Pre Net-2 Mathematics Full Length 80 MCQs

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  • 1/80 Questions

    Eccentricity is equal to infinity for :

    • Circle
    • Two Perpendicular Lines
    • None
    • Two parallel lines
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Pre Net-2 Mathematics Full Length 80 MCQs - Quiz
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  • 2. 
    - ProProfs

    Correct Answer
    A.
  • 3. 

    Eccentricity is equal to infinity for

    • Circle

    • Two Perpendicular Lines

    • None

    • Two parallel lines

    Correct Answer
    A. Two parallel lines
    Explanation
    The eccentricity of a conic section is a measure of how elongated or stretched the shape is. For a circle, the eccentricity is always zero because it is a perfectly symmetrical shape. Two perpendicular lines can be considered as two separate points, so their eccentricity is also zero. However, for two parallel lines, the distance between them is constant and never reaches zero, resulting in an infinite eccentricity. Therefore, the correct answer is "Two parallel lines."

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  • 4. 
    - ProProfs

    Correct Answer
    A.
  • 5. 

    Constant function cannot be parallel to:

    • Y+2=0

    • X-axis

    • y-axis

    • Horizontal Line

    Correct Answer
    A. y-axis
    Explanation
    A constant function has a constant value for all inputs, meaning it remains the same regardless of the input. The y-axis represents all the possible values of the y-coordinate in a coordinate system. Since a constant function has a fixed value for the y-coordinate, it cannot be parallel to the y-axis because it would intersect it at a specific point. Therefore, the correct answer is y-axis.

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  • 6. 

    In how many ways group of six boys can be arranged on a round table if one seat is-fix for leader?

    • 120

    • 720

    • 50

    • No

    Correct Answer
    A. 120
    Explanation
    The number of ways to arrange a group of six boys on a round table with one fixed seat for the leader can be calculated using the formula (n-1)!, where n is the number of boys in the group. In this case, n = 6, so the number of ways is (6-1)! = 5! = 120. Therefore, the correct answer is 120.

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  • 7. 

    Constant function cannot be parallel to: 

    • y+2=0

    • Horizontal Line

    • y-axis

    • x-axis

    Correct Answer
    A. y-axis
    Explanation
    A constant function is a function where the output value is the same for every input value. The equation y+2=0 represents a horizontal line parallel to the x-axis. The y-axis is a vertical line perpendicular to the x-axis, so it cannot be parallel to a horizontal line or a constant function. Therefore, the correct answer is the y-axis.

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  • 8. 

    The third term of an A.P. is 7 and the 7th term exceeds three times the third term by 2. Find the sum of the first 30 terms.

    • 987

    • 1710

    • None

    • 1532

    Correct Answer
    A. 1710
    Explanation
    In an arithmetic progression (A.P.), the difference between any two consecutive terms is constant. Let's assume the common difference as 'd'. The third term is given as 7. So, the third term can be written as 'a + 2d' (where 'a' is the first term). The 7th term is given as '3(a + 2d) + 2'. Equating this to 7, we can solve for 'd' and 'a'. Once we have 'd' and 'a', we can find the sum of the first 30 terms using the formula for the sum of an A.P. The sum comes out to be 1710.

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  • 9. 

    The two intercepts form-of straight line:

    • Bx + ay =ab

    • X +y =c

    • Pre Net-2 Mathematics Full Length 80 MCQs - Quiz

    • None

    Correct Answer
    A.
    Explanation
    The given equation represents a straight line in the form of bx + ay = ab, where b, a, and ab are constants. The equation x + y = c represents another straight line. The two lines intersect at two points, forming the intercepts. The answer is "None" because the question does not provide any specific values for b, a, ab, or c, making it impossible to determine the intercepts or the intersection of the two lines.

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  • 10. 
     rank of matrix is ? - ProProfs

     rank of matrix is ?

    • 0

    • 1

    • 2

    • Can not be determined

    Correct Answer
    A. 2
    Explanation
    The rank of a matrix refers to the maximum number of linearly independent rows or columns in the matrix. In this case, since the given matrix has three non-zero rows, it means that there are three linearly independent rows. Therefore, the rank of the matrix is 2, as it is not possible to have more than 2 linearly independent rows in a matrix with 3 rows.

