In a five digit number 1b6a3 a is the greatest single digit perfect cube and twice of it exceeds b by 7 .Then the sum of the number and it cube root is__________
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In the expansion of `(3^(-x//4)+3^(5x//4))^n` the sum of binomial coefficient is 64 and term with the greatest binomial coefficient exceeds the third
Correct Answer - A To get sum of coefficients put `x = 0` Given that sum of coefficient is `2^(n) = 64` or `n = 6` The greatest binomial coefficeint is...
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A six-faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice, the probability that
Correct Answer - D Let the probability for getting an odd number be p. Therfore the probability for getting an even number is 2p. `thereforep+2p=1orp=1/3` Sum of two numbers is even...
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Number of six-digit numbers such that any digit that appears in the number appears at least twice, where the digits of each number are from the set `{
Correct Answer - C `(c )` Case I : All six digits alike i.e. `111111`, `222222`……..etc. `=5` ways Case II : `2` alike `+2` other alike. Select any three in `"^(5)C_(3)`...
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All the five digit numbers in which each successive digit exceeds its predecessor are arranged in the increasing order of their magnitude. The `97^(th
Correct Answer - B `(b)` All the possible number are `"(9)C_(5)` (none containing the digit `0`)=`126` Total numbers starting with `1` `="(8)C_(4)=70` (using `2,3,4,5,6,7,8,9`) `1 _ _ _ _` Total numbers...
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When twice a non zero positive numbr is divided by its cube root the quotient is obtained as 32 .If the cube of the number is divided by the number it
Correct Answer - `4^(6)`
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Write the following in exponential form and redical form. (i) Cube root of 729 (ii) Fifth root of 1990 (iii) Square root of 2001 (iv) Seventh root of
Correct Answer - (i) `(729)^(1/3), root(3)(729)` (ii) `(1990)^(1/5), root(5)(1990)` (iii) `(2001)^(1/2), sqrt(2001)` (iv) `(777)^(1/7), root(7)(777)`
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(i) Simplify `(2^(2/3)-2^((-2)/3))(2^(4/3)+1+2^((-4)/3))` (ii) `[(root(6)(7))^(2)+(root(6)(7))^(-2)][(root(6)(7))^(4)-1+(root(6)(7))^(-4)]`
Correct Answer - (i) `15/4` (ii) `50/7`
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Arrange the following surds in an ascending order of magnitude: `root(3)(9),root(9)(5),root(3)(7)`
Correct Answer - `root(9)(5),root(6)(9),root(3)(7)`
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Five years ago, the sum of the ages of a father and two sons was \( x \) years, then after five years, the sum of the ages of all will be years.
5 years after age of each of father and his two sons will be 10 years more than it was 5years ago. Hence after 5years the sum of thieir age...
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If 45 is subtracted from twice the greater of two numbers, it results in the other number. If 21 is subtracted from twice the smaller number, it resul
Correct Answer - 37,29
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