Maths-
General
Easy
Question
If nCr denotes the number of combinations of n things taken r at a time, then the expression nCr+1 + nCr –1 + 2 × nCr equals-
- n + 1Cr +1
- n+2Cr
- n+2Cr+1
- n+1Cr
Hint:
By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Here we have given nCr denotes the number of combinations of n things taken r at a time, we have to find the expression nCr+1 + nCr –1 + 2 × nCr.
The correct answer is: n+2Cr+1
A permutation is the non-replaceable selection of r items from a set of n items in which the order is important.
![P presuperscript n subscript r equals space fraction numerator left parenthesis n factorial right parenthesis space over denominator left parenthesis n minus r right parenthesis factorial end fraction](data:image/png;base64,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)
A combination is created by selecting r items from a group of n items without replacing them and without regard to their order.
![C presuperscript n subscript r equals space fraction numerator left parenthesis n factorial right parenthesis space over denominator left parenthesis n minus r right parenthesis factorial cross times r factorial end fraction](data:image/png;base64,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)
Here we have given: nCr denotes the number of combinations of n things taken r at a time, so
![C presuperscript n subscript r plus 1 end subscript plus C presuperscript n subscript r minus 1 end subscript plus 2 cross times C presuperscript n subscript r
S o l v i n g space t h i s comma space w e space g e t colon
C presuperscript n subscript r plus 1 end subscript plus C presuperscript n subscript r minus 1 end subscript plus C presuperscript n subscript r plus C presuperscript n subscript r
N o w space u s i n g space t h e space f o r m u l a colon
C presuperscript n subscript i plus C presuperscript n subscript i minus 1 end subscript equals C presuperscript n plus 1 end presuperscript subscript i
A p p l y i n g space t h i s comma space w e space g e t colon
C presuperscript n subscript r plus 1 end subscript plus C presuperscript n plus 1 end presuperscript subscript r
A p p l y i n g space t h e space s a m e space f o r m u l a space a g a i n comma space w e space g e t colon
C presuperscript n plus 2 end presuperscript subscript r plus 1 end 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The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is .
Related Questions to study
maths-
The number of ways is which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question is -
The number of ways is which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question is -
maths-General
physics-
An intense stream of water of cross-sectional area
strikes a wall at an angle
with the normal to the wall and returns back elastically. If the density of water is
and its velocity is
,then the force exerted in the wall will be
![](data:image/png;base64,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)
An intense stream of water of cross-sectional area
strikes a wall at an angle
with the normal to the wall and returns back elastically. If the density of water is
and its velocity is
,then the force exerted in the wall will be
![](data:image/png;base64,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)
physics-General
