CUET UG Mathematics Mock Test

CUET UG Mathematics Mock Test for free online practice of entrance exam 2025-2026.

Subject: Mathematics
Medium: English
Questions: 50

Results

#1. Let n(A) = 4 and n(B) = 6. Then, the number of one-one functions from A to B is

120

360

#2. A relation R from A to B is an arbitrary subset of

A x B

B x A

A x A

B x B

#3. Let A = {1, 2, 3}. Then, number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive, is

#4. Let f : R – $ \{-\frac43\}$ $ \rightarrow$R be a function defined as f[x]= $ \frac{4x}{3x+4}$ The inverse of f is the map g : range f $ \rightarrow$R – $ \{-\frac43\}$ given by

g(y) = $ \frac{3y}{3-4y}$

g(y) = $ \frac{4y}{4-3y}$

g(y) = $ \frac{4y}{3-4y}$

g(y) = $ \frac{3y}{4-3y}$

#5. The domain in which sine function will be one-one, is

$ [\frac{-\pi}{2},\frac{\pi}{2}] $

$ [\frac{\pi}{2},\frac{3\pi}{2}] $

$ [0,\pi] $

Both (a) and (b)

#6. cosec x is not defined for

all integral multiples of $ \frac{\pi}{2}$

all integral multiples of $ \pi$

all integral multiples of $ \frac{3\pi}{4}$

None of the above

#7. The principal value of $ cos^{-1} (\frac12)-2sin^{-1}(-\frac{1}{2})$ is

$ \frac \pi3$

$ \frac{-\pi}{3}$

$ \frac {2\pi}{3}$

$ \frac \pi6$

#8. The value of $ sin^1(sin\frac{2\pi}{3}) $ is ……. Here, X refers to

$ \frac\pi2 $

$ \frac\pi6 $

$ \frac\pi3 $

#9. The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is

512

#10. If A and B are two matrices of the order 3 x m and 3 x n, respectively and m=n, then the order of the matrix (5A – 2B)is

m x 3

3 x 3

m x n

3 x n

#11. Two matrices A = [a_ij] and B =[b_ij] are said to be equal, if they are of same order and for all i and j

a_ij = b_ji

a_ij = b_ij

a_ij = – b_ij

a_ij + b_ij = 0

#12. If A is a 3 x 2 matrix, B is a 3 x 3 matrix and C is a 2 x 3 matrix, then the elements in A, B and C are respectively

6, 9, 8

6, 9, 6

9, 6, 6

6, 6, 9

#13. The area of the triangle, whose vertices are (3, 8), (-4, 2) and (5, 1), is

$ \frac{61}{2}$

#14. If each element of a row (or a column) of a determinant is multiplied by a constant k, then its value gets …A… by k. Here, A refers to

added

subtracted

divided

multiplied

#15. If the value of the determinant $ \begin {vmatrix} a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c \end {vmatrix}$ is positive, then

abc > 1

abc > – 8

abc < – 8

abc > – 2

#16. If $ \triangle = \begin{vmatrix} a & h & g \\ h & b & f \\ g & f & c\end {vmatrix} $, then the cofactor $ A_{21}$ is

-(hc + fg)

fg – hc

fg + hc

hc – fg

#17. The function $ f(x) = \begin{Bmatrix} 1, \text{if x} \neq 0 \\ 2 , \text{if x} = 0 \end{Bmatrix} $ is not continuous at

x = 0

x = 1

x = -1

None of these

#18. Continuity of a function at a point is entirely dictated by the…A… of the function at that point. Here, A refers to

limit

value

Both (a) and (b)

None of these

#19. A function is said to be differentiable in an interval [a, b ], if it is differentiable at every point of [a, b ]

including a and b

excluding a and b

including a but not b

including b but not a

#20. Let b > 1be a real number. Then, logarithm of a to the base b is x, if

b^a = x

a^b = x

b^x = a

None of these

#21. The radius of a circle is increasing uniformly at the rate of 3 cm/s. At radius of 10 cm, the area of the circle is increasing at the rate of

