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  • Question 1
    1 / -0

    If a and b are two prime numbers, then LCM (a, b) is

    Solution

    Given that a and b are prime numbers.

    Therefore, HCF (a, b) = 1.

    We know that for any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b.

    Therefore, LCM (a, b) = abHCF(a,b) = ab1 = ab.

    Hence, if a and b are prime numbers then LCM (a, b) = a × b.

  • Question 2
    1 / -0

    The system of equations is as follows:

    2x + 5y = 17,

    5x + 3y = 14

    Given system of equations has

    Solution

    Given system of equations are

    2x + 5y = 17,

    5x + 3y = 14.

    Comparing given system of equations with

    a1x+b1y=c1

    a2x+b2y=c2

    We get a1=2, b1=5, c1=17

    And a2=5,b2=3,c2=14

    Now, a1a2=25 and b1b2=5325=a1a2

    Since, a1a2b1b2

    Therefore, given system of equations has a unique solution.

  • Question 3
    1 / -0

    The circumference of a circle is 8 cm. Then the area of the sector whose central angle is 72° is:

    Solution

    Let the radius of the circle is r cm.

    Given that the circumference of the circle is 2πr = 8 cm.

     r = \frac{8}{2\pi} = \frac{4}{\frac{22}{7}} = \frac{14}{11}cm.

    \because Area of the circle is \pi r^2

    \therefore Area of the sector whose central angle is 360° = \pi r^2\,cm^2.

    \therefore Area of the sector whose central angle is 1° = \frac{\pi r^2}{360^o}cm^2

    \therefore Area of the sector whose central angle is 72° = \frac{\pi r^2}{360^o}\times 72^o cm^2

    \frac{22}{7}\times \frac{14}{11}\times \frac{14}{11}\times \frac{72}{360} = 2\times 2\times \frac{14}{11}\times \frac{1}{5} = \frac{56}{55} = 1.02cm^2

    Hence, the area of the sector whose central angel is 72° is 1.02cm^2.

  • Question 4
    1 / -0

    A die is thrown once. The probability of getting an even prime number is

    Solution

    A die is thrown once.

    Therefore, possible outcomes are {1, 2, 3, 4, 5, 6}.

    Hence, total possible outcomes = n(S) = 6.

    Let the event E be the event of getting an even prime number.

    Since, only even prime number is 2.

    Therefore, number of outcomes favorable to event E is n(E) = 1.

    Hence, the probability of getting an even prime number = \frac{n(E)}{n(S)}=\frac{1}{6}

  • Question 5
    1 / -0

    The dimensions of a metallic cuboid are 100 cm × 80 cm × 64 cm. It is melted and recast into a cube.

    If the edge of the cube be ‘a’, then volume of cube is given by:

    Solution

    If the edge of the cube is a then, the volume of the cube is given by = a^3.

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