List of top Mathematics Questions

Let the vectors \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) represent three coterminous edges of a parallelepiped of volume \(V\). Then the volume of the parallelepiped, whose coterminous edges are represented by \(\mathbf{a} + \mathbf{b} + \mathbf{c}\) and \(\mathbf{a} + 2\mathbf{b} + 3\mathbf{c}\), is equal to:
For the system of linear equations  
2x+4y+2az=b
x+2y+3z=4 
2x-5y+2z=8 
which of the following is NOT correct ?  
Let s1, s2, s3,…..,s10 respectively be the sum to 12 terms of 10 A.P.s whose first terms are 1,2,3, …. ,10 and the common differences are 1, 3, 5, …. , 19 respectively. Then  \(10∑^{10}_{i=1} s_i\) is
\((S1) : lim_{n→∞}\frac{1}{ n ^2} ( 2 + 4 + 6 + . . . . + 2n) = 1\)
\((S2):  lim_n→∞\frac{1}{n^{16}}( 1^15 +2^15 +3^15 + . . . . + n^15 ) = \frac{1}{16} \)
Let a =\(\^i+4\^j​+2\^k,b=3\^i−2\^j​+7\^k \,\,\,\,and\,\,\.\ c=2\^i−\^j​+4\^k\). Find a vector d satisfies \(\overrightarrow{d}\times{\overrightarrow{b}}=\overrightarrow{c}\times{\overrightarrow{b}}\) and \(\overrightarrow{d}.\overrightarrow{a}=24\), then \(|\overrightarrow{d}|^2\) is equal to
\(max\\{0≤x≤π}\) \(\{x−2\,\, sin. x \,\,cos+\frac{1}{3} sin\,\, 3x \}=\)
The distance of the point ( -1,2,3) from the plane \(\overrightarrow{r}( \^i−2 \^j+3 \^k )=10\) parallel to the line of the shortest distance between the lines \(\overrightarrow{r}=(\^i=\^j)+λ(2\^i+\^k)\) and  \(\overrightarrow{r}=(2\^i=\^j)+μ(\^i+\^j+\^k)\)  is 
A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If X denotes the number of tosses of the coin, then the mean of X is
The negation of the statement \(((A\land(B\lor C)) ⇒ (A\lor B)) ⇒ A\) is
If the system of equations  
x + y + az = b  
2x + 5y + 2z = 6  
x + 2y + 3z = 3  
Has infinitely many solutions, then 2a + 3b is equal to
If the equation of the plane passing through the line of intersection of the planes 2x – y + z = 3, 4x– 3y +5z + 9 = 0 and parallel to the line  \(\frac{x+1}{−2} =\frac{ y+3}{4}= \frac{z−2}{5}\) is ax by+cz+6=0. then a + b + c is equal to 
\(5\^{i}+5\hat{j}+2λ\hat{k},\hat{i}+2\hat{j}+3\hat{k},-2\hat{i}+λ\hat{j}+4\hat{k}\) and \(-\hat{i}+5\hat{j}+6\hat{k}.\) Let the set S = {λ∈ \(\mathbb{R}\) : The points A, B, C and D are coplanar}. Then \(\displaystyle\sum_{λ∈S}^{}(λ+2)^2\) is equal to
Let D be the domain of the function f(x)=sin−1(\( log_{3 x} (\frac{6+2log_3x}{−5x}\))) If the range of the function g : D → R defined by g ( x ) = x − [ x ] is the greatest integer function), is ( α , β ) , then α 2 +\(\frac{ 5}{ β}\) is equal to 
let \(A=\begin{bmatrix} 1 & \frac{1}{51} \\ 0& 1 \end{bmatrix}\) if \(B=\begin{bmatrix} 1 &2\\ -1& -1 \end{bmatrix} A=\begin{bmatrix} -1 &2\\ 1& 1 \end{bmatrix}\) then the sum of all the elements of the matrix \(∑ ^{50}_{n=1}\) Bn is Equal to 
Let C be the circle in the complex plane with centre z0 = \(\frac{1}{2}\) (1+3i) and radius r = 1. Let z1 = 1+ i and the complex number z2 be outside the circle C such that |z1 – z0| |z2 – z0| = 1. If z0, z1 and z2 are collinear, then the smaller value of |z2|2 is equal to
Let be a sequence such that a1+a2+....+ an=\(\frac{n^2+3n}{ (n+1 ) (n+2)}\). If  \(28∑^{10}_{k=1}\frac{1}{a_k} =\) P1P2P3 . . . Pm ,  where p1, p2, …..pm are the first m prime numbers, then m is equal to
If the local maximum value of the function f x)=\((\frac{√3e}{2 sin x} ) sin^2x ,\) \(x∈(0 ,\frac{π}{2}) \), is k/e , then  ( \(\frac{k}{ e}\) ) 8 + \(\frac{k^8}{e^ 5}\) + k 8  is equal to
If the point \((α ,\frac{7√3}{3}) \)lies on the curve traced by the mid-points of the line segments of the lines x cosθ + y sinθ = 7, θ ∈ (0 , \(\frac{π}{2}\) )  between the coordinates axes, then α is equal to 
Let the lines l1: \(\frac{x+5}{3} = \frac{y+4}{1}=\frac{z−α}{−2}\) and l2: 3x + 2y + z – 2 = 0 = x – 3y + 2z - 13 be coplanar. If the point P(a, b, c) on l1 is nearest to the point Q(- 4, -3, 2), then |a| + |b|+|c| is equal to
Two dice A and B are rolled, Let the numbers obtained on A and B be α and β respectively. If the variance of α - β is \(\frac{p}{q}\), where p and q are coprime, then the sum of the positive divisors of p is equal to
if A=\(\frac{1}{5! 6! 7!}\begin{bmatrix} 5! & 6! & 7!\\ 6! & 7! & 8! \\ 7! & 8! & 9! \end{bmatrix}\), then |adj(adj(2A))| is equal t

Let g(x) = f(x) + f(1 - x) and f''(x) > 0, x ∈ (0,1). If g is decreasing in the interval (0, α) and increasing in the interval (α, 1), then tan-1 (2α) + tan-1 (\(\frac{1}{α}\)) + tan-1\((\frac{α+1}{α})\) is equal to

For, α, β, γ, δ ∈ \(\mathbb{N},\) if \(∫\left((\frac{x}{e})^{2x}+(\frac{e}{x})^{2x}\right)log_e\,xdx=\) \(\frac{1}{\alpha}(\frac{x}{e})^{βx}-\frac{1}{γ}(\frac{e}{x})^{δx}+c,\) Where \(e=\displaystyle\sum_{n=10}^{∞}\frac{1}{n!}\) and C is constant of integration, then α + 2β + 3γ - 4δ is equal to
Let \(\overrightarrow{a}=2\^i+7\^j−\^k ,\overrightarrow{b} =3\^i+5 \^k\) and \(\overrightarrow{c}=\^i=\^j+2\^k\) . Let \(\overrightarrow{d}\) be a vector which is perpendicular to both \(\overrightarrow{a}\) and \(\overrightarrow{b}\) , and \(\overrightarrow{c}.\overrightarrow{d}=12\). Then \((-\^i+\^j=\^k).(\overrightarrow{c}\times\overrightarrow{d})\) is equal to

Let m be the mean and σ be the standard deviation of the distribution

xi012345
fik+22kk2-1k2-1k2+1k-3

where ∑fi = 62. if [x] denotes the greatest integer ≤ x, then [μ2 + σ2] is equal