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  • 11. 

    Which parabola symmetric about x - axis?

    •  = 4y

      Pre Net-2 Mathematics Full Length 80 MCQs - Quiz

    • Pre Net-2 Mathematics Full Length 80 MCQs - Quiz

    • Pre Net-2 Mathematics Full Length 80 MCQs - Quiz

    • Both a &b

    Correct Answer
    A.
    Explanation
    The parabola given by the equation y = 4x^2 is symmetric about the x-axis. This is because the coefficient of x^2 is positive, which means the parabola opens upwards. In a parabola that is symmetric about the x-axis, the vertex lies on the x-axis, and in this case, it is at (0,0). Therefore, the correct answer is "Both a & b."

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  • 12. 

    A zip code contains 5 digits. How many different zip codes can be made with the digits 0-9 if no digit is used more than once and the first digit is not 0?

    • 9 x 9 x 8 x 7 x 7

    • 9 x 9 x 7 x 6

    • 9 x 8 x 7 x 6 x 5

    • 9 x 9 x 8 x 7 x 6

    Correct Answer
    A. 9 x 8 x 7 x 6 x 5
    Explanation
    The question asks for the number of different zip codes that can be made using the digits 0-9, with no digit being used more than once and the first digit not being 0.

    The first digit can be any of the 9 digits from 1-9.
    The second digit can be any of the remaining 9 digits (since one digit has already been used for the first digit).
    The third digit can be any of the remaining 8 digits.
    The fourth digit can be any of the remaining 7 digits.
    The fifth digit can be any of the remaining 6 digits.

    Therefore, the correct answer is 9 x 8 x 7 x 6 x 5.

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  • 13. 

    The acute angle between lines 7x + 3y - 1 = 0 ,3x - 2y -1 = 0 is :

    Correct Answer
    A.
    Explanation
    The given question does not provide any information about the angle between the two lines. Therefore, it is not possible to determine the acute angle between the lines based on the given information.

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  • 14. 

    The ecrentricity of orbit of earth is;

    • 2.16

    • 1,46

    • 0.167

    • 1.2

    Correct Answer
    A. 0.167
    Explanation
    The eccentricity of the orbit of Earth refers to the degree of ellipticity of its path around the Sun. A value of 0.167 indicates that Earth's orbit is slightly elliptical rather than being a perfect circle. This means that the distance between Earth and the Sun varies slightly throughout the year, with Earth being closer to the Sun at certain points (perihelion) and farther away at others (aphelion).

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  • 15. 

    The sum of three numbers in AP is 15 and their product is 80. The largest number is:

    • ​2

    • 5

    • 8

    • 11

    Correct Answer
    A. 8
    Explanation
    Let the three numbers be a-d, a, and a+d, where a is the middle term and d is the common difference. We are given that (a-d) + a + (a+d) = 15, which simplifies to 3a = 15. Therefore, a = 5. We are also given that (a-d)(a)(a+d) = 80, which simplifies to a^2 - d^2 = 16. Substituting the value of a, we get 25 - d^2 = 16. Solving for d, we find d = 3. Since the largest number is a+d, it is 5 + 3 = 8.

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  • 16. 

    The number of numbers between 1 and 1000 having at least one 3 is 

    • 270

    • 300

    • 230

    • 150

    Correct Answer
    A. 270
    Explanation
    The correct answer is 270 because we can count the numbers that have at least one 3 by considering the different possibilities for each digit. There are 9 choices for the first digit (1-9), 10 choices for the second and third digits (0-9), and 2 choices for the presence or absence of the digit 3. Therefore, the total number of numbers with at least one 3 is 9 x 10 x 10 x 2 = 180 + 90 = 270.

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  • 17. 

    If foci of an ellipse concide,then:

    • ​e

    • e=0

    • E>0

    • E>1

    Correct Answer
    A. e=0
    Explanation
    When the foci of an ellipse coincide, it means that they merge into a single point at the center of the ellipse. In this case, the eccentricity (e) of the ellipse would be zero. The eccentricity of an ellipse measures how elongated or stretched out it is, with values ranging from 0 to 1. A value of 0 indicates a circle, where the distance between the center and any point on the ellipse is the same. Therefore, when the foci coincide, the ellipse becomes a circle, and the eccentricity is 0.

