Physics
General
Easy
Question
As shown in the figure a particle starts its motion from 0 to A. And then it moves from. A to B.
Is an are find the Path length
![](data:image/png;base64,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)
- 2r
- r+
![straight pi over 3](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAfCAYAAADnTu3OAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAATRJrTQAAAAMlJREFUeNpjYMAOBIH4AhD/AeL/eDDRwBiIW4GYBYvGHwwUgqFn4B9KDfxDwAKSABMWL34DYjZyDZQH4i9oYseBuBaItcgxMAuId6CJeUFd2cUwCmgO/lOIR8FQBI5AvA2azUAFxC0gngDEwuQauB+Ig9BKFgMseZti8ImahikB8Q1qGCQOxInQcPSiZnYsoJZXQRV/ABCfBGJ7aoYhD9RQqoIf1DRMDxoxZIGDQBwKbd8wQXPOfSCOJ9dAWyDeAvXiD2jO8SGkCQCF40Pb/yTXFQAAAH10RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPiYjeDNDMDs8L21pPjxtbj4zPC9tbj48L21mcmFjPjwvbWF0aD6whL7CAAAAAElFTkSuQmCC)
- r(1+
)
(r+1)
The correct answer is: r(1+
)
Related Questions to study
Maths-
Assertion (A):
is divisible by the square of14 where n is a natural number Reason (R): ![left parenthesis 1 plus x right parenthesis to the power of n end exponent equals 1 plus to the power of n end exponent C subscript 1 end subscript x plus horizontal ellipsis. plus to the power of n end exponent C subscript n end subscript x to the power of n end exponent for all n element of N](data:image/png;base64,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)
Assertion (A):
is divisible by the square of14 where n is a natural number Reason (R): ![left parenthesis 1 plus x right parenthesis to the power of n end exponent equals 1 plus to the power of n end exponent C subscript 1 end subscript x plus horizontal ellipsis. plus to the power of n end exponent C subscript n end subscript x to the power of n end exponent for all n element of N](data:image/png;base64,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)
Maths-General
maths-
Assertion (A): Number of the dissimilar terms
in the sum of expansion
is 206
Reason (R): Number of terms in the expansion of
is n+1
Assertion (A): Number of the dissimilar terms
in the sum of expansion
is 206
Reason (R): Number of terms in the expansion of
is n+1
maths-General
Maths-
B=600!,
then
B=600!,
then
Maths-General
maths-
The arrangement of the following with respect to coefficient of
in ascending order where
A)
in
where
B)
where
C)
in
where
D)
in ![left parenthesis 1 plus x right parenthesis to the power of 4 end exponent](data:image/png;base64,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)
The arrangement of the following with respect to coefficient of
in ascending order where
A)
in
where
B)
where
C)
in
where
D)
in ![left parenthesis 1 plus x right parenthesis to the power of 4 end exponent](data:image/png;base64,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)
maths-General
maths-
A: If the term independent of
in the expansion of
is 405, then n=
: If the third term in the expansion of
is 1000, then n=(here n<10)
: If in the binomial expansion of
the coefficients of 5th
6th and 7th terms are in A.P then n= [Arranging the values of n in ascending order]
A: If the term independent of
in the expansion of
is 405, then n=
: If the third term in the expansion of
is 1000, then n=(here n<10)
: If in the binomial expansion of
the coefficients of 5th
6th and 7th terms are in A.P then n= [Arranging the values of n in ascending order]
maths-General
maths-
The arrangement of the following binomial expansions in the ascending order of their independent terms A
B
C
D ![left parenthesis fraction numerator 3 over denominator 2 end fraction x to the power of 2 end exponent minus fraction numerator 1 over denominator 3 x end fraction right parenthesis to the power of 9 end exponent](data:image/png;base64,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)
The arrangement of the following binomial expansions in the ascending order of their independent terms A
B
C
D ![left parenthesis fraction numerator 3 over denominator 2 end fraction x to the power of 2 end exponent minus fraction numerator 1 over denominator 3 x end fraction right parenthesis to the power of 9 end exponent](data:image/png;base64,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)
maths-General
maths-
A:
B:
term independent of x in
C:
then
A:
B:
term independent of x in
C:
then
maths-General
maths-
I The sum of the binomial coefficients of the expansion
is ![2 to the power of n end exponent](data:image/png;base64,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)
II The term independent of x in the expansion of
is
when is even.
Which of the above statements is correct?
I The sum of the binomial coefficients of the expansion
is ![2 to the power of n end exponent](data:image/png;base64,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)
II The term independent of x in the expansion of
is
when is even.
