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Mathematics Tes...

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  • Question 1
    1 / -0

    Consider the following statements

    I. \(\lim _{x \rightarrow 0} \sin \frac{1}{x}\) does not exist.
    II. \(\lim _{x \rightarrow 0} x \sin \frac{1}{x}\) exists.
    Which of the above statement(s) is/are correct?

  • Question 2
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    Find the area of the region bounded by \(y^{2}=x, x=1, x=4\) and the \(x-\) axis.

  • Question 3
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    Prithvi spent Rs. 89,745 on his college fees, Rs. 51,291 on personality development classes and the remaining 27% of the total amount he had as cash with him .what was the total amount?

  • Question 4
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    Let \(n(U)=700, n(A)=200, n(B)=300, n(A \cap B)=100,\) then \(n\left(A^{\prime} \cap B^{\prime}\right)\) is equal to

  • Question 5
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    Find the equation of the sphere having the centre (–2, 2, 3) and passing through the point (3, 4, –1).

  • Question 6
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    What is \(\int e^{x}\left(\sqrt{x}+\frac{1}{2 \sqrt{x}}\right) d x\) is equal to?

  • Question 7
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    \(\mathrm{A} \mathrm{no} \cdot \frac{129}{2^{2} \mathrm{s}^{7} 7^{5}}\) is

  • Question 8
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    Two pillars of equal height and on either side of a road, which is 100m wide. The angles of elevation of the top of the pillars are 60° and 30° at a point on the road between the pillars. Find the height of each pillar.

  • Question 9
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    \(\frac{\cot ^{2} 15^{\circ}-1}{\cot ^{2} 15^{\circ}+1}\) is equal to

  • Question 10
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    The two ends of latus rectum of a parabola are the points (3, 6) and (–5, 6), then the focus is

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