The acceleration of a moving practicle whose spacetime equation is given by s = 3t^{2} + 2t  5 is
The area bounded by the curve y = 4x  x^{2} and xaxis is
If r and n are positive integers ; r > 1, n > 2 and coefficient of (r + 2)th term and (3r)th term in the expansion of (1 + x)^{2n} are equal, then n equals
Let [ ] denote the greatest integer function and f(x) = [tan^{2}x]. Then
If ω is nonreal cube root of unity then
[(1 + 2ω + 3ω^{2}) /(2 + 3ω + ω^{2})] + [(2 + 3ω + 3ω^{2})/(3 + 3ω + 2ω^{2})] is equal to
The volume of a solid which is obtained by revolving area bounded by an ellipse x^{2}+9y^{2}=9 and straight line x+3y=3 about yaxis is
The equation x^{2} + y^{2} + x + y + 1 = 0 represents a circle whose centre is at
The coordinates of three vertices of parallelogram are (1,3)(2,0) and (5,1), then its 4th vertex is
The eccentricity of parabola is
Parabola is the locus of a point, say P, which moves such that its distance from a fixed point, say S, is equal to its distance from a fixed line say l.
Eccentricity is defined as the ratio of the distance of the moving point P from the fixed point S, to its distance from a fixed line l.
It is denoted by e. Draw PM perpendicular to l. Then, eccentricity e = PS/PM
Since the two distances are equal in case of a parabola, PS = PM. So, PS/PM = 1.
Therefore, we say eccentricity of a parabola is 1.
In case of an ellipse it is less than 1 and in case of a hyperbola it is greater than 1.
The roots of the equation
If x dy = y(dx + y dy), y > 0 and y (1) = 1, then y (3) is equal to
sec^{2}(tan⁻^{1} 2) + cosec^{2}(cot⁻^{1} 3) =
What is the value of
If A and B are nonsingular matrix, then
The inverse of
The strength of a beam varies as the product of its breadth b and square of its depth d. A beam cut out of a circular log of radius r would be strong when
Strength of the beam S = kbd^{2}
The mode of the following observation is 10,8,9,12,15,0,23,3,2,13,24,28,35,42
The S.D. of a distribution is 5. The value of the fourth central moment μ4 , in order that the distribution be mesokurtic should be
If ^{n}P_{r}=840, ^{n}C_{r}=35, then n=
A coin is tossed 10 times. The probability of getting exactly six heads, is
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
In , then the triangle is
If the roots of the equation ax^{2} + bx + c = 0 are l and 2l, then
1 + (3/2) + (5/2^{2}) + (7/2^{3}) + ... to ∞ is equal to
In Rule Method the null set is represented by
The derivative of with respect to
The equation of line joining points (5,6) and (3,10) is
P(2,2) and are two points on the parabola y^{2} =2x. The coordinates of the point R on the parabola, where the tangent to the curve is parallel to the chord PQ, is
The solution set of (2cosx1) (3+2cosx) = 0 in the interval 0≤x≤2π is
1+cos2x+cos4x+cos6x=
The area of a parallelogram is 5√3, its diagonals are
The sine of the angle between the vectors î  2 ĵ + 3 k̂ and 2 î + ĵ + k̂ is
If 3 is the mean and 3/2 is the S.D. of a binomial distribution, then distribution is
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