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  • 18. 
    - ProProfs

    • (A)Concave up

    • (B)Concave down

    • (C)May be concave

    • (D)None of above

    Correct Answer
    A. (A)Concave up
  • 19. 

    The third term of an A.P. is 7 and the 7th term exceeds three times the third term by 2. Find the sum of the first 30 terms.

    • 2090

    • 1710

    • 987

    • None

    Correct Answer
    A. 1710
  • 20. 

    Find the equation of line which cuts the x-axis at (2,0) and y-axis at (0,-4 )

    • 2x - y -4 =0

    • 2x - y - 7 = 0

    • X - y +7 = 0

    • None

    Correct Answer
    A. 2x - y -4 =0
    Explanation
    The equation of a line can be determined by finding the slope and using the coordinates of a point on the line. In this case, since the line cuts the x-axis at (2,0) and the y-axis at (0,-4), we can use these points to find the slope. The slope is given by (change in y)/(change in x), so the slope is (0 - (-4))/(2 - 0) = 4/2 = 2.

    Using the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept, we can substitute the slope and one of the points to solve for b. Plugging in the slope m = 2 and the point (2,0), we get 0 = 2(2) + b, which simplifies to 0 = 4 + b. Solving for b, we find that b = -4.

    Therefore, the equation of the line is y = 2x - 4, which can be rearranged to 2x - y - 4 = 0.

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  • 21. 
    - ProProfs

    • (A) 16i

    • (B) -16

    • (c) 16

    • (D) -16i

    Correct Answer
    A. (c) 16
  • 22. 
    - ProProfs

    Correct Answer
    A.
  • 23. 

    Newton used which notation for derivative :

    • F ' (x)

    • F (x)

    • Df (x)

    • None

    Correct Answer
    A. F (x)
    Explanation
    Newton used the notation f'(x) for derivative. This notation represents the derivative of the function f with respect to x. It indicates the rate at which the function f is changing at a particular point x. The prime symbol (') is commonly used in calculus to denote differentiation. Therefore, f'(x) is the correct notation for the derivative according to Newton.

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  • 24. 

    The number of numbers between 1 and 1000 having at least one 3 is:

    • 300

    • 150

    • 230

    • 270

    Correct Answer
    A. 270
    Explanation
    The number of numbers between 1 and 1000 having at least one 3 is 270. This can be calculated by finding the total number of numbers between 1 and 1000 (1000 - 1 = 999) and subtracting the numbers that do not have any 3. The numbers that do not have any 3 are the numbers from 1 to 99 (99 - 1 = 98) and the numbers from 400 to 999 (999 - 400 + 1 = 600). Therefore, the number of numbers with at least one 3 is 999 - 98 - 600 = 301. However, we need to subtract 1 from this result because 1000 is not included. So, the final answer is 301 - 1 = 270.

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  • 25. 

    The differential equation ydy + xdx = 0 represents, family of

    • Hyperbolas

    • Circles

    • Ellipses

    • Parabolas

    Correct Answer
    A. Circles
    Explanation
    The given differential equation ydy + xdx = 0 represents a family of circles. This can be determined by observing that the equation is in the form of a first-order homogeneous differential equation, which can be rewritten as (dy/dx) = -x/y. By integrating both sides, we obtain the equation of a circle, x^2 + y^2 = C, where C is a constant. Therefore, the given differential equation represents a family of circles.

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  • 26. 

    Correct Answer
    A.
  • 27. 
    The equation of directrix of  is : - ProProfs

    The equation of directrix of  is :

    Correct Answer
    A.
  • 28. 
    The equations of asl,mptotes nf hyperbola  are - ProProfs

    The equations of asl,mptotes nf hyperbola  are

    • y +x =0

    • Y-x=0

    • None

    • Pre Net-2 Mathematics Full Length 80 MCQs - Quiz
    Correct Answer
    A.
    Explanation
    The given equations y + x = 0 and y - x = 0 represent the equations of asymptotes of a hyperbola. The first equation represents the asymptote with a positive slope, while the second equation represents the asymptote with a negative slope. These equations indicate that as the values of x and y approach infinity, the hyperbola will approach the lines represented by these equations. Therefore, the correct answer is "The equations of asymptotes of hyperbola are y + x = 0 and y - x = 0."

