal radii a and with centres (2,3) and (5,6) cut each other at right angle then, a=
If in the expansion of [(x^{4})+(1/x^{3})]^{15} in r^{th} term x^{4} occurs, then r=
The correct statement regarding the position of point (6,2) with respect to lines 2x+3y4=0 and 6x+9y+8=0 is
Equation [(x^{2})/(2r)]+[(y^{2})/(r5)]+1=0 represents an ellipse if
[(12i)/(2+i)] + [(4i)/(3+2i)] =
The area bounded by two curves y^{2}=4ax and x^{2}=4ay is
Given, y^{2} = 4ax  (1)
x^{2} = 4ay (2)
(1) and (2) intersects
hence
x = y^{2}/4a (a > 0)
(y^{2}/4a)^{2} = 4ay
y^{4} = 64a^{3}y
y^{4} – 64a^{3}y = 0
y[y^{3} – (4a)^{3}] = 0
y = 0, 4a
When y = 0, x = 0 and when y = 4a, x = 4a.
The points of intersection of (1) and (2) are O(0, 0) and A(4a, 4a).
The area of the region between the two curves
= Area of the shaded region
= _{0}∫^{4a}(y1 – y^{2})dx
= _{0}∫^{4a}[√(4ax) – x2/4a]dx
= [2√a.(x3/2)/(3/2) – (1/4a)(x^{3}/3)] 0^{4a}
= 4/3√a(4a)3/2 – (1/12a)(4a)^{3} – 0
= 32/3a^{2} – 16/3a^{2}
= 16/3a^{2} sq. units
The degree and order of the differential equation of the family of all parabolas whose axis is xaxis are respectively
f(x)=x^{2}27x+5 is increasing when
∫[(1)/(1sinx)]dx=
If cot⁻^{1}[(cos α)^{1∕2}]  tan⁻^{1}[(cot α)^{1∕2}] = x, then sin x =
All diagonal elements of skew symmetric matrix are
The value of lim
Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)
Let f(x) = x.
f'(0) ≠ 0 but f(x) has a minimum at x = 0.
The inverse of matrix
The number of partition values in case of quartiles is:
Given the following data:
No. of observation = 1000
Arithmetic mean = 1000
Variance = 256.0
The coefficient of variance will be equal to
The equation of pair of lines passes through (1,1) and perpendicular to lines 3x^{2}7xy2y^{2}=0 is
In an election there are five candidates for three places. A man can vote for maximum number of candidates. In how many total ways can a men vote?
The probability that a card drawn from a pack of 52 cards will be diamond or king is
In a Δ ABC , the inradius and three exradii are r , r_{1} , r_{2} and r_{3} respectively. In usual notations the value of r. r_{1}.r_{2}.r_{3} is equal to
If α, β are the roots of the equation x^{2} + x + 1 = 0 and (α/β), (β/α) are the roots of x^{2} + px + q = 0, then p is equal to
The sum of the series 1.3^{2}+ 2.5^{2} + 3.7^{2} +.....upto 20 terms is
In the set W of whole numbers an equivalence relation R is defined as follows :
aRb iff both a and b leave same remainder when divided by 5. The equivalence class of 1 is given by
If lines 2x+3ay1=0 and 3x+4y+1=0 are metually perpendicular, then a =
The tangent to a given curve y=f(x) is perpendicular to xaxis if
A random variable X has the following distribution
The value of k and P X < 3 are equal to
If sec4θsec2θ=2, the general value of θ is
The value of cos^{2} π/12+cos^{2}π/4+cos^{2}5π/12 is
Vector B=3j+4k, is equal to the sum of B₁ and B₂. If B₁ and B₂ are parallel and perpendicular to A=i+j, then B₁=
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