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Thread: TestFunda Answers - Modern Maths

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    Default TestFunda Answers - Modern Maths

    This thread contains questions, answers and solutions in Modern Maths from TestFunda Answers.

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    Post TestFunda Answers - Modern Maths

    option 4......just do calculations. equate all the three eqns and find three values of x, Put it in the eqn and get the answer...

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    Post TestFunda Answers - Modern Maths

    The categories depend upon how many numbers are common. There can be 1 number common e.g. 2222, 222. Let us call these 1 integer categories.
    Similarly, there 2 integer, 3 integer or 4 integer categories. 

    No of 1 integer categories = 9 (excluding number 0)
    No of 2 integer categories = 10C2 = 45
    No of 2 integer categories = 10C3 = 120
    No of 2 integer categories = 10C4 = 210

    So total number of categories comes to 384.

    Hence, option 1. 

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    Post TestFunda Answers - Modern Maths

    The given point (2, 5) lies on both the lines as it satisfies both the line equations. This means (2, 5) is the intersection point of the 2 lines. So it is possible to find 2 points each on every line which are at a distance of 5 units from the point (2, 5). Hence the required number of points is 4.

    Hence, option 4. 

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    Post TestFunda Answers - Modern Maths

    We can find the distance of the perpendicular from the point (2,-1) to the line. This is the height of the triangle from which we can find the side of triangle. 

    The formula for distance = |Am + Bn + C|/√(A2 + B2), where Ax + By + C = 0 represents the equation of the line.
    Here A = 1, B = 1, C = -2, m = 2, n = -1.

    From the formula the distance = 1/√2

    The height of an equilateral triangle with side a = √3a/2 = 1/√2

    Hence a = √(2/3)

    Hence, option 2.

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    Post TestFunda Answers - Modern Maths

    For a rectangle, the lengths of perpendiculars drawn from 2 vertices on the diagonal joining other 2 vertices should be same. This should follow from the symmetrical nature of a rectangle. 

    The formula for distance = |Am + Bn + C|/√(A2 + B2), where Ax + By + C = 0 represents the equation of the line and (m,n) is the point.

    Doing it for the 2 points (1,3) and (5,1) we get the following equation.

    |1 - c| = |-9 - c|

    Taking one case for the modulus sign we get, 1 - c = -9 - c which is not valid.
    Taking the other case, 1 - c = 9 + c, c = -4

    Hence, option 2. 

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    Post TestFunda Answers - Modern Maths

    From the answer to question [12451] we know c = -4. So the equation of the line is y = 2x - 4.

    None of the given option pairs satisfy the equation y = 2x - 4.

    Hence, option 4. 

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    Post TestFunda Answers - Modern Maths

    Consider the 2 perpendicular lines as x-axis and y-axis for simplicity. Now we have to consider locus of all such points (x,y) such that |x| + |y| = 1.

    In quadrant 1, x > 0 and y > 0. So the equation |x| + |y| = 1 represents x + y = 1
    Similarly, in quadrant 2, the equation becomes -x + y = 1. 

    If we do this construction for all the 4 quadrants, it turns out to be 4 straight lines intersecting each other at right angles and forming a square such that the lengths of sides are equal. 

    Hence, option 1.


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    We have to use integration to find the area. The integration needs to be done from one intersection point to the other intersection point. 

    By observation, the intersection points for the 2 curves are (1,1) and (-1,1).

    So now, we have integrate the difference between the y coordinates for the 2 curves over x = -1 to x = 1.

    Bounded Area = ∫1-1 (2 - x2 - x2/3)dx = [2x - x3/3 - x5/3/(5/3)]-11 = 32/15 = 2 + 2/15

    Hence, option 3. 

