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If A=[(1, 0), (2, 1)], B=[(x, 0), (1, 1)] and A=B², then x equals

If for a square matrix A, A² - A + I = O then A⁻¹ equals

The number of feasible solutions of the linear programming problem given as Maximize $z=15x+30y$ subject to constraints : $3x+y\le12, x+2y\le10, x\ge0, y\ge0$ is

16. Which of the following points satisfies both the inequations $2x+y\le10$ and $x+2y\ge8$?

15. The solution set of the inequation $3x+5y<7$ is:

If $P(A\cap B)=\frac{1}{8}$ and $P(\bar{A})=\frac{3}{4}$ then $P(\frac{B}{A})$ is equal to :

If\~P(\frac{A}{B})=0\cdot3, P(A)=0\cdot4 and P(B)=0\cdot8, then P(\frac{B}{A}) is equal to :

Five fair coins are tossed simultaneously. The probability of the events that atleast one head comes up is

If for any two events A and B, P(A)=4/5 and P(A ∩ B)=7/10, then P(B/A) is equal to

The value of $\lambda$ for which the angle between the lines $\vec{r}=\hat{i}+\hat{j}+\hat{k}+p(2\hat{i}+\hat{j}+2\hat{k})$ and $\vec{r}=(1+q)\hat{i}+(1+q\lambda)\hat{j}+(1+q)\hat{k}$ is $\frac{\pi}{2}$ :

If the direction cosines of a line are $(\frac{1}{a}, \frac{1}{a}, \frac{1}{a})$ then:

14. Distance of the point $(p, q, r)$ from y-axis is :

Direction cosines of the line \frac{x-1}{2}=\frac{1-y}{3}=\frac{2z-1}{12} are:

The angle between the lines 2x=3y=-z and 6x=-y=-4z is

If a line makes angles of 90°, 135° and 45° with the x, y and z axes respectively, then its direction cosines are

If \vec{a}+\vec{b}=\hat{i} and \vec{a}=2\hat{i}-2\hat{j}+2\hat{k}, then |\vec{b}| equals:

The value of (\hat{i}\times\hat{j})\cdot \hat{j}+(\hat{j}\times\hat{i}) \hat{k}:

The value of p for which the vectors 2\hat{i}+p\hat{j}+\hat{k} and -4\hat{i}-6\hat{j}+26\hat{k} are perpendicular to each other, is:

The magnitude of the vector 6î - 2î + 3ê is

Two vectors →a = a₁î + a₂î + a₃ê and →b = b₁î + b₂î + b₃ê are collinear if