List of top Mathematics Questions

Suppose X has a binomial distribution B\(\bigg(6,\frac{1}{2}\bigg).\)Show that X=3 is the most likely outcome.

Find the equation of the tangent line to the curve \(y = x^2 − 2x + 7\) which is:
(a) parallel to the line \(2x − y + 9 = 0 \)
(b) perpendicular to the line \(5y − 15x = 13\)

In an examination,20 questions of true-false are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads ,he answers 'true'. if it falls tails, he answers 'false'. Find the probability that he answers at least 12 questions correctly.

If either vector \(\vec {a}=\vec{0}\space or\space  \vec{b}=\vec{0}\), then \(\vec{a}.\vec{b}=0\).But the converse need not be true.Justify your answer with an example.

For given vectors,\(\vec{a}=2\hat{i}-\hat{j}+2\hat{k}\) and \(\vec{b}=-\hat{i}+\hat{j}-\hat{k}\),find the unit vector in the direction of the vector \(\vec{a}+\vec{b}.\)

Find the position vector of point R which divides the line joining two points P and Q whose position vector is (2\(\vec a\)+\(\vec b\))and(\(\vec a\)-3\(\vec b\))externally in the ratio 1:2. Also, show that P is the midpoint of the line segment RQ.

Find the unit vector in the direction of vector \(\vec{PQ}\) ,where \(P\) and \(Q\) are the points \((1,2,3)\) and \((4,5,6)\) respectively.

A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag ,what is the probability that none is marked with the digit 0?

Find the unit vector in the direction of the vector \(\vec{a}=\hat{i}+\hat{j}+2\hat{k}.\)
Find the sum of the vectors \(\vec{a}=\hat{i}-2\hat{j}+\hat{k},\vec{b}=-2\hat{i}+4\hat{j}+5\hat{k}\) and \(\vec{c}=\hat{i}-6\hat{j}-7\hat{k}.\)

The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs. 
I. none
II. not more than one
III. more than one
IV. at least one
will fuse after 150 days of use.

If  \(\vec{a}.\vec{a}=0\) and  \(\vec{a}.\vec{b}=0,\)then what can be concluded about the vector \(\vec{b}\)?

Using the method of integration find the area of the region bounded by lines:
\(2x+y=4,3x–2y=6\) and \(x–3y+5=0\)
Using the method of integration find the area of the triangle ABC,coordinates of whose vertices are A(2,0),B(4,5)and C(6,3)
Find the area bounded by curves{\((x,y):y≥x^2\) and \(y=|x|\)}

Find the area of the smaller region bounded by the ellipse \(\frac{x^2}{a^2}\)+\(\frac{y^2}{b^2}\)=1 and the line \(\frac{x}{a}\)+\(\frac{y}{b}\)=1

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that:
 (i) all the five cards are spade?
 (ii) only 3 cards are spades?
 (iii) none of spade?

Using the method of integration find the area bounded by the curve\(|x|+|y|=1\)
[Hint:the required region is bounded by lines \(x+y=1,x–y=1,–x+y=1\) and \(–x–y=11\)]
Find the area of the region enclosed by the parabola \(x^2=y\),the line \(y=x+2\) and \(x-axis\)

Determine order and degree(if defined)of differential equation \(\frac{d^4y}{dx^4}\)+sin(y''')=0

\(If ƒ(x)=∫_0^xt\ sin\ t\ dt,\ then  ƒ'(x)is\)

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.

Show that the points A(1,-2,-8),B(5,0,-2),and C(11,3,7)are collinear,and find the ratio with B devides AC.

There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?

The area bounded by the \(y-axis,y=cosx\) and \(y=sinx\) when \(0≤x≤\frac{π}{2}\)