physics-
The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with above spring of half length, the line
will
![](data:image/png;base64,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)
The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with above spring of half length, the line
will
![](data:image/png;base64,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)
physics-General
physics-
Two small particles of equal masses start moving in opposite directions from a point
in a horizontal circular orbit. Their tangential velocities are
and
, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at
, these two particles will again reach the point ![A](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIdJREFUeNpjYMAPChhIAOFA/AuIWYhRLAjEl4B4NxAHEKNhJhBHAnE8EE8hpNgSiLdA2eJAfBefYpB7zwCxLJLYOSDWwKWhHohL0MRagTgLm2INqGnowB6IN2HTcBiI/+PAGMGbBsQT8PhtORB7wTiS0DDnwaMhGdnAVUDsQyCopYH4FgM5AACEKxqdNkqvogAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PC9tYXRoPkHiA+IAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
Two small particles of equal masses start moving in opposite directions from a point
in a horizontal circular orbit. Their tangential velocities are
and
, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at
, these two particles will again reach the point ![A](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIdJREFUeNpjYMAPChhIAOFA/AuIWYhRLAjEl4B4NxAHEKNhJhBHAnE8EE8hpNgSiLdA2eJAfBefYpB7zwCxLJLYOSDWwKWhHohL0MRagTgLm2INqGnowB6IN2HTcBiI/+PAGMGbBsQT8PhtORB7wTiS0DDnwaMhGdnAVUDsQyCopYH4FgM5AACEKxqdNkqvogAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PC9tYXRoPkHiA+IAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
physics-General
maths-
In a model, it is shown that an arch of abridge is semi-elliptical with major axis horizontal. If the length of the base is 9 m and the highest part of the bridge is 3 m from the horizontal, the best approximation of the height of the arch, 2 m from the centre of the base is
In a model, it is shown that an arch of abridge is semi-elliptical with major axis horizontal. If the length of the base is 9 m and the highest part of the bridge is 3 m from the horizontal, the best approximation of the height of the arch, 2 m from the centre of the base is
maths-General
maths-
The number of non-negative integral solutions of x + y + z n, where n N is -
The number of non-negative integral solutions of x + y + z n, where n N is -
maths-General
maths-
Between two junction stations A and B there are 12 intermediate stations. The number of ways in which a train can be made to stop at 4 of these stations so that no two of these halting stations are consecutive is -
Between two junction stations A and B there are 12 intermediate stations. The number of ways in which a train can be made to stop at 4 of these stations so that no two of these halting stations are consecutive is -
maths-General
maths-
If n objects are arranged in a row, then the number of ways of selecting three of these objects so that no two of them are next to each other is -
If n objects are arranged in a row, then the number of ways of selecting three of these objects so that no two of them are next to each other is -
maths-General
Maths-
The number of numbers between 1 and 1010 which contain the digit 1 is -
The number of numbers between 1 and 1010 which contain the digit 1 is -
