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NDA - Mixed Mathematics Test 17
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NDA - Mixed Mathematics Test 17
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  • Question 1/25
    1 / -0.33
    If C(28, 2r) = C(28, 2r – 4), then what is r equal to?
    Solutions

    Correct Answer is option B

    Formula used:

    1.  if r = n - r

    2.

    Calculation:

    Given C(28, 2r) = C(28, 2r – 4)

    So, 2r = 28 – 2r + 4

    r = 8

  • Question 2/25
    1 / -0.33
    The sum of
    Solutions
    let the sum, , It is a G.P. whose common ratio is  and is of (2n+1) terms. So,

  • Question 3/25
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    What is be equal to?
    Solutions

    Correct Answer is option C

    Given:

  • Question 4/25
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    Solution set of the inequality  :
    Solutions
    we have

    If

    Then

    From above []

  • Question 5/25
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    If , then find the interval of :
    Solutions
    we have

    First of all

    So,

    Since,  then  or

  • Question 6/25
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    The cofactor of the element 4 in the determinant  is
    Solutions

    Correct Answer is option C

    Formula used:

    Cofactor of element  is defined as

    Where  is determinant obtained by the deleting  row and  column from the given matrix.

    Calculation:

    Element 4 in 2nd row and 1st column so ,

  • Question 7/25
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    The value of  is-
    Solutions

    ………[]

  • Question 8/25
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    Odds in favour of an event  are 2 to 1 and odds in favour of  are 3 to 1 . Consistent with this information the smallest and largest values for the probability of an event  are given by
    Solutions
    We have,

     ,

     

     

     

    Now,

     

     

  • Question 9/25
    1 / -0.33
    If α and β are the roots of the equation , then find the equation whose roots are .
    Solutions

    Given that,

    α and β are the roots of the equation ,

    let  ,

    then,

    Now, put value of α in eqn.

    Now, p is replaced by x, and we get equation

  • Question 10/25
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    In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then, the common ratio of this progression equals.
    Solutions

    Correct Answer is option D

    Let be the terms of G.P

    Given,

  • Question 11/25
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    Two finite sets have m and n elements, then total number of subsets of the first set is  more than the total number of subsets of the second.  The values of m and n are
    Solutions

    Correct Answer is option A

    Total number of subsets of the first is  while total number of subsets of the second is

    Now,

    Hence compare the terms

    Hence,

  • Question 12/25
    1 / -0.33
    The mean of 100 observations is 50 and their standard deviation is 5.The sum of the squares of all observations is
    Solutions

    Let  be 100 observations.

    Standard deviation =

     

    Then,

    Variance =

     

     

  • Question 13/25
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    In a binary number system, assume that  and  then in decimal system  , which is equal to:
    Solutions

    Correct Answer is option C

    We have,

  • Question 14/25
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    Find
    Solutions

    Let

    By using the formula

    Here

    Now

  • Question 15/25
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    If  ,  and  , then  is
    Solutions

    We have,

    For differentiate  wrt  , firstly differentiate  wrt  and  wrt

     

     

    And,

     

     

    Now,

  • Question 16/25
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    If , then which one the following option is correct.
    Solutions

    Therefore  then is continuous at x=4.

  • Question 17/25
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    For what values of  is the rate of increase of  twice the rate of increase of  ?
    Solutions
    Let  . Then,

    When  , we have

     

     

     

  • Question 18/25
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    If  where k is a constant of integration, then A+B+C equals:
    Solutions

  • Question 19/25
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    Integrating factor of differential equation
    Solutions

  • Question 20/25
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    The area enclosed between the curve  and the coordinate axes, is
    Solutions

    The area enclosed by  and the coordinate axes is shaded in figure.

    Let  be the required area. Then,

      

     

  • Question 21/25
    1 / -0.33
    The image of the point  in the plane , is
    Solutions

    We know that the coordinates of the image of a point  in the plane  are given by

    Let  be the image of the point  in the plane . Then,

     

      ,  ,

    Hence, the image has the coordinates  .

  • Question 22/25
    1 / -0.33
    The equation of the plane passing through the line of intersection of the planes  and perpendicular to the plane  is given by
    Solutions

    Given planes : x+y+z=1

     :2x+3y+4z =7

    So , equation of plane passing through intersection of planes P1 and P2 is

    ⇒ x+y+z-1+k(2x+3y+4z-7)=0

    ⇒ x+y+z-1+2kx+3ky+4kz-7k=0

    ⇒ x(1+2k) +y( 1+3k) + z ( 1+4k) -1 -7k = 0\

    this is perpendicular to x-5y+3z = 5

    ⇒ x-5y+3z-5=0

    So

    ⇒ 1(1+2k) – 5( 1+3k ) + 3 (1+4k )=0

    ⇒ 1+2k-5-15k+3+12k = 0

    ⇒ k-1 = 0

    ⇒ k=-1

    equations of plane is

    ⇒ x+y+z-1-1(2x+3y+4z-7)=0

    x+y+z-1-2x-3y-4z+7 = 0

    ⇒ -x+2y+3z-6=0

    ⇒ x+2y+3z-6=0

  • Question 23/25
    1 / -0.33
    The angle of elevation of a cloud C from a point P, above a still lake is . If the angle of depression of the image of C in the lake from the point P is , then PC (in m) is equal to:
    Solutions

    Correct option is C

                                                               

  • Question 24/25
    1 / -0.33
    Consider the following statements :

    1.

    2. There exist  where  such that  .

    Which of the above is/are correct?

    Solutions

    Statement 1.

    Statement 2.

    So from the above solution Statements 1 is incorrect and 2nd is also incorrect.

  • Question 25/25
    1 / -0.33
    The value of  equals to
    Solutions

    From the given equation

    =

    =  =

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