Ncert Solutions Maths class 12th

In a hurdle race, a runner has probability p of jumping over a specific hurdle. Given that in 5 trials, the runner succeeded 3 times, the conditional probability that the runner has succeeded in the first trial is

Let a, b, c be the roots of the equation x³ – 9x² + 15x + 2 = 0. The volume of a parallelopiped with nonparallel sides aî + bĵ + ck̂, bî + cĵ + ak̂ and cî + aĵ + bk̂ is

The lines L₁ : x = y = z, L₂ : x = $\frac{y}{2}=\frac{z}{3}$ <!-- [if gte mso 9]><xml> </xml><![endif]--> and a line L₃ is passing through (1, 1, 1) form a triangle of area $\sqrt[]{6}$ <!-- [if gte mso 9]><xml> </xml><![endif]--> units, (1, 1, 1) being one of the vertices of the triangle. Then the point of intersection of the L₃ with L₂ is

The value of 'a' for which the straight line 4x – 3y + 4z – 2 = 0 = 3x – 2y + z – 5 is parallel to the plane 2x – y + az – 7 = 0, is:
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If value of $\frac{\left\{\left(\overrightarrow{a}-\overrightarrow{b}\right)\times \left(\overrightarrow{a}-\overrightarrow{b}-\overrightarrow{c}\right)\right\}.\left(\overrightarrow{a}+2\overrightarrow{b}-\overrightarrow{c}\right)}{\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]}$  is k then $\frac{k}{4}$  is

If the value of $\underset{x\to 0}{Lim}{\left\{si{n}^2\left(\frac{\pi }{2-3x}\right)\right\}}^{se{c}^2\left(\frac{\pi }{2-5x}\right)}$ <!-- [if gte mso 9]><xml> </xml><![endif]--> is e^-A then ‘A’ is

The equation of plane which passes through the point of intersection of lines r = i+2j+3k + λ(3i+j+2k) and r = 3i+j+2k + µ(i+2j+3k) where λ,µ ∈ R and has the greatest distance from the origin is :
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If ${\displaystyle \underset{-a}{\overset{a}{\int }}\left(\left|x\right|+\left|x-2\right|\right)dx=22,\left(a>2\right)and\left[x\right]}$ <!-- [if gte mso 9]><xml> </xml><![endif]--> denotes the greatest integer $\le x,$ then ${\displaystyle \underset{a}{\overset{-a}{\int }}\left(x+\left[x\right]\right)dx}$ <!-- [if gte mso 9]><xml> </xml><![endif]--> is equal to__________.

A quadratic function f(x) satisfies f(x) ≥ 0 for all real x. If f(2) = 0 and f(4) = 12, then the value of f(6) is :
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Let B_i (i = 1, 2, 3) be three independent events in a sample space. The probability that only B₁ occurs is a, only B₂ occurs is b and B₃ occurs is <!-- [if gte mso 9]><xml> </xml><![endif]--> Let p be the probability that none of the events B₁ occurs and these 4 probabilities satisfy the equations (a - 2b) = ab and (b - 3 <!-- [if gte mso 9]><xml> </xml><![endif]-->p = <!-- [if gte mso 9]><xml> </xml><![endif]--> (All the probabilities are assumed to lie in the integral (0, 1)). The <!-- [if gte mso 9]><xml> </xml><![endif]--> is equal to_________.