Maths-General
Maths-
The number of rectangles in the adjoining figure is –
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASQAAADRCAMAAABSDz/AAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAJ2UExURf////z8/Pj4+PX19fLy8v39/f7+/ufn59ra2tDQ0Nzc3Pf39+zs7OLi4uPj4/n5+eTk5MHBwcDAwODg4Ojo6PHx8fb29vv7+4uLi1paWj4+PjY2NkZGRlhYWHFxcZWVlb6+vuXl5erq6oqKil5eXkdHRz09PUxMTGdnZ42Njbm5ud7e3t3d3e3t7c7Ozvr6+s/Pz+Hh4cbGxr29vbi4uKCgoG1tbYODg4aGhpycnLq6uqGhoW5uboGBgba2tvDw8KampjIyMisrKyoqKiMjIxUVFRsbGxwcHBQUFCIiIhoaGikpKSwsLEhISMXFxX9/fwEBATo6OggICGZmZicnJwcHB0REREpKSgkJCSEhIWVlZSUlJRAQEKqqqn19fZ+fnygoKK6urry8vF9fX3R0dKenpyYmJqysrMPDw3Z2dsnJyS8vL35+fiQkJKKiom9vb7CwsGFhYXd3d6ioqC0tLbu7u7W1ta2trWBgYHV1dRMTE0BAQElJSREREWRkZA8PD0tLS2NjY7Kyso+PjwwMDB8fHx0dHSAgIFFRUVdXV3x8fK+vr8fHx3h4eM3NzTAwMGlpaaWlpbOzs3l5eYCAgGtra3Nzcy4uLoKCgqurq8LCwnp6etfX111dXZOTk2pqahgYGDs7O5GRkRYWFhkZGTg4OAYGBg4ODgUFBQ0NDYWFhdXV1WJiYllZWRcXFzk5OTU1NYmJiWxsbMjIyL+/v7e3t8rKyp6enrS0tPPz8xISEkNDQ01NTVNTU46OjqSkpFtbW5CQkJaWlpubm3t7e5iYmAAAADQ0ND8/P0FBQTw8PEJCQt/f39bW1tnZ2djY2Nvb2wAAABbHfvIAAADSdFJOU///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////APyIqu8AAAAJcEhZcwAAFxEAABcRAcom8z8AAAV7SURBVHhe7Z1BkqM6DIb7QHAIll5TxS6XSBVLH4ANd+EQ5FxPBs90pl8ykiWeU376Pzu2oDo4sX9k4ST0FwAAAAAAAAAAAKrQ5xq8pevWLpvgDX3fdegkAMCH6dZ5XrueyDvAT/p5W6ZhmJZxn+G133B00jQNy7ihk95D5xlN/XS+5e3/D+aor1+zoaNa1Jk8ppJ9vGdLyW0b9xtVRz457O+U8tvHPm6psrDKlHsLemKu1UTbEYxPJyaZlLfHMCpZHiFbWobHNI53MtLjIG8854NX9RTt7d9yN/yde5D93QvmMGZLyxjmbGmwty9984ZOWgf7i7R00hXt/+eddLtgJNtQ0hb2bBVzxemmHiFiDUu2tFRQ0hUjCSWxWJU0GgN0KEmAvJM8+6QIJbE48EnzsMAncUBJAkhJ2dICJQmQdxJ8EguUJMC3T0KcxONASbh2E1BPSb6v3aAkHumbh08SYBjMNdyzpcWopIofBFiUdMlI0kFUmXwS1WSUp5R/t8+zxWlZRk0+Pxz8uVeeKYU4UanNZ/tHJkpKqo9XEISdtMcYBkqlmYrwSB8z/7lbmHOLkY5AxnmU8vJon/mbl2WqUxmFp/s9budXBwpLqrewHBv0KMoZspaQGl+PneXlHqbf9llI7JPTWKSnm/DvXkCzS7a02By3/RNc6ZuX+q4X+ImTPtxJ6saJ1cfKZCvfKvloxG1Uko9rNyhJgE1JF6xxt7Ay2c433VpWUra0yDsJSmLx7ZOgJB4fSsqWFihJgLyTGo64zSujiJN4pG8e124CoCQBTSvJxXcBMLsJsCmJ2oeSOOoNku+IG3ESjw8lwSdx1BskrEwKgJIEtBxxwyfxQEkCnPxyErObAJuSECcJqDdIvn0SlMTjQEnwSQLqDZLvazfESTzSNw+fJABKEtC2krKlBUoSIO+kdiNu+CSeeoOE9SQBUJIAxEkCoCQBLc9uWE/iqTdI8EkCoCQBH/41t0VJF7RfI0767L1Kqg1SN8Zl33TpHodUHbaumOKYLB37GAb1s1P7+yq7605/m/K9LBSkm2jYeJiOYG1/2CaRkvtTSTrSSB5jUljkkupTSdpESj6Ookgpb7dZev8mg0+64v5Jln+BU2/icH2vEmknmWY364u03a7MTcRtCwGcXLu1oaQPrwKYLku8fILbhpIa9kluVgGgJBZrnITZjaWekhqe3ShOgk/iqKektme3bGlBnCTAh5LgkzjqKcn3tRuUxCN9802vJzm5fxKUxGKOuLOlBT5JgLyTPPskKIlH+uZbjrihJB4oSQBWAQTUU1Lb127wSRz1lOTbJ0FJPA6UdMHv3TC78chPt3aVhFUAnnpKant2Q5zEASUJgE8SUE9Jvq/dECfxOPBJuHYTACUJQJwkoJ6SfH+rBLMbjwOf5Ob+SVASi1FJuHbjqackQydd8RtYo0/KlpZNPLul040cYHm+pZH8196CTEpKnXRsKBIp6WmrOFGWKnmL07IsoyZPMfzcVZhDHM7G/9wtzL/az4coKKlI9TiIOykOIaXSTMWDnvq8qzjHB5W/0pMpS0f7lL4LqX3WYYjC030L93nVpS1Mz5vlaV3C9rQpTrnac/vfhcz+TovYcat95xV3mLA5buvEIb1zRNOfuzUQAviJkz4ccZs6ycsat+V0g5IEuFnjbkNJH57dLEpy84sA+CQWq5KcrHFDSSxWJcEnsdQbpKZnN8RJLPUGyeSTrCNpvcDF95NYavok9evsli1bWvbFcltXe/sFi25916vyet+ToU/9fp+fNksTtf+8WZ76UXi6bY8waQlDNrQM+rYT5vajsJNu9FKnQZPTK0yGIanbztn09FSMwtO9c03uBAAAAAAAAAAAAAAA1Hx9/QOI8eMC9B3cvwAAAABJRU5ErkJggg==)
The number of rectangles in the adjoining figure is –
![](data:image/png;base64,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)
Maths-General
chemistry-
Assertion :this equilibrium favours backward direction.
