Maths-
General
Easy
Question
A random variable X has the probability distribution :
![](data:image/png;base64,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)
For the events E = {X is a prime number} and F = {X < 4}, the probability
is-
- 0.35
- 0.77
- 0.87
- 0.50
The correct answer is: 0.77
Related Questions to study
maths-
A fair coin is tossed 3 times. Consider the events A : first toss is head ; B : second toss is head C : exactly two consecutive heads or exactly two consecutive tails
Statement - I A,B,C are independent events.
Statement - II A,B,C are pairwise independent.
A fair coin is tossed 3 times. Consider the events A : first toss is head ; B : second toss is head C : exactly two consecutive heads or exactly two consecutive tails
Statement - I A,B,C are independent events.
Statement - II A,B,C are pairwise independent.
maths-General
maths-
An experiment resulting in sample space as S = {a, b, c, d, e, f}
Let three events A, B and C are defined as A = {a, c, e,}, B = {c, d, e, f} and C = {b, c, f}.
then the correct order sequance is
An experiment resulting in sample space as S = {a, b, c, d, e, f}
Let three events A, B and C are defined as A = {a, c, e,}, B = {c, d, e, f} and C = {b, c, f}.
then the correct order sequance is
maths-General
maths-
An ellipse is drawn with major and minor axes of lengths 10 and 8 respectively. Using one focus as centre, a circle is drawn that is tangent to the ellipse, with no part of the circle being outside the ellipse. The radius of the circle is
An ellipse is drawn with major and minor axes of lengths 10 and 8 respectively. Using one focus as centre, a circle is drawn that is tangent to the ellipse, with no part of the circle being outside the ellipse. The radius of the circle is
maths-General
maths-
From a point P, perpendicular tangents PQ and PR are drawn to ellipse
Locus of circumcentre of triangle PQR is
From a point P, perpendicular tangents PQ and PR are drawn to ellipse
Locus of circumcentre of triangle PQR is
maths-General
maths-
The least integral value that contained is the range of the function f defined by
is ___
The least integral value that contained is the range of the function f defined by
is ___
maths-General
maths-
Let
then
Let
then
maths-General
maths-
If m is the slope of tangent to the curve
then
If m is the slope of tangent to the curve
then
maths-General
maths-
If
is equal to e7, then ![stack l i m with x greater-than or slanted equal to 0 below fraction numerator f open parentheses x close parentheses over denominator x to the power of 3 end exponent end fraction equals horizontal ellipsis horizontal ellipsis](data:image/png;base64,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)
If
is equal to e7, then ![stack l i m with x greater-than or slanted equal to 0 below fraction numerator f open parentheses x close parentheses over denominator x to the power of 3 end exponent end fraction equals horizontal ellipsis horizontal ellipsis](data:image/png;base64,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)
maths-General
maths-
Set of all values of x such that
is non-zero and finite number when n N
is
Set of all values of x such that
is non-zero and finite number when n N
is
maths-General
maths-
The period of the function
is
The period of the function
is
maths-General
maths-
Let
is a prime number and [x] = the greatest integer
The number of points at which f(x) is not differentiable is _______
Let
is a prime number and [x] = the greatest integer
The number of points at which f(x) is not differentiable is _______
maths-General
maths-
If the line
is one of the angle bisectors of the lines
and
then the value of k is
If the line
is one of the angle bisectors of the lines
and
then the value of k is
maths-General
physics-
A particle when projected in vertical plane moves along smooth surface with initial velocity 20m/s at an angle of 60°, so that its normal reaction on the surface remains zero throughout the motion. Then the slope of the tangent to the surface at height 5 m from the point of projection will be
![](data:image/png;base64,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)
A particle when projected in vertical plane moves along smooth surface with initial velocity 20m/s at an angle of 60°, so that its normal reaction on the surface remains zero throughout the motion. Then the slope of the tangent to the surface at height 5 m from the point of projection will be
![](data:image/png;base64,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)
physics-General
physics-
Consider a particle moving without friction on a rippled surface, as shown. Gravity acts down in the negative h direction. The elevation h(x) of the surface is given by h(x) = d cos(kx). If the particle starts at x = 0 with a speed v in the x direction, for what values of v will the particle stay on the surface at all times?
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)
Consider a particle moving without friction on a rippled surface, as shown. Gravity acts down in the negative h direction. The elevation h(x) of the surface is given by h(x) = d cos(kx). If the particle starts at x = 0 with a speed v in the x direction, for what values of v will the particle stay on the surface at all times?
![](data:image/png;base64,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)
physics-General
physics-
System shown in figure is released from rest. Pulley and spring is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is (Take force constant of spring ![open k equals 40 N divided by m blank a n d blank g equals 10 m divided by s to the power of 2 end exponent close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
System shown in figure is released from rest. Pulley and spring is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is (Take force constant of spring ![open k equals 40 N divided by m blank a n d blank g equals 10 m divided by s to the power of 2 end exponent close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General