List of top Mathematics Questions asked in CBSE Class XI

A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that
(i) all will be blue.
(ii) at least one will be green.

If f(x) = \(f(x)=\left\{\begin{matrix} mx^2+n, &\,\,\,\,x<0 \\ nx+m,&\,\,\,\, 0\leq x\leq1 \\ nx^3+m,&\,\,\,\, x>1 \end{matrix}\right.\). For what integers m and n does both \(\lim_{x\rightarrow 1}\)f(x) and \(\lim_{x\rightarrow 1}\) f(x) exist?

If the function f(x) satisfies \(\lim_{x\rightarrow 1}\) \(\frac{f(x)-2}{x^2-1}\) =\(\pi\), evaluate \(\lim_{x\rightarrow 1}\) f(x).

Expand the expression \((1- 2x)^ 5\).

Two dice are thrown. The events A, B, and C are as follows: A: getting an even number on the first die. B: getting an odd number on the first die.C: getting the sum of the numbers on the dice ≤ 5 Describe the events (i) A'(ii)not B(iii)A or B(iv) A and B(v)A but not C(vi)B or C(vii)B and C(viii)\(A∩B'∩C'\)

Three coins are tossed. Describe (i)Two events which are mutually exclusive. (ii)Three events which are mutually exclusive and exhaustive.(iii)Two events, which are not mutually exclusive.(iv)Two events which are mutually exclusive but not exhaustive.(v)Three events which are mutually exclusive but not exhaustive.

Let a₁, a₂,..., a_n be fixed real numbers and define a function f(x)=(x-a₁)(x-a₂)...(x-a_n).
What is \(\lim_{x\rightarrow a_1}\) f(x)?
For some a ≠ a₁, a₂ .....a_n, Compute \(\lim_{x\rightarrow a}\) f(x).

Three coins are tossed once. Let \(A\) denote the event ‘three heads show”, \(B\) denote the event “two heads and one tail show”, \(C\) denote the event” three tails show and \(D\) denotes the event a head shows on the first coin”. Which events are (I) mutually exclusive? (ii) simple? (iii) Compound?

The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is the probability of passing the Hindi examination?

In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0.7. The probability of passing at least one of them is 0.95. What is the probability of passing both?

An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events: \(A:\) the sum is greater than \(8\), \(B:\)\(2\) occurs on either die \(C:\)The sum is at least \(7\), and a multiple of \(3\). Which pairs of these events are mutually exclusive?

A die is thrown. Describe the following events:
(i) \(A: a\) number less than \(7\)
(ii) \(B: a\) number greater than \(7\)
(iii) \(C: a\) multiple of \(3\)

(iv) \(D: a\) number less than \(4\)
(v) \(E: a\) even number greater than \(4\)
(vi) \(F: a\) number not less than \(\)\(3\)
Also, find \(A∪B, A∩B, B∪C, E∩F, D∩E, A-C, D-E, E∩F', F'\)

A die is rolled. Let \(E\) be the event “die shows \(4\)” and \(F \) be the event “die shows even number”. Are \(E\) and \(F\) mutually exclusive?

Events E and F are such that P(not E or not F) = 0.25, State whether E and F are mutually exclusive.

If E and F are events such that \(P(E)=\frac{1}{4},P(F)=\frac{ 1}{2}\) and P(E and F)\(=\frac{1}{8}\), find (i) P(E or F), (ii) P(not E and not F).

Given \(P(A)= \frac{3}{5}\) and \(P(B)=\frac{1}{5}\). Find P(A or B), if A and B are mutually exclusive events.

Fill in the blanks in following table:

	P(A)	P(B)	P(A∩B)	P(A∪B)
(i)	\(\frac{1}{3}\)	\(\frac{1}{5}\)	\(\frac{1}{15}\)	…
(ii)	0.35	….	0.25	0.6
(iii)	0.5	0.35	….	0.7

Find the value of p so that the three lines \( 3x + y - 2 = 0, px + 2y - 3 = 0\) and \(2x - y - 3 = 0\) may intersect at one point

Solve the inequalities and represent the solution graphically on number line: 2(x–1) < x+5, 3(x+2) > 2-x.

Solve the inequalities and represent the solution graphically on number line: 5x + 1 > – 24, 5x – 1 < 24.