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Mathematics Tes...

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  • Question 1
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    Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is

  • Question 2
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    The tangent to the circle x2 + y2 = 5 at (1, − 2) also touches the circle x2 + y2 − 8x + 6y + 20 = 0. Then the point of contact is

  • Question 3
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    Events \(A , B , C\) are mutually exclusive events such that \(P(A)=\frac{3 x+1}{3}, P(B)=\frac{1-x}{4},\) and \(P(C)=\frac{1-2 x}{2}\)
    Then set of possible values of \(x\) are in the interval:

  • Question 4
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    Given vectors \(\overrightarrow{ x }=3 \widehat{ i }-6 \widehat{ j }-\widehat{ k }, \overrightarrow{ y }=\widehat{ i }+4 \widehat{ j }-3 \widehat{ k }\) and \(\vec{z}=3 \widehat{ i }-4 \widehat{ j }-12 \widehat{ k }\) then the projection of \(\overrightarrow{ x } \times \overrightarrow{ y }\) on \(\overrightarrow{ z }\) is

  • Question 5
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    The plane through the intersection of the planes \(x+y+z=1\) and \(2 x+3 y-z+4=0\) and parallel to \(y\) -axis also passes through the point.

  • Question 6
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    f \(\int_{-1}^{-4} f(x) d x=4\) and \(\int_{2}^{-4}(3-f(x)) d x=7,\) then the value of \(\int_{-2}^{1} f(-x) d x\) is

  • Question 7
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    \begin{equation}\operatorname{lf} g[f(x)]=|\sin x| \text { and } f[g(x)]=(\sin \sqrt{x})^{2} \text { then, }\end{equation}

  • Question 8
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    \begin{equation}\text { The distance between the line } \vec{r}=2 \vec{i}-2 \vec{j}+3 \vec{k}+\lambda(\vec{i}-\vec{j}+4 \vec{k}) \text { and the Plane } \vec{r} .(\vec{i}+5 \vec{j}+\vec{k})=5 \text { is }\end{equation}

  • Question 9
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    If \(g ( x )\) satisfies the conditions of Rolle's theorem in [1,2] and \(g ^{\prime}( x )= f ( x ),\) then \(\int_{1}^{2} f(x) d x\) is equal to

  • Question 10
    1 / -0

    Which of the following is logically equivalent to ∼ (∼p ⇒ q) ?

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