Which of the above statements is correct?
maths-General
maths-
: The fourth term in the expansion of
is equal to the second term in the expansion of
then the positive value of
is ![fraction numerator 1 over denominator 2 square root of 3 end fraction](data:image/png;base64,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)
:In the expansion of
, the coefficients of
and
are equal, then the positive value of a is 8
: The fourth term in the expansion of
is equal to the second term in the expansion of
then the positive value of
is ![fraction numerator 1 over denominator 2 square root of 3 end fraction](data:image/png;base64,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)
:In the expansion of
, the coefficients of
and
are equal, then the positive value of a is 8
maths-General
maths-
S1: If the coefficients of
and
in the expansion of
are equal, then the number ofdivisors ofn is 12.
S2: If the expansion of
for positive integer n has 13 th term independent of x Then the sum of divisors of
is 39.
S1: If the coefficients of
and
in the expansion of
are equal, then the number ofdivisors ofn is 12.
S2: If the expansion of
for positive integer n has 13 th term independent of x Then the sum of divisors of
is 39.
maths-General
maths-
I Three consecutive binomial coefficients cannot be in GP.
II Three consecutive binomial coefficients cannot be in A.P.
Which of the above statement is correct?
I Three consecutive binomial coefficients cannot be in GP.
II Three consecutive binomial coefficients cannot be in A.P.
Which of the above statement is correct?
maths-General
maths-
I The no of distinct terms in the expansion of
is ![n plus 2 c subscript 3 end subscript](data:image/png;base64,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)
II The no of irrational terms in the expansion
is 55
I The no of distinct terms in the expansion of
is ![n plus 2 c subscript 3 end subscript](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADcAAAARCAYAAAB5LjRtAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAWhJREFUeNpjYBgYYA3Ea4D4ExD/AuILQBzNMEzAQSCOBGIeKF8LiI9CxQYt+E+BXnkgvkQrh9UDcQkQiwPxfCD+BsTvgDiPTp4DgR84xEEx3AXET6HJeB0QC5Ji8CqoR0AeswdiJiCWhlrIRQfPWUKTJjaPnQPiViDmA2I2aCT4kGL4LSBOwyIOij1hGnuOA4hPQgsadNABxJMoSQ6gWPqCRZwFmjzxeYYQJgRAyWsDELvhcNdrUpMgOjAH4v04ksp+GuY5JajHVHDImwLxYUoLk0hoXiNWnBqe0wDi2QTysxe08GAgIvXA6kuMFABK08lYNOISp9Rz4tACjIWAOmMgvkFigD1EF1wHDSVixSn13BaoQ4gBF6AlJQu0tCzAUfDA8ug7bCUiB46SkoNGlT2xBZAstEXzB1rJ40pJoBJ9ChAnMgwzAAuYWIZhCvigyTeNYRiDH8PVY7ZAfGY45jdQjO2A9i7AAACCRFtkNGxj+QAAAH50RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+bjwvbWk+PG1vPis8L21vPjxtbj4yPC9tbj48bXN1Yj48bWk+YzwvbWk+PG1uPjM8L21uPjwvbXN1Yj48L21hdGg+ixPmuwAAAABJRU5ErkJggg==)
II The no of irrational terms in the expansion
is 55
maths-General
maths-
If
then ![a subscript 0 end subscript minus fraction numerator a subscript 1 end subscript over denominator 2 end fraction minus fraction numerator a subscript 2 end subscript over denominator 2 end fraction plus a subscript 3 end subscript minus fraction numerator a subscript 4 end subscript over denominator 2 end fraction minus fraction numerator a subscript 5 end subscript over denominator 2 end fraction plus a subscript 6 end subscript](data:image/png;base64,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)
If
then ![a subscript 0 end subscript minus fraction numerator a subscript 1 end subscript over denominator 2 end fraction minus fraction numerator a subscript 2 end subscript over denominator 2 end fraction plus a subscript 3 end subscript minus fraction numerator a subscript 4 end subscript over denominator 2 end fraction minus fraction numerator a subscript 5 end subscript over denominator 2 end fraction plus a subscript 6 end subscript](data:image/png;base64,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)
maths-General
maths-
If
denotes fractional part of
then ![left curly bracket fraction numerator 2 to the power of 2003 end exponent over denominator 17 end fraction right curly bracket equals](data:image/png;base64,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)
If
denotes fractional part of
then ![left curly bracket fraction numerator 2 to the power of 2003 end exponent over denominator 17 end fraction right curly bracket equals](data:image/png;base64,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)
maths-General
maths-
maths-General