List of top Mathematics Questions asked in CBSE CLASS XII

Write down a unit vector in plane,making an angle of \(30°\)with the positive direction of \(x-axis.\)

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P (E∩F) = 0.2, find P(E|F ) and P(F|E).

Let the vectors \(\vec{a}\) and   \(\vec{b}\)  be such that |\(\vec{a}\)|\(=3\) and |\(\vec{b}\)|\(=\sqrt{\frac{2}{3}}\) ,then \(\vec{a}\times\vec{b}\) is a unit vector,if the angle between \(\vec{a} \) and \(\vec{b}\) is

In a hostel \(60\%\) of the students read Hindi newspaper,\(40\%\) read English newspaper and \(20\%\) read both Hindi and English newspapers.A student is selected at random.
(a)Find the probability that she reads neither Hindi nor English newspapers.
(b)If she reads Hindi newspaper,find the probability that she reads English newspaper.
(c) If she reads English newspapers,find the probability she reads Hindi newspaper.
Minimise Z=x+2y
Subject to 2x+y≥3,x+2y≥6,x,y≥0.

Find the shortest distance between the lines
\(\overrightarrow r=(\hat i+2\hat j+\hat k)+\lambda(\hat i-\hat j+\hat k)\) and
\(\overrightarrow r=2\hat i-\hat j-\hat k+\mu\,(2\hat i+2\hat j+2\hat k)\)

An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on each executive class ticket and a profit of Rs 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class.However, at least 4 times as many passengers refer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximize the profit for the airline. What is the maximum profit?

Probability of solving specific problem independently by A and B are \(\frac{1}{2}\) and \(\frac{1}{3}\) respectively.If both try to solve the problem independently, find the probability that:
(i)the problem is solved.
(ii)exactly one of them solves the problem.
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls.Find the probability that:
(i)both balls are red.
(ii)first ball is black and second is red.
(iii)one of them is black and other is red.

Find the area of the parallelogram whose adjacent sides are determined by the vector \(\vec{a}=\hat{i}-\hat{j}+3\hat{k}\) and \(\vec{b}=2\hat{i}-7\hat{j}+\hat{k}.\)

A die is tossed thrice. Find the probability of getting an odd number at least once.
Maximise Z=5x+3y
Subject to 3x+5y≤15,5x+2y≤10,x≥0,y≥0.

Find the vector equation of the line passing through the point (1, 2, -4)and perpendicular to the two lines: \(\frac {x-8}{3}=\frac {y+19}{-16}=\frac {z-10}{7}\) and \(\frac {x-15}{3}=\frac {y-29}{8} =\frac {z-5}{-5}\)

Maximise Z=3x+2y
Subject to x+2y≤10,3x+y≤15,xy≥0.
Given two independent events \(A\) and \(B\) such that \(P(A)=0.3,P(B)=0.6.\) Find:
(A)\(P(A\, and\, B)\)
(B)\(P(A\, and\, not\, B)\)
(C)\(P(A or B)\)
(D)\(P(neither\, A\, nor\, B)\)

If l1,m1,n1 and l2,m2,n2 are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m1n2-m2n1,n1l2-n2l1,l1m2-l2m1.

Minimise Z=3x+5y
such that x+3y≥3,x+y≥2,x,y≥0

Prove that if a plane has the intercepts a, b, c and is at a distance of P units from the origin, then \(\frac {1}{a^2}+\frac {1}{b^2}+\frac {1}{c^2} =\frac {1}{p^2}\).

Events \(A\) and \(B\) are such that \(P(A)=\frac{1}{2},P(B)=\frac{7}{12}\) and (not \(A\) or not \(B\))\(=\frac{1}{4}\).State whether \(A\) and \(B\) are independent.
Minimise Z=-3x+4y
Subject to x+2y≤8,3x+2y≤12,x≥0,y≥0.

Maximise Z=3x+4y
Subject to the constrains:x+y≤4,x≥0,y≥0.

Show that the line joining the origin to the point(2,1,1)is perpendicular to the line determined by the points(3,5,-1),(4,3,-1).

Distance between the two planes: 2x+3y+4z = 4 and 4x+6y+8z = 12 is

\(The\  planes: 2x-y+4z=5 \ and \ 5x-2.5y+10z=6\  are\)

Find the angle between the planes whose vector equations are 

\(\overrightarrow r.(2\hat i+2\hat j-3\hat k)=5\) and \(\overrightarrow r.(3\hat i-3\hat j+5\hat k)=3\)