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Mathematics Tes...

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  • Question 1
    4 / -1

    Find the possible value of \(k\) for which the distance between two plane \(6 x+\) \(3 y-2 z+k=0\) and \(3 x+1.5 y-z+2=0\) is \(5\).

  • Question 2
    4 / -1

    What is the domain of the function \(\mathrm{f}(\mathrm{x})=\cos ^{-1}(\mathrm{x}-2)\)?

  • Question 3
    4 / -1

    Find the sum of the series 3 + 9 + 27 + 81 + ..... + 6561.

  • Question 4
    4 / -1

    The solution of the differential equation \(\cos x d y=y(\sin x-y) d x, 0

  • Question 5
    4 / -1

    Match each of the set on the left described in the roster form with thesame set on the right described in the set-builder form.

    (i) {P, R, I, N, C, A, L} (a) {\(x: x\) is a positive integer and is a divisor of 18}
    (ii) {0} (b) {\(x : x\) is an integer and \(x^{2}\) – 9 = 0}
    (iii){1, 2, 3, 6, 9, 18} (c){\(x : x\) is an integer and \(x\) + 1= 1}
    (iv){3, –3} (d){\(x : x\) is a letter of the word PRINCIPAL}

  • Question 6
    4 / -1

    In the given figure, \(\mathrm{A}\) is the centre of the circle. If diameters \(X Y\) and \(\mathrm{MN}\) bisect each other perpendicularly at \(\mathrm{A}\) and \(\mathrm{XM}=5 \mathrm{~cm}, \mathrm{NY}\) is equal to:

  • Question 7
    4 / -1

    There is an unlimited number of identical balls of three different colours. How many arrangements of almost 7 ball in a row can be made by using them?

  • Question 8
    4 / -1

    What is the area of the region enclosed between the curve \({y}^{2}=2 {x}\) and the straight line \(y=x ?\)

  • Question 9
    4 / -1

    Let \(\mathrm{R}\) be the relation in the set \( \{1,2,3,4\} \) given by\(\mathrm{R}=\{(1,2),(2,2),(1,1),(4,4),(1,3),(3,3),(3,2)\} .\) Choose the correct answer.

  • Question 10
    4 / -1

    If \(\theta\) is an acute angle such that \(\cos \theta=\frac{3}{5}\), then \(\frac{\sin \theta \tan \theta-1}{2 \tan ^2 \theta}=\)

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