List of top Mathematics Questions asked in CBSE CLASS XII

If either \(\vec{a}=0\) or \(\vec{b}=0\),then \(\vec{a}\times\vec{b}=0\). Is the converse true? Justify your answer with an example.

Examine the applicability of Mean Value Theorem for all three functions given in the above exercise 2.

Let A and B independent events, \(P(A)=0.3\) and \(P(B)=0.4\).Find:
(A)\(P(A\cap B)\)
(B)\(P(A\cup B)\)
(C)\(P(A|B)\)
(D)\(P(B|A)\)

Find the equation of the plane through the line of intersection of the planes
x+y+z=1 and 2x+3y+4z=5 which is perpendicular to the plane x-y+z= 0

Given that \(\vec{a}.\vec{b}=0\) and \(\vec{a}\times\vec{b}=0\).What can you conclude about the vectors \(\vec{a}\) and \(\vec{b}\) ?

Given that the events \(A\) and \(B\) are such that \(P(A)=\frac{1}{2},P(A∪B)=\frac{3}{5}\) and \(P(B)=ρ.\)
Find \(ρ\) if they are(i) mutually exclusive,(ii) independent.

Let E and F be events with \(P(E)=\frac{3}{5},P(F)=\frac{3}{10}\) and \(P(E∩F)=\frac{1}{5}\) .Are E and F independent?

Show that
\((\vec{a}-\vec{b})\times(\vec{a}+\vec{b})=2(\vec{a}\times \vec{b})\)

The cartesian equation of a line is \(\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}\). Write its vector form.

A die marked 1,2,3 in red and 4,5,6 in green is tossed.Let A be the event ‘number is even’ and B be the event ‘number is red’. Are A and B independent?

Find the cartesian equation of the line that passes through the point(-2,4,-5)and parallel to the line given by \(\frac{x+3}{3}\)=\(\frac{y-4}{5}\)=\(\frac{z+8}{6}\)

A fair coin and an unbiased die are tossed.Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’.Check whether A and B are independent events or not.

Find the vector equation of the plane passing through the intersection of the planes

\(\overrightarrow r.(2\hat i+2\hat j-3\hat k)=7\),\(\overrightarrow r.(2\hat i+5\hat j+3\hat k)=9\) and through the point ( 2, 1, 3 ).

Find the equation of the line in vector and in cartesian form that passes through the point with position vector 2\(\hat i\)-\(\hat j\)+4\(\hat k\) and is in the direction \(\hat i\)+2\(\hat j\)-\(\hat k\).