Maths-
General
Easy
Question
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.
- Only
is true
- Only
is true
- Both
and
are true
- Neither
nor
is true
The correct answer is: Both
and
are true
Related Questions to study
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,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)
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,iVBORw0KGgoAAAANSUhEUgAAAE0AAAAnCAYAAABKZsWMAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAAAkRJREFUeNrtWjFLAzEUfpQOIiIUKeJUKKWIk2sRKQXpIB26FCni4CLi4D9w9B+4iZODIA4ipbgUEREpiIhTcXN0cehQpBTOF+4VzjN3l1yj3uXywTfc5Th4X16+JC8BUA+LOETeIwucb2rIHrEm2e78/zOyChohhdxDPrnel5C3yDniDb0TbXdiEfkGGuLT9XyJLDueV5FXEu3ujvnQTbAyZY0TfQrWGXhfon0MloVHyO0oC7CCvKAAxn6y6fP9AnlanuNJbgwl2p2+thX1rGEZ00TO0PMSidLkfFtEtkg4CMi0dECmpT0ybRZ5iNyJ2/DLIV84GdamoHhwe1aZBBZtD/LMWBp9m2Y1L5RoRswgs5TB6xLt4JokHuMmWImGKM9vnOStw15p5tuXbB//k3XWNWV7bDCF7NIEYSCADHlP1UghhjwJVjBSiIEZ/DFy2kghhnnkOa2bDATRClhKJA5F8qmBzzeWD6OMwW95MKtbVTROijWKUSmsBIwmy4gWgRiHCRBtFMKrPT2bVSUeEiBaF/ilqtBp25ygF6JIHjZUDtEc+NerdEHboyISthN812e6QHmx0syeRrS/iXGU4CVHaHSQdfh+CqRqT3sA9nFfmNlZBVIUW0e1aOwA4wT4R2WT4BTsIzZZARpg1+1UoE+xZXX2E1a3uwP7DCLRkBGN3dtYBgNh0XbJAw0ERcvR/tCU0yVEYyfpFSOVuGgN2hsaCIrG1lE9Y/5yotXh58U/gwDRziDitxn/Q6ygrdE72HdDYoMvzmXdzoY5JpMAAACbdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPns8L21vPjxtZnJhYz48bXN1cD48bW4+MjwvbW4+PG1uPjIwMDM8L21uPjwvbXN1cD48bW4+MTc8L21uPjwvbWZyYWM+PG1vPn08L21vPjxtbz49PC9tbz48L21hdGg+o2oGLgAAAABJRU5ErkJggg==)
maths-General
maths-
maths-General
Maths-
The number of rational terms in the expansion of
is
The number of rational terms in the expansion of
is
Maths-General
maths-
If
divided by 7, the remainder is
If
divided by 7, the remainder is
maths-General
maths-
The remainder when
is divided by 53 is
The remainder when
is divided by 53 is
maths-General
maths-
If
, then ![not stretchy sum subscript r equals 0 end subscript superscript 5 end superscript C subscript 6 r end subscript equals](data:image/png;base64,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)
If
, then ![not stretchy sum subscript r equals 0 end subscript superscript 5 end superscript C subscript 6 r end subscript equals](data:image/png;base64,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)
maths-General
maths-
If
, then
![plus C subscript 28 end subscript equals](data:image/png;base64,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)
If
, then
![plus C subscript 28 end subscript equals](data:image/png;base64,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)
maths-General
physics
A particle goes from point A to B. Its displacement is X and pathlength is y. So ![x over y](data:image/png;base64,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)
A particle goes from point A to B. Its displacement is X and pathlength is y. So ![x over y](data:image/png;base64,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)
physicsGeneral
physics
A car goes from one end to the other end of a semicircular path of diameter ' d '. Find the ratio between path length and displacement.
A car goes from one end to the other end of a semicircular path of diameter ' d '. Find the ratio between path length and displacement.
physicsGeneral
physics
A particle moves from A to P and then it moves from P to B as shown in the figure. Find path length and displacement.
![](data:image/png;base64,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)
A particle moves from A to P and then it moves from P to B as shown in the figure. Find path length and displacement.
![](data:image/png;base64,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)
physicsGeneral
physics-
If the thickness of the wire is doubled, then the breaking force in the above question will be
If the thickness of the wire is doubled, then the breaking force in the above question will be
physics-General
physics-
The Young’s modulus of the material of a wire is
If the elongation strain is
, then the energy stored in the wire per unit volume in
is
The Young’s modulus of the material of a wire is
If the elongation strain is
, then the energy stored in the wire per unit volume in
is
physics-General