$ 20\pi cm^2/ S $

$ 40\pi cm^2/ S $

$ 60\pi cm^2/ S $

$ 80\pi cm^2/ S $

#22. The function given f(x)=e^2x is …A… on R. Here, A refers to

strictly increasing

strictly decreasing

neither increasing nor decreasing

decreasing

#23. The function given by f(x) = x³ – 3x² + 3x – 100 is

increasing on R

decreasing on R

strictly decreasing on R

None of these

#24. The approximate value of f(2.01), if f(x) =4x² + 5x + 2, is

28.21

18.24

21.28

29.30

#25. If the derivative of a function sec^-1x is $ \dfrac{1}{x \sqrt{x^2-1}}$ then the anti-derivative of $ \dfrac{1}{x \sqrt{x^2-1}}$ is

sec^-1 x

sec^-1x+C

2 sec^-1x

None of these

#26. The anti-derivative of [ sec x (sec x + tan x)] is

2sec x + C

tan x + sec x + C

sec² x + sec x tan x + C

None of these

#27. The integral of the function tan⁴ x is

$ \dfrac{\text{tan}^3x}{3}-\text{tan}x-x+C $

$ \dfrac{\text{tan}^3x}{3}+\text{tan}x-x+C $

$ \dfrac{\text{tan}^3x}{3}-\text{tan}x+x+C $

$ \dfrac{\text{tan}^3x}{3}+\text{tan}x+x+C $

#28. The value of $ \dfrac{1}{\sqrt{7-6x-x^2}} $ is

$ \text{log}[2x + \sqrt{7 – 6x – x^2}]+C $

$ \frac12\text{log}\begin{vmatrix} \frac {x+3}{x-3}\end{vmatrix}+C $

$ sin^{-1} (\dfrac{x + 3}{4})+C $

None of the above

#29. If the area between x = y² and x = 4 is divided into two equal parts by the line x = a, then the value of a is

(4)^1/3

(4)^4/3

(4)^2/3

None of these

#30. Area of the region bounded by the curve y = cos x between x = 0 and x = $ \pi$ is

2 sq units

4 sq units

3 sq units

1 sq unit

#31. Area (in sq units) lying between the curves y² = 4x and y = 2x is

$ \dfrac23 $

$ \dfrac13 $

$ \dfrac14 $

$ \dfrac34 $

#32. The area of the circle x² + y² = 16 exterior to the parabola y² = 6x is

$ \dfrac43(4\pi-\sqrt3) $ sq units

$ \dfrac43(4\pi+\sqrt3) $ sq units

$ \dfrac43(8\pi-\sqrt3) $ sq units

$ \dfrac43(8\pi+\sqrt3) $ sq units

#33. The equation of the form $ 2\dfrac{d^2y}{dx^2}+(\dfrac{dy}{dx})^3 $=0 is a\an

cubic equation

quadratic equation

ordinary differential equation

None of the above

#34. The equation y = mx + c, where m and c are parameters, represents family of

straight lines

circles

parabola

hyperbola

#35. The equation of a curve whose tangent at any point on it different from origin has slope $ y +\dfrac yx, $ is

y = ex

y = $ kx.e^x $

y = kx

y = $ x \cdot e^{x^2} $

#36. A differential equation of the form $ \dfrac{dy}{dx}$=F(x, y) is said to be homogeneous, if F(x, y) is a homogeneous function of degree

#37. If two or more vectors are parallel to the same line then they are called

collinear vectors

coinitial vectors

equal vectors

zero vectors

#38. If four points A(3,2,1), B(4, x, 5), C (4,2,-2) and D (6, 5,-1) are coplanar, then the value of x is

#39. In $ \triangle $ABC (fig), which of the following is not true?

AB + BC + CA = O

AB + BC – AC = O

AB + BC – CA = O

AB – CB + CA = O

#40. If α,β,γ be the direction angles of a vector and cos α =$ \dfrac{14}{15} $, cosβ =$ \dfrac13 $, then cos γ=……..K……. Here, K refers to

±$ \dfrac{2}{15} $

$ \dfrac15 $

±$ \dfrac{1}{15} $

None of these

#41. The angle between the lines whose direction cosines are given by the equations 3l + m + 5n = 0 and 6mn – 2nl + 5lm=0, is

cos^-1 $ (\dfrac{1}{\sqrt6}) $

cos^-1 $ (\dfrac{1}{3}) $

cos^-1 $ (\dfrac{-1}{6}) $

cos^-1 $ (\dfrac{-2}{3}) $

#42. The lines $ \dfrac{x + 3}{-3}$= $ \dfrac{y-1}{1}$= $ \dfrac{z-5}{5}$ and $ \dfrac{x + 1}{-1}$= $ \dfrac{y-2}{2}$= $ \dfrac{z-5}{5}$ are

coplanar

non-coplanar

skew

None of these

#43. The distance of the plane $ r \cdot (\dfrac27 \hat i+\dfrac37 \hat j-\dfrac67 \hat k) $=1 from the origin is

