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Maths-

General

Easy

Question

1.ⁿC₁ + 2.ⁿC₂ + 3.ⁿC₃ + ….+ n.ⁿC_n is equal to

$\frac{n (n + 1)}{n} . 2^{n}$
$2^{n + 1} - 3$
$n . 2^{n - 1}$
none of these.

The correct answer is: $n.2 to the power of n minus 1 end exponent$

Since r. ⁿC_r = n.^n-1C_r-1
\ reqd. sum
$equals n open square brackets n minus 1 C subscript 0 end subscript plus to the power of n minus 1 end exponent C subscript 1 end subscript plus to the power of n minus 1 end exponent C subscript 2 end subscript plus.... plus to the power of n minus 1 end exponent C subscript n minus 1 end subscript close square brackets equals n.2 to the power of n minus 1 end exponent$

Related Questions to study

$open square brackets 5 square root of 5 plus 11 close square brackets to the power of 2 n plus 1 end exponent$ is always

$open square brackets 5 square root of 5 plus 11 close square brackets to the power of 2 n plus 1 end exponent$ is always

A watch of meritorius students of the coaching institute is to be formed. For this a student must obtain at least 80% aggregate marks in a test of Physics, Chemistry and Math. (M.M. = 100 each).
The number of ways in which a student can qualify for the batch of meritorius students is

A watch of meritorius students of the coaching institute is to be formed. For this a student must obtain at least 80% aggregate marks in a test of Physics, Chemistry and Math. (M.M. = 100 each).
The number of ways in which a student can qualify for the batch of meritorius students is

The number of positive integers satisfying the inequality $n plus 1 C subscript n minus 2 end subscript minus to the power of n plus 1 end exponent C subscript n minus 1 end subscript less or equal than 100$ is

The number of positive integers satisfying the inequality $n plus 1 C subscript n minus 2 end subscript minus to the power of n plus 1 end exponent C subscript n minus 1 end subscript less or equal than 100$ is

parallel

If the (n + 1) numbers a, b, c, d,…….. be all different and each of them a prime number, then the number of different factors (other than 1) of a^m.b. c.d….. is

If the (n + 1) numbers a, b, c, d,…….. be all different and each of them a prime number, then the number of different factors (other than 1) of a^m.b. c.d….. is

If first, fifth and last terms of an A.P. is l, m, p respectively and sum of the A.P. is $fraction numerator open parentheses l plus p close parentheses open parentheses 4 p plus m minus s l close parentheses over denominator K open parentheses m minus l close parentheses end fraction comma text then end text K text is end text$

If first, fifth and last terms of an A.P. is l, m, p respectively and sum of the A.P. is $fraction numerator open parentheses l plus p close parentheses open parentheses 4 p plus m minus s l close parentheses over denominator K open parentheses m minus l close parentheses end fraction comma text then end text K text is end text$

The sum of n terms of the series $fraction numerator 1 to the power of 2 end exponent over denominator 1 end fraction plus fraction numerator 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent over denominator 1 plus 2 end fraction plus fraction numerator 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent plus 3 to the power of 2 end exponent over denominator 1 plus 2 plus 3 end fraction$ +….. is

The sum of n terms of the series $fraction numerator 1 to the power of 2 end exponent over denominator 1 end fraction plus fraction numerator 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent over denominator 1 plus 2 end fraction plus fraction numerator 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent plus 3 to the power of 2 end exponent over denominator 1 plus 2 plus 3 end fraction$ +….. is

parallel

If every pair from among the equations x² + px + qr = 0, x² + qx + rp = 0 and x² + rx + pq = 0 have a common root, then $open parentheses fraction numerator s u m blank o f blank r o o t s over denominator p r o d u c t blank o f blank r o o t s end fraction close parentheses$ is

If every pair from among the equations x² + px + qr = 0, x² + qx + rp = 0 and x² + rx + pq = 0 have a common root, then $open parentheses fraction numerator s u m blank o f blank r o o t s over denominator p r o d u c t blank o f blank r o o t s end fraction close parentheses$ is

Which is U.P. spirit (containing ethyl alcohol by volume)?

Which is U.P. spirit (containing ethyl alcohol by volume)?

Chemistry-General

When vapours of an alcohol are passed over hot reduced copper, alcohol is converted into alkene, the alcohol is:

When vapours of an alcohol are passed over hot reduced copper, alcohol is converted into alkene, the alcohol is:

Chemistry-General

parallel

Primary amine on treatment with $N a N O subscript 2 end subscript$ and HCI yields:

Primary amine on treatment with $N a N O subscript 2 end subscript$ and HCI yields:

Chemistry-General

Alcoholic fermentation is brought by:

Alcoholic fermentation is brought by:

Chemistry-General

HBr reacts fastest with:

HBr reacts fastest with:

Chemistry-General

parallel

Which one of the following alcohols reacts most readily with Lucas reagent?

Which one of the following alcohols reacts most readily with Lucas reagent?

Chemistry-General

In this reaction,

the molecule (A) and the reagent (B) are :

In this reaction,

the molecule (A) and the reagent (B) are :

Chemistry-General

Propene on reaction with carbon monoxide and hydrogen at high temperature under pressure in presence of cobalt carbonyl catalyst gives:

Propene on reaction with carbon monoxide and hydrogen at high temperature under pressure in presence of cobalt carbonyl catalyst gives:

Chemistry-General

parallel

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