A bolt manufacturing factory has three products A, B and C. 50% and 30% of the products are A and B type respectively and remaining are C type. Then probability that the product A is defective is 4%, that of B is 3% and that of C is 2%. A product is picked randomly picked and found to be defective, then the probability that it is type C.
If \( A = \begin{bmatrix} 1 & 5 \\ \lambda & 10 \end{bmatrix} \), \( A^{-1} = \alpha A + \beta I \) and \( \alpha + \beta = -2 \), then \( 4\alpha^2 + \beta^2 + \lambda^2 \) is equal to:
If the points with position vectors \(a\hat{i} +10\hat{j} +13\hat{k}, 6\hat{i} +11\hat{k} +11\hat{k},\frac{9}{2}\hat{i}+B\hat{j}−8\hat{k}\) are collinear, then (19α-6β)2 is equal to
If the equation of the plane containing the line x+2y+3z-4=0=2x+y-z+5 and perpendicular to the plane \(\vec{r}=(\vec{i}-\vec{j})+\lambda(\vec{i}+\vec{j}+\vec{k})+\mu(\vec{i}-2\vec{j}+3\vec{k})\) is ax+by+cz=4, then (a-b+c) is equal to
Let A = \(\left\{ \theta \in (0, 2\pi) : \frac{1 + 2i \sin \theta}{1 - i \sin \theta} \text{ is purely imaginary} \right\}\). Then the sum of the elements in A is.
The area of the region {(x,y): x2 ≤ y ≤8-x2, y≤7} is
Let \(I(x)=\int\frac{x+1}{x(1+xe^x)^2} dx\), x>0. If \(\lim\limits_{x\rightarrow\infin}I(x)=0\), then I(1) is equal to
Let SK = \(\frac{1+2+...+ K}{K}\) and \(\displaystyle\sum_{j=1}^{n}S_j^2=\frac{n}{A}(Bn^2+Cn+D)\), where A,B,C,D∈N and A has least value. Then
If the coefficients of three consecutive terms in the expansion of (1+x)n are in the ratio 1:5:20, then the coefficient of the fourth term of the expansion is?
Consider the word INDEPENDENCE. The number of words such that all the vowels are together is?
Let P = \(\left[\begin{matrix} \frac{\sqrt3}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt3}{2} \end{matrix}\right]\) A = \(\left[\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}\right]\) and Q = PAPT. If PTQ2007P = \(\left[\begin{matrix} a & b \\ c & d \end{matrix}\right]\), then 2a+b-3c-4d equal to
Let α, β, γ be the three roots of the equation x3+bx+c=0. If βγ =1=-α, then b3+2c3-3α3-6β3-8γ3 is equal to
If for z=α+iβ, |z+2|=z+4(1+i), then α +β and αβ are the roots of the equation
For two groups of 15 sizes each, mean and variance of first group is 12, 14 respectively, and second group has mean 14 and variance of σ2. If combined variance is 13 then find variance of second group?
Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}|=\sqrt{14},|\vec{b}|=\sqrt{6}$ and $|\vec{a} \times \vec{b}|=\sqrt{48}$ Then $(\vec{a} \cdot \vec{b})^2$ is equal to
If 5f(x) + 4f (\(\frac{1}{x}\)) = \(\frac{1}{x}\)+ 3, then \(18\int_{1}^{2}\) f(x)dx is:
Let $a_1, a_2, \ldots, a_n$ be in AP If $a_5=2 a_7$ and $a_{11}=18$, then $12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots+\frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)$ is equal to
The remainder on dividing $5^{99}$ by 11 is
Let $\theta$ be the angle between the planes $P_1: \vec{r} \cdot(\hat{i}+\hat{j}+2 \hat{k})=9$ and $P_2: \hat{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=15$ Let $L$ be the line that meets $P_2$ at the point $(4,-2,5)$ and makes an angle $\theta$ with the normal of $P_4$ If $\alpha$ is the angle between $L$ and $P_2$, then $\left(\tan ^2 \theta\right)\left(\cot ^2 \alpha\right)$ is equal to