$ \dfrac17 $

None of these

#44. The conditions $ x \ge 0, y \ge 0 $ are called

restrictions only

negative restrictions

non-negative restrictions

None of these

#45. The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5) (15, 15), (0, 20). Let Z = px + qy, where p, q > 0. Then, the condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20), is

p = q

p = 2q

q = 2p

q = 3p

#46. A diet is to contain atleast 80 units of vitamin A and 100 units of minerals. Two foods F1 and F2 are available. Food F1 costs ₹ 4 per unit and food F2 costs ₹ 6 per unit. One unit of food F1 contains 3 units of vitamin A and 4 units of minerals. One unit of food F2 contains 6 units of vitamin A and 3 units of minerals. Then, the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements, is

₹ 100

₹ 105

₹ 103

₹ 104

#47. One kind of cake requires 200g of flour and 25g of fat and another kind of cake requires 100g of flour and 50g of fat. Then, the maximum number of cakes which can be made from 5kg of flour and 1kg of fat assuming that there is no storage of the other ingredients used in making the cakes, is

₹ 20

₹ 10

₹ 30

₹ 40

#48. Let A and B be two events. If P(A)= 0.2, P(B) = 0.4 and P $ (A \cup B)$ = 0.6, then P(A / B) is equal to

0.8

0.5

0.3

#49. Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, the probability of getting a sum 3, is

$ \dfrac {1}{18} $

$ \dfrac {5}{18} $

$ \dfrac {1}{5} $

$ \dfrac 25 $

#50. A description giving the values of the random variable along with the corresponding probabilities is called …K… of the random variable X. Here, K refers to

conditional probability

probability distribution

mean

None of the above

FINISH

Results

#1. Let n(A) = 4 and n(B) = 6. Then, the number of one-one functions from A to B is

#2. A relation R from A to B is an arbitrary subset of

#3. Let A = {1, 2, 3}. Then, number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive, is

#4. Let f : R – $ \{-\frac43\}$ $ \rightarrow$R be a function defined as f[x]= $ \frac{4x}{3x+4}$ The inverse of f is the map g : range f $ \rightarrow$R – $ \{-\frac43\}$ given by

#5. The domain in which sine function will be one-one, is

#6. cosec x is not defined for

#7. The principal value of $ cos^{-1} (\frac12)-2sin^{-1}(-\frac{1}{2})$ is

#8. The value of $ sin^1(sin\frac{2\pi}{3}) $ is ……. Here, X refers to

#9. The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is

#10. If A and B are two matrices of the order 3 x m and 3 x n, respectively and m=n, then the order of the matrix (5A – 2B)is

#11. Two matrices A = [aij] and B =[bij] are said to be equal, if they are of same order and for all i and j

#12. If A is a 3 x 2 matrix, B is a 3 x 3 matrix and C is a 2 x 3 matrix, then the elements in A, B and C are respectively

#13. The area of the triangle, whose vertices are (3, 8), (-4, 2) and (5, 1), is

#14. If each element of a row (or a column) of a determinant is multiplied by a constant k, then its value gets …A… by k. Here, A refers to

#15. If the value of the determinant $ \begin {vmatrix} a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c \end {vmatrix}$ is positive, then

#16. If $ \triangle = \begin{vmatrix} a & h & g \\ h & b & f \\ g & f & c\end {vmatrix} $, then the cofactor $ A_{21}$ is

#17. The function $ f(x) = \begin{Bmatrix} 1, \text{if x} \neq 0 \\ 2 , \text{if x} = 0 \end{Bmatrix} $ is not continuous at

#18. Continuity of a function at a point is entirely dictated by the…A… of the function at that point. Here, A refers to

#19. A function is said to be differentiable in an interval [a, b ], if it is differentiable at every point of [a, b ]

