Ncert Solutions Maths class 12th

If the foot of the perpendicular drawn from the point $(\mathrm{1,0},3)$ on a line passing through $(\alpha ,\mathrm{7,1})$ is $\left(\frac{5}{3},\frac{7}{3},\frac{17}{3}\right)$ , then $\alpha$  is equal to          

If the system of linear equations,

$\mathrm{x}+\mathrm{y}+\mathrm{z}=6$
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$x+2y+3z=10$
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$3x+2y+\lambda z=\mu$
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has more than two solutions, then $\mu -{\lambda }^2$  is equal to

Let the vectors a,b,c be such that |a|=2, |b|=4 and |c|=4. If the projection of b on a is equal to the projection of c on a and b is perpendicular to c, then the value of |a+b-c| is

In a workshop, there are five machines and the probability of any one of them to be out of service on a day is $\frac{1}{4}$ <!-- [if gte msEquation 12]>14 <!--[endif]--><!--[endif]-->. If the probability that at most two machines will be out of service on the same day is ${\left(\frac{3}{4}\right)}^{3}k$ , then $k$  is equal to:
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Let $A$ $$ and $$ $B$ be two independent events such that $P\left(A\right)=\frac{1}{3}$ $\frac{}{}$ and $P\left(B\right)=\frac{1}{6}$ $\frac{}{}$ . Then, which of the following is TRUE?

If for some α ∈ R, the lines L₁: (x+1)/2 = (y-2)/(-1) = (z-1)/1 and L₂: (x+2)/α = (y+1)/(5-α) = (z+1)/1 are coplanar, then the line L₂ passes through the point:

The shortest distance between the lines $\frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1}$ $\frac{}{}\frac{}{}\frac{}{}$ and $\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{4}$ $\frac{}{}\frac{}{}\frac{}{}$ is:

Let $y=y\left(x\right)$ be a function of $x$ satisfying $y\sqrt[]{1-x^2}=k-x\sqrt[]{1-y^2}$ where $k$ is a constant and $y\left(\frac{1}{2}\right)=-\frac{1}{4}$ . Then $\frac{dy}{dx}$ at $x=\frac{1}{2}$ , is equal to:
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Let a curve y = f(x) pass through the point (2, (logₑ2)²) and have slope 2y/(xlogₑx) for all positive real value of x. Then the value of f(e) is equal to……….

A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of n is………….