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  • Question 1
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    If \(\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}\) are unit vectors such that the vector \(\overrightarrow{\mathrm{a}}+3 \overrightarrow{\mathrm{b}} \quad\) is perpendicular to \(7 \overrightarrow{\mathrm{a}}-5 \overrightarrow{\mathrm{b}}\) and \(\overrightarrow{\mathrm{a}}-4 \overrightarrow{\mathrm{b}} \quad\) is
    perpendicular to \(7 \overrightarrow{\mathrm{a}}-2 \overrightarrow{\mathrm{b}},\) then the angle between \(\overrightarrow{\mathrm{a}}\) and \(\overrightarrow{\mathrm{b}}\) is

  • Question 2
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    Let \(\mathrm{a}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}} \& \dot{\mathrm{b}}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}} \cdot\) Then, the value of \(\lambda\) for which the vector \(\overrightarrow{\mathrm{c}}=\lambda \hat{\mathrm{i}}+\hat{\mathrm{j}}+(2 \lambda-1 \hat{\mathrm{k}}\) is parallel to the plane
    containing \(\overrightarrow{\mathrm{a}} \& \overrightarrow{\mathrm{b}},\) is

  • Question 3
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    The plane passing through the point (−2, −2, 2) and containing the line joining the points,,,,
    (1, 1, 1) and (1, −1, 2) makes intercepts on the coordinates axes the sum of whose lengths is

  • Question 4
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    All the values of x satisfying the equation \(\left|\begin{array}{lll}x+1 & x+2 & 1 \\ x+2 & x+4 & 2 \\ x+3 & x+6 & 3\end{array}\right|\)= 0 are given by,

  • Question 5
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    The solution of the equation (2x + y + 1) dx + (4x + 2y – 1) dy = 0 is

  • Question 6
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    One angle of a triangle is 2x/3 grad, another is 3x/2 degrees, whilst the third is πx/75 radians. Express all angles in degress.

  • Question 7
    1 / -0

    If \(\tan x=\frac{4}{3},\) then the value of \(\sqrt{\frac{(1-\sin x)(1+\sin x)}{(1+\cos x)(1-\cos x)}}\) is

  • Question 8
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    \(\mathrm{f} y=\log \left(\frac{\sqrt{(x+1)}-1}{\sqrt{(x+1)}+1}\right)+\frac{\sqrt{x}}{\sqrt{(x+1)}},\) then by using
    substitution \(x=\tan ^{2} \theta, y\) reduces to

  • Question 9
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    Find the value of sin∠M in the right angled triangle shown in the figure.

    question

  • Question 10
    1 / -0

    (cosec θ−sinθ)(secθ−cosθ)(tanθ+cotθ)=.......

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