List of top Mathematics Questions asked in CBSE Class XI

Solve the inequality: \(7 ≤ \frac{(3x+11)}{2} ≤ 11\)
Solve the inequality \( -12 < 4-\frac{3x}{-5} ≤ 2\).
Solve the inequality  \(-15 < \frac{3(x-2)}{5} ≤ 0\).
Solve the inequality: \(-3 ≤ 4-\frac{7x}{2} ≤ 18\)
Solve the inequality 6 ≤ –3(2x – 4) < 12.
Solve the inequality 2 ≤ 3x – 4 ≤ 5
A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5 cm longer than the second?
Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23.
To receive Grade 'A' in a course, one must obtain an average of 90 marks or more in five examinations (each of 100 marks). If Sunita's marks in first four examinations are 87, 92, 94 and 95, find minimum marks that Sunita must obtain in fifth examination to get grade 'A' in the course.
Solve the given inequality and show the graph of the solution on number line: \(\frac{x}{2} ≥ \frac{(5x-2)}{3} -\frac{ (7x-3)}{5}\).
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false,
give an example.
(i) If x \(\in\) A and A \(\in\) B, then x \(\in\) B
(ii) If A \(⊂\) B and B \(\in\) C, then A \(\in\) C
(iii) If A \(⊂\) B and B \(⊂\) C, then A \(⊂\) C
(iv) If A \(⊄\) B and B \(⊄\) C, then A \(⊄\) C
(v) If x\( ∈\) A and A \(⊄\) B, then x \(∈\) B
(vi) If A\( ⊂\) B and x \(∉\) B, then x \(∉\) A
Decide, among the following sets, which sets are subsets of one and another:
A = {x: x \(\in\) R and x satisfy \( x^2 - 8x + 12 = 0\)},
B = {2, 4, 6}, C = {2, 4, 6, 8…}, D = {6}.
Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A' ?
Solve the given inequality and show the graph of the solution on number line: 5x – 3 ≥ 3x – 5.
An equilateral triangle is inscribed in the parabola y2 = 4 ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.
Solve the given inequality and show the graph of the solution on number line: 3x - 2 < 2x +1.
A man running a racecourse note that the sum of the distances from the two flag posts form him is always 10 m and the distance between the flag posts is 8 m. find the equation of the posts traced by the man.

Solve the given inequality for real \(x:\frac{ (2x -1)}{3} ≥ \frac{(3x -2)}{4} - \frac{(2-x)}{5}\).

Solve the given inequality for real\(x: \frac{x}{4} < \frac{(5x-2)}{3} -\frac{ (7x-3)}{5}\).

Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latus rectum.
Solve the given inequality for real x: 37 – (3x + 5) ≥ 9x – 8(x – 3)
Solve the given inequality for real x: 2(2x + 3) - 10 < 6 (x - 2).
A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.

Solve the given inequality for real\(x: \frac{1}{2}(\frac{3x}{5}+4) ≥ \frac{1}{3}(x-6)\).

Solve the given inequality for real \(x: \frac{3(x - 2)}{5} ≤ \frac{5(2 - x)}{3}\).