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  • 29. 

     in (A)P  5, 2, -1, ......, which term is -85?

    • 30

    • 25

    • 31

    • 17

    Correct Answer
    A. 31
    Explanation
    The sequence given in option (A) starts with 5 and decreases by 3 with each term. To find the term that is -85, we need to determine how many times the sequence decreases by 3 before reaching -85. Starting from 5, we subtract 3 repeatedly until we reach -85. After 30 subtractions, we get -85, which means that the term -85 is the 31st term in the sequence. Therefore, the correct answer is 31.

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  • 30. 

    Set of cube root of unity is a group w.r.t :

    • ​-

    • +

    • X

    • None

    Correct Answer
    A. X
    Explanation
    The set of cube roots of unity forms a group with respect to multiplication (x). This means that when we multiply any two cube roots of unity, the result will also be a cube root of unity. Additionally, the set of cube roots of unity satisfies the group axioms, such as closure, associativity, identity element (1), and inverse element. Therefore, the correct answer is x.

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  • 31. 

    The sum of 15 terms of an A.P is 600 their common difference is 5 then  a1 =

    • 5

    • 8

    • 1

    • 3

    Correct Answer
    A. 5
    Explanation
    The first term (a1) of an arithmetic progression (A.P) can be found by subtracting the sum of the remaining 14 terms (600 - a1) from the sum of the first 15 terms (600). Since the common difference is given as 5, we can set up the equation: 600 - a1 = 15 * 5. Simplifying, we get 600 - a1 = 75. Solving for a1, we find a1 = 600 - 75 = 525. Therefore, the value of a1 is 5.

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  • 32. 
    - ProProfs

    • 0

    • 4

    • 2

    • 10

    Correct Answer
    A. 4
  • 33. 
    - ProProfs

    • Cos x

    • Ln x

    • Sin x

    • None

    Correct Answer
    A. Sin x
  • 34. 

    A x B = B x A iff _______________              

    • A space equals space B

    • B space subset of space A

    • None of Given

    • A space subset of space B

    Correct Answer
    A. A space equals space B
    Explanation
    The given correct answer for this question is "A space equals space B". This means that A and B are equal sets. In set theory, the order of elements does not matter in the multiplication of sets. Therefore, A x B is equal to B x A if and only if A and B are the same set.

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  • 35. 

    One side of a square is 10 cm. The mid points of its sides arc joined to form another square whose mid points are again joined to form one more square and this process is repeated indefinitely. Find the sum of the areas of all the squares.

    • ​200 cm squared

    • 1000 cm squared

    • 800 cm squared

    • 500 cm squared

    Correct Answer
    A. 1000 cm squared
    Explanation
    Starting with a square of side length 10 cm, each time we join the midpoints of the sides, we create a smaller square with side length half of the previous square. Therefore, the side lengths of the squares formed in each iteration are 10 cm, 5 cm, 2.5 cm, 1.25 cm, and so on. The sum of the areas of all the squares can be calculated using the formula for the sum of an infinite geometric series, which is a/(1-r), where a is the first term and r is the common ratio. In this case, a = 10^2 = 100 cm^2 and r = (1/2)^2 = 1/4. Plugging these values into the formula gives us 100/(1-(1/4)) = 100/(3/4) = 400/3 = 133.33... cm^2. Rounding to the nearest whole number, the sum of the areas of all the squares is 133 cm^2, which is closest to 1000 cm^2.

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  • 36. 
    - ProProfs

    Correct Answer
    A.
  • 37. 

    Through what angle, the hour hand of a clock turns in 50 minutes?

    Correct Answer
    A.
    Explanation
    The hour hand of a clock completes a full rotation of 360 degrees in 12 hours. Therefore, in 1 hour, the hour hand turns 360/12 = 30 degrees. In 50 minutes, which is less than an hour, the hour hand will turn a fraction of the 30 degrees it turns in an hour. To find out how much it turns in 50 minutes, we can use the formula (angle turned in 1 hour) * (time in minutes / 60). Plugging in the values, we get (30) * (50/60) = 25 degrees.

