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Mathematical Ability Test-1

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Mathematical Ability Test-1
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  • Question 1
    1 / -0

    A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale:

    Solution

    Given,

    A box of oranges.

    Let A,B and C denotes respectively the events that the first, second and third drawn orange is good.

    Now, 

    P(A)=P (good orange in first draw) =12/15

    Because the second orange is drawn without replacement so, now the total number of good oranges will be 11 and the total oranges will be 14 that is the conditional probability of B given that A has already occurred.

    Now,

    P(B/A) = P (good orange in second draw) =11/14

    Because the third orange is drawn without replacement so, now the total number of good oranges will be 10 and total orangs will be 13 that is the conditional probability of C given that A and B has already occurred.

    Now,

     

  • Question 2
    1 / -0

    In a town the ratio of men, women, and children is 9 : 8 : 3. 80% men are literate and 30% women are illiterate. If 90% of children are literate, then the illiteracy rate of that town is:

    Solution

     

  • Question 3
    1 / -0

    tan 54° can be expressed as

    Solution

     

  • Question 4
    1 / -0

    What is the least value of 25 cosec2 x + 36 sec2 x?

    Solution

     

  • Question 5
    1 / -0

    An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high. Determine the angle of elevation of the top of the tower from the eye of the observer.

    Solution

    Given:

    AB = 22 m

    PQ = 1.5 m = MB

    QB = PM = 20.5 m

    AM = AB−MB =22 − 1.5 = 20.5 m

    Let the angle of elevation of the tower from the eye of the observer be θ.

    Now in triangle APM,

     

  • Question 6
    1 / -0

    Anil and Mukesh entered into a partnership and invested Rs 3000 and Rs 4000 respectively. After 5 months, Umang entered and invested Rs 5000, Anil invested Rs 2000 more, and Mukesh withdrew Rs 1000. After 3 more months, Umang withdrew Rs 1000. If Umang is to be provided Rs 1000 as a monthly salary, what is the profit at the end of the year if Umang earned a total of Rs 10,100 (including the salary) from the partnership?

    Solution

    According to the question,

    Anil and Mukesh entered into a partnership and invested Rs 3000 and Rs 4000 respectively. After 5 months, Umang entered and invested Rs 5000, Anil invested Rs 2000 more, and Mukesh withdrew Rs 1000. After 3 more months, Umang withdrew Rs 1000. If Umang is to be provided Rs 1000 as a monthly salary, then the profit at the end of the year if Umang earned a total of Rs 10,100 (including the salary) from the partnership will be-

    Profit will be shared in the ratio-

    (3000 × 5 + 5000 × 7) : (4000 × 5 + 3000 × 7) : (5000 × 3 + 4000 × 4)

    = 50 : 41 : 31

    Let the total profit at the end of the year be Rs 'p'

    Profit to be shared = p - 1000 × 7 Rs (p - 7000)

    Given,

     

  • Question 7
    1 / -0

    Solution

    Let a1,a2,a3 and a4 be the coefficients of 4 consecutive terms viz. the rth, (r + 1) th, (r + 2) th and (r + 3) th terms.

     

  • Question 8
    1 / -0

    A circle with center 'O' and radius 2.6 cm. The angle drawn in the minor sector is 108°. What is the angle drawn in the major sectors?

    Solution

    Given:

    Radius = 2.6 cm

    The angle of minor Sector = 108°

    According to the formula:

    The angle of minor Sector + Angle of major Sector = 360°

    Let the angle of the major sector be x.

    108° + x = 360°

    ⇒ x = 360° - 108°

    ⇒ x = 252° 

    ∴ The angle of the major sector is 252°.

     

  • Question 9
    1 / -0

    An urn contains 5 red and 5 black balls. A ball is drawn at random, its color is noted, and is returned to the urn. Moreover, 2 additional balls of the color drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?

    Solution

    Given,

    An urn contains 5 red and 5 black balls.

    Let in the first attempt the ball drawn is of red colour.

    P (probability of drawing a red ball) = 5/10 = 1/2

    Now the two balls of same colour (red) are added to the urn then the urn contains 7 red and 5 black balls.

    P (probability of drawing a red ball) = 7/12

    Now,

    Let in the first attempt the ball is drawn is of black colour.

    P (probability of drawing a black ball) = 5/10 = 1/2

    Now the two balls of the same colour (black) are added to the urn then the urn contains 5 red and 7 black balls.

    P (probability of drawing a red ball) = 5/12

     

  • Question 10
    1 / -0

    Solution

     

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