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Mathematics Tes...

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  • Question 1
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    Fifteen coupons are numbered 1,2,3,....15 respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9, is :

  • Question 2
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    The number of common tangents to the circles x2 + y2 = 4 and x2 + y2 - 6x - 8y = 24 is :

  • Question 3
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    If \(f(x+y)=f(x)+f(y)-x y-1\) for all \(x, y \in R\) and \(f(1)=1\) then \(\sum_{h=1}^{5} f(h)\) is equal to :

  • Question 4
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    All the spades are taken out from a pack of cards. From these cards, cards are drawn one by one without replacement till the ace of spades comes. The probability that the ace comes in the 4th draw is :

  • Question 5
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    If unit vector \(\overrightarrow{\mathrm{c}}\) makes an angle \(\frac{\pi}{3}\) with \(\hat{\mathrm{i}}+\mathrm{j},\) then minimum and maximum values of \((\hat{i} \times \hat{j}) \cdot \overrightarrow{\mathrm{c}}\) respectively are :

  • Question 6
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    Let \(S=\frac{8}{5}+\frac{16}{65}+\ldots+\frac{128}{2^{18}+1},\) then :

  • Question 7
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    A lady wants to select one cotton saree and one polyester saree from a textile shop. If there are 10 cotton varieties and 12 polyester varieties, in how many ways can she choose the two sarees ?

  • Question 8
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    Find the value(s) of the parameter 'a'(a>0) for each of which the area of the figure bounded by the straight line, \(y=\frac{a^{2}-a x}{1+a^{4}} \&\) the parabola \(y=\frac{x^{2}+2 a x+3 a^{2}}{1+a^{4}}\) is the greatest :

  • Question 9
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    In the expansion of \(\left(\sqrt[3]{\frac{a}{b}}+\sqrt[3]{\frac{b}{\sqrt{a}}}\right)^{21}\) the term containing same powers of a and \(b\) is -

  • Question 10
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    The parameter, on which the value of the determinant
    \(\left|\begin{array}{ccc}1 & \mathrm{a} & \mathrm{a}^{2} \\ \cos (\mathrm{p}-\mathrm{d}) \mathrm{x} & \cos \mathrm{px} & \cos (\mathrm{p}+\mathrm{d}) \mathrm{x} \\ \sin (\mathrm{p}-\mathrm{d}) \mathrm{x} & \sin \mathrm{px} & \sin (\mathrm{p}+\mathrm{d}) \mathrm{x}\end{array}\right|\)
    does not depend upon, is :

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