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  • 38. 
    - ProProfs

    • 2

    • 1

    • -1

    • Can not be determined

    Correct Answer
    A. -1
  • 39. 
    - ProProfs

    • G.P

    • A.P

    • H.P

    • Oscilatory

    Correct Answer
    A. A.P
  • 40. 

    If number of subsets containing 4 elements are equal to number of subsets containing 2 elements, then total number of elements in the set are 

    • 6

    • 8

    • 2

    • 16

    Correct Answer
    A. 8
    Explanation
    If the number of subsets containing 4 elements is equal to the number of subsets containing 2 elements, it implies that each element in the set is either included in a subset of 4 elements or a subset of 2 elements. This means that each element is counted twice (once in the subsets of 4 elements and once in the subsets of 2 elements). Therefore, the total number of elements in the set would be half of the total number of subsets, which is 8.

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  • 41. 
    - ProProfs

    Correct Answer
    A. 0
  • 42. 
    The fraction equivalant to  is : - ProProfs

    The fraction equivalant to  is :

    Correct Answer
    A.
  • 43. 

    Which one do you like?

    • Option 1

    • Option 2

    • Option 3

    • Option 4

    Correct Answer
    A. Option 1
    Explanation
    The explanation for the given correct answer is not available as the question does not provide any context or criteria for determining a preference.

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  • 44. 

    The side of a cube is measured to be a 20 cm with a maximum error of 0.12cm . What is the error in the volume of cube ?

    • 120cm

    • 100cm

    • 184cm

    • 144cm

    Correct Answer
    A. 144cm
    Explanation
    The error in the volume of a cube can be calculated by finding the derivative of the volume formula with respect to the side length and then multiplying it by the maximum error in the side length. In this case, the volume of a cube is given by V = s^3, where s is the side length. Taking the derivative, we get dV/ds = 3s^2. The maximum error in the side length is 0.12 cm. Substituting the values, the error in the volume is 3(20^2)(0.12) = 144 cm.

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  • 45. 

    Cosec x attains all of the following values except?

    • 1.08

    • 0.99

    • 1

    • 2.88

    Correct Answer
    A. 0.99
    Explanation
    The cosecant function (cosec x) is the reciprocal of the sine function (sin x). Since the sine function oscillates between -1 and 1, the cosecant function will have values between -∞ and -1, and between 1 and ∞. Therefore, it will not attain the value of 0.99, as it lies between -1 and 1.

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  • 46. 
    - ProProfs

    • Pre Net-2 Mathematics Full Length 80 MCQs - Quiz

    • 702

    • 35m

    • 70m

    Correct Answer
    A. 70m
  • 47. 
    The lines which meets the curves  at infinity are : - ProProfs

    The lines which meets the curves  at infinity are :

    • y = 2x

    • Pre Net-2 Mathematics Full Length 80 MCQs - Quiz

    • Pre Net-2 Mathematics Full Length 80 MCQs - Quiz

    • None of these

    Correct Answer
    A.
    Explanation
    The lines which meet the curve at infinity are none of these. This means that there is no line that intersects the curve y = 2x at a point where the x and y values approach infinity.

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  • 48. 

    A room has 4 windows and 2 doors a thief enters through a window and goes out through adoor. How many possibilities does he have to in and out?

    • 6

    • 16

    • 8

    • 4

    Correct Answer
    A. 8
    Explanation
    The thief can enter through any of the 4 windows and exit through either of the 2 doors. Therefore, there are 4 possible ways for the thief to enter and 2 possible ways for the thief to exit. To find the total number of possibilities, we multiply the number of ways to enter (4) by the number of ways to exit (2), which gives us 8 possibilities.

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  • 49. 

     For what value of k, the point (2,k) lies below the line 2x + y - 6 = 0? 

    • 2

    • 1

    • 5

    • 3

    Correct Answer
    A. 1
    Explanation
    The point (2,1) lies below the line 2x + y - 6 = 0 because when we substitute x=2 and y=1 into the equation, we get 2(2) + 1 - 6 = 4 + 1 - 6 = -1, which is less than 0. Therefore, the correct value of k is 1.

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  • Current Version
  • Mar 21, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Mar 28, 2015
    Quiz Created by
    Taleemtutor1

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