#20. Let b > 1be a real number. Then, logarithm of a to the base b is x, if

#21. The radius of a circle is increasing uniformly at the rate of 3 cm/s. At radius of 10 cm, the area of the circle is increasing at the rate of

#22. The function given f(x)=e2x is …A… on R. Here, A refers to

#23. The function given by f(x) = x3 – 3x2 + 3x – 100 is

#24. The approximate value of f(2.01), if f(x) =4x2 + 5x + 2, is

#25. If the derivative of a function sec-1x is $ \dfrac{1}{x \sqrt{x^2-1}}$ then the anti-derivative of $ \dfrac{1}{x \sqrt{x^2-1}}$ is

#26. The anti-derivative of [ sec x (sec x + tan x)] is

#27. The integral of the function tan4 x is

#28. The value of $ \dfrac{1}{\sqrt{7-6x-x^2}} $ is

#29. If the area between x = y2 and x = 4 is divided into two equal parts by the line x = a, then the value of a is

#30. Area of the region bounded by the curve y = cos x between x = 0 and x = $ \pi$ is

#31. Area (in sq units) lying between the curves y2 = 4x and y = 2x is

#32. The area of the circle x2 + y2 = 16 exterior to the parabola y2 = 6x is

#33. The equation of the form $ 2\dfrac{d^2y}{dx^2}+(\dfrac{dy}{dx})^3 $=0 is a\an

#34. The equation y = mx + c, where m and c are parameters, represents family of

#35. The equation of a curve whose tangent at any point on it different from origin has slope $ y +\dfrac yx, $ is

#36. A differential equation of the form $ \dfrac{dy}{dx}$=F(x, y) is said to be homogeneous, if F(x, y) is a homogeneous function of degree

#37. If two or more vectors are parallel to the same line then they are called

#38. If four points A(3,2,1), B(4, x, 5), C (4,2,-2) and D (6, 5,-1) are coplanar, then the value of x is

#39. In $ \triangle $ABC (fig), which of the following is not true?

#40. If α,β,γ be the direction angles of a vector and cos α =$ \dfrac{14}{15} $, cosβ =$ \dfrac13 $, then cos γ=……..K……. Here, K refers to

#41. The angle between the lines whose direction cosines are given by the equations 3l + m + 5n = 0 and 6mn – 2nl + 5lm=0, is

#42. The lines $ \dfrac{x + 3}{-3}$= $ \dfrac{y-1}{1}$= $ \dfrac{z-5}{5}$ and $ \dfrac{x + 1}{-1}$= $ \dfrac{y-2}{2}$= $ \dfrac{z-5}{5}$ are

#43. The distance of the plane $ r \cdot (\dfrac27 \hat i+\dfrac37 \hat j-\dfrac67 \hat k) $=1 from the origin is

#44. The conditions $ x \ge 0, y \ge 0 $ are called

#45. The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5) (15, 15), (0, 20). Let Z = px + qy, where p, q > 0. Then, the condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20), is

#47. One kind of cake requires 200g of flour and 25g of fat and another kind of cake requires 100g of flour and 50g of fat. Then, the maximum number of cakes which can be made from 5kg of flour and 1kg of fat assuming that there is no storage of the other ingredients used in making the cakes, is

#48. Let A and B be two events. If P(A)= 0.2, P(B) = 0.4 and P $ (A \cup B)$ = 0.6, then P(A / B) is equal to

#49. Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, the probability of getting a sum 3, is

#50. A description giving the values of the random variable along with the corresponding probabilities is called …K… of the random variable X. Here, K refers to

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#11. Two matrices A = [a_ij] and B =[b_ij] are said to be equal, if they are of same order and for all i and j

#22. The function given f(x)=e^2x is …A… on R. Here, A refers to

#23. The function given by f(x) = x³ – 3x² + 3x – 100 is

#24. The approximate value of f(2.01), if f(x) =4x² + 5x + 2, is

#25. If the derivative of a function sec^-1x is $ \dfrac{1}{x \sqrt{x^2-1}}$ then the anti-derivative of $ \dfrac{1}{x \sqrt{x^2-1}}$ is

#27. The integral of the function tan⁴ x is

#29. If the area between x = y² and x = 4 is divided into two equal parts by the line x = a, then the value of a is

#31. Area (in sq units) lying between the curves y² = 4x and y = 2x is

#32. The area of the circle x² + y² = 16 exterior to the parabola y² = 6x is