There are `10` different books in a shelf. The number of ways in which three books can be selected so that exactly two of them are consecutive is

Correct Answer - D Three-digit numbers are 100, 101, …, 999. Total number of such numbers is 900. The three-digit numbers (which have all same digits) are 111, 222, 333, …,...

Correct Answer - C We have, `n(S) = 5^(5)` For computing favorable outcomes, 2 boxes which are to remain empty, can be selected in `.^(5)C_(2)` ways and 5 marbles can be...

Correct Answer - A::C Given equation is `x^(2) + 2x sin(cos^(-1) y) + 1 =0` Since x is real, `D ge 0`. Therefore, `4(sin(cos^(-1)y))^(2) -4 ge 0` or `(sin(cos^(-1)y))^(2) ge 1`...

Correct Answer - B Let `P(S)=P(1 or 2)=1//3` `P(F)=P(3or4or5or6)=2//3` `P(A "wins")=P[(SS orSFSSorSFSFSSor..)or(FSSorFSFFSSor...)]` `=((1)/(9))/(1-(2)/(9))+((2)/(27))/(1-(2)/(9))` `= 1/9xx9/7+2/27xx9/7` `=1/7+2/21=(3+2)/(21)=5/21` P(A swining)`=5/21,` P(B winning)`=16/21`

Correct Answer - A `(a)` Selecting any two pairs, number of ways `=.^(12)C_(2)` Now we have to select remaining three shoes from `10` pairs such that no pair is selected. Three...

Correct Answer - C `(c )` First arrange `8` blue alike bottles `to ` number of ways `=1` Now select one gap out of `9` gaps created to put two green...

Correct Answer - B `(b)` `n(A)=^(3+2-1)C_(2-1)xx^(3+2-1)C_(2-1)=16` `n(B)=n(C )=16` `n(AnnB)=^(3+2-1)C_(1-1)xx^(3+2-1)C_(1-1)` `=1=n(BnnC)=n(AnnC)` `n(AnnBnnC)=0` Required no. of ways `=100-(16+16+16-1-1-1+0)=55`

Correct Answer - B `(b)` Each ball can be placed in 5 ways. `:.` Total number of ways, `n(S)=5^(5)` `2` empty boxes, can be selected in `"^(5)C_(2)` ways and `5` balls...

Correct Answer - C `(c )` Let event `S to A` is getting `1` or `2` Event `F to B` is getting `3,4,5,6` `P(S)=P(1 or 2)=1//3` `P(F)=P(3 or 4 or 5...

Correct Answer - `(i) 3/8 (ii) 3/8 (iii) 7/8 (iv) 1/2 (v) 7/8`