Reason :
is stronger base than ![C H subscript 2 end subscript C O O to the power of minus end exponent](data:image/png;base64,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)
Assertion :this equilibrium favours backward direction.
Reason :
is stronger base than ![C H subscript 2 end subscript C O O to the power of minus end exponent](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE8AAAARCAYAAACcsPEBAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAeNJREFUeNrtmEFERFEUhsczkhbRMkmMkbRIm6RFEq3Sok2LVkm0SIsWkSQt2qVVu5EnSSLJLEabjLSYbZIk0SKtEiMjGW3qP5zHk3fvO+e+GUrz863O75y51z33njepVLQyYAtcgw/wBDZB2w8fxTxDDlssTtL6pD7ggxdQAfug15Jb6v+yYNQyKIDh0OI7wRLYC/my4MaQwxaLk7Q+aR3kwQB7iUne7MGI3Fq/SitgV+ilokcOsVrVXwM5Q2yUT20Sv0rd4BGkhf4NXqw2Vov65L2PuRYqoTbX+tXa5taQ6phPmDZWi/rkXYzxnHPru/jVuuO7SqqHmEu1o471b0FXjOcZtDr6VaLjXFX63w2xNL+Q9arvCfLTb3hz9KvVxD0vFb1MRUNsCFzUsb7EOwUOHP1OopPUIvROR4wNtljQyp+gZGhPaX2P89gu/1Jo9ND6neTzjCXRDpizxOYtC18AVwnr0xw4a4itRowkWr9adKGWOVnwZDeDCV7YWMh7CsYNefKWWKBqwvpZHj1mQqNNP7dezjC0a/xOyvLnSoXbjC7Rk4jNKPPComSLkUbAZcL6wVeHz/VewSHftyZp/b9O7Xy/ZFINqb8gCryBDSlP3JnrEPrfRRvX09gGN6n+E/sr+gYWspix7n20kAAAALl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1Yj48bXJvdz48bWk+QzwvbWk+PG1pPkg8L21pPjwvbXJvdz48bW4+MjwvbW4+PC9tc3ViPjxtc3VwPjxtcm93PjxtaT5DPC9taT48bWk+TzwvbWk+PG1pPk88L21pPjwvbXJvdz48bW8+LTwvbW8+PC9tc3VwPjwvbWF0aD6kqiZ7AAAAAElFTkSuQmCC)
chemistry-General
Physics-
A 0.098 kg block slides down a frictionless track as shown. The vertical component of the velocity of block at
is
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/904353/1/923693/Picture33.png)
A 0.098 kg block slides down a frictionless track as shown. The vertical component of the velocity of block at
is
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/904353/1/923693/Picture33.png)
Physics-General
physics-
Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are
respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at
,these two particles will again reach The point ![A ?](data:image/png;base64,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)
![](data:image/png;base64,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)
Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are
respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at
,these two particles will again reach The point ![A ?](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
physics-
The trajectory of a particle moving in vast maidan is as shown in the figure. The coordinates of a position
are
The coordinates of another point at which the instantaneous velocity is same as the average velocity between the points are
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486211/1/923664/Picture20.png)
The trajectory of a particle moving in vast maidan is as shown in the figure. The coordinates of a position
are
The coordinates of another point at which the instantaneous velocity is same as the average velocity between the points are
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486211/1/923664/Picture20.png)
physics-General
physics-
The potential energy of a particle varies with distance
as shown in the graph.
The force acting on the particle is zero at
![](data:image/png;base64,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)
The potential energy of a particle varies with distance
as shown in the graph.
The force acting on the particle is zero at
![](data:image/png;base64,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)
physics-General