Science (English Medium) कक्षा ११ - CBSE Question Bank Solutions

Solve the following systems of inequations graphically: 

 5x + y ≥ 10, 2x + 2y ≥ 12, x + 4y ≥ 12, x ≥ 0, y ≥ 0

Show that the following system of linear equations has no solution:  

\[x + 2y \leq 3, 3x + 4y \geq 12, x \geq 0, y \geq 1\]

Show that the solution set of the following system of linear inequalities is an unbounded region:  

\[2x + y \geq 8, x + 2y \geq 10, x \geq 0, y \geq 0\] 

Mark the correct alternative in each of the following:

If x\[<\]7, then

Write the solution of the inequation\[\frac{x^2}{x - 2} > 0\]

If ²⁰C_r = ²⁰C_r−10, then ¹⁸C_r is equal to

If ²⁰C_r = ²⁰C_{r + 4} , then ^rC₃ is equal to

If ¹⁵C_3r = ¹⁵C_{r + 3} , then r is equal to

If ²⁰C_{r + 1} = ²⁰C_{r − 1} , then r is equal to

If C (n, 12) = C (n, 8), then C (22, n) is equal to

If ^mC₁ = ⁿC₂ , then

If ⁿC₁₂ = ⁿC₈ , then n =

If ⁿC_r + ⁿC_{r + 1} = ^n + 1C_x , then x =

If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =

⁵C₁ + ⁵C₂ + ⁵C₃ + ⁵C₄ +⁵C₅ is equal to

Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to

There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is

Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?

In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?