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    Post TestFunda Answers - Modern Maths

    How many 3 digit numbers abc are there such that either a > b > c or a < b < c?
    Options
    1) 
    9C3 + 9C2
    2) 
    10C3
    3) 
    9C3 + 10C2
    4) 
    none of the above

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    Post TestFunda Answers - Modern Maths

    Lets consider 4 cases.














































    Case 1 First Card Red (Queen), Other Card Queen

    6
    Case 2 First Card red (Not Queen), Other Card Queen

    96
    Case 3 First Card Queen (Red), Second Card Red

    50
    Case 4 First Card Queen (Black), Second Card Red

    52


    Total Ways 204


    Total number of ways of drawing two cards = 51*52

    So probability of drawing the cards = 204/51*52 = 1/13

    Hence, option 4.

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    Post TestFunda Answers - Modern Maths

    A and B start moving towards each other simultaneously on a straight line from cities P and Q respectively. After travelling some distance, B takes a 30° turn to his left with respect to his original direction. 2 hour after B turns, A takes a 90° turn to his right. A travels 60 km after turning, before meeting B. They meet 10 hour after starting their journey. A and B together travel 170 km with time ratio 8:9 respectively before turning and arrive at the meeting point simultaneously. If A and B had not turned, after how many hours would they have met?
    Options
    1) 
    2) 
    Additional Notes: please need a detail solution...

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    Post TestFunda Answers - Modern Maths

    The right answer is 143 numbers. It is not there in any of the options.

    If a number leaves a remainder of 3 in base 8 when divided by 9, it should leave a remainder of 3 when divided by 9 in base 10 also.

    So we have to find 4 digit numbers which leave a remainder of 3 when divided by 9 and are also a multiple of 7.

    First such number is 1029. Next number is 1092. So there is a gap of 63 in all such numbers. We can find 143 such numbers till 9999 with a gap of 63 in each.

    Hence, required answer is 143.

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    Post TestFunda Answers - Modern Maths

    Lets find values of x when 3x + 8 > 25 - 4x
    x > 17/7
    Lets find values of x when 3x + 8 > 12 - x
    x > 1
    So for x >17/7, f(x) = 3x + 8 and it is an ever increasing function of x.

    Lets find values of x when 25 - 4x > 12 - x
    x < 13/3 < 17/7

    So for x < 17/7, f(x) = 25 - 4x and it is an ever increasing function of x as x goes on decreasing.

    So the minimum value will occur when x = 17/7.
    f(17/7) = 107/7

    Hence, option 4.

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    Post TestFunda Answers - Modern Maths

    A box contains 10 red balls and 15 blue balls.One ball from the box is lost.Two balls are then drawn from the box and are found to be red ones.Find the chance that the missing ball is a blue ball.
    Options
    1) 
    15/23
    2) 
    8/23
    3) 
    3/4
    4) 
    1/3
    5) 
    2/3

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    Post TestFunda Answers - Modern Maths

    The first 23 natural numbers are written in increasing order beside each other to form a single number. What is the remainder when this number is divided by 18?

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    Post TestFunda Answers - Modern Maths

    Option 1
    Assume question as, trying to pick one blue ball out of total 23 balls. And, 15 balls out of 23 are blue balls.


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    Post TestFunda Answers - Modern Maths

    Answer is 7.

    Take 18 as 9*2.

    Remainder when divided by 2 is: 1 (odd number)
    Now let's add all digits: There will be 0 to 9 two times (1 to 9 & unit digit of 10 to 19) + 0 to 3 one time (20 to 23) + 10 1's (10th digit of 10 to 19) + 4 2's (10th digit of 20 to 23)
    That means we have, 2*45 + 6 + 10 + 8; which leaves remainder 6 when divided by 9.

    Now, for 87 (8+7 = 15, 6 is remainder when divided by 9), remainder is 6. Similarly, one can check for other numbers.

    Total remainder: 6+1=7

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    Post TestFunda Answers - Modern Maths

    A die is thrown and a coin is tossed as many times as the number shown by the die.what is the probability of getting more number of heads than tails?
    Options
    1) 
    47/192
    2) 
    61/192
    3) 
    77/192
    4) 
    53/192
    5) 
    71/192

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