Download CUET -UG exams mathematics sample paper and more Exams Mathematics in PDF only on Docsity!
Maximum Marks : 200 Time : 45 Min.
General Instructions :
(i) Section A will have 15 questions covering both i.e., Mathematics/Applied Mathematics which will be
compulsory for all candidates.
(ii) Section B1 will have 35 questions from Mathematics out of which 25 questions need to be attempted. Section
B2 will have 35 questions purely from Applied Mathematics out of which 25 questions will be attempted.
(iii) Correct answer or the most appropriate answer : Five marks (+ 5)
(iv) Any incorrect option marked will be given minus one mark (– 1).
(v) Unanswered/Marked for Review will be given no mark (0).
(vi) If more than one option is found to be correct then Five marks (+5) will be awarded to only those who have
marked any of the correct options.
(vii) If all options are found to be correct then Five marks (+5) will be awarded to all those who have attempted the
question.
(viii) If none of the options is found correct or a Question is found to be wrong or a Question is dropped then all
candidates who have appeared will be given five marks (+5).
(ix) Calculator / any electronic gadgets are not permitted.
Section - A
Mathematics/Applied Mathematics
1. If
1 if ( ) 2 , sin , if 2
mx x f x x n x
(^) + ≤^ π = (^) + >
p
is continuous at
x = p 2 then (1) m = 1, n = 0 (2) m = n^ p+ 2
(3) n = m p 2
(4) m = n = p 2
2. If
x x x + 3 = 0 , (^) then the value of x is
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as: (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true but R is NOT the correct explanation of A (C) A is true but R is false (D) A is false and R is True
3. Assertion (A):
π (^) π
∫ +
/ 2
0 sin^ cos^4
cos x (^) dx x x
Reason (R): (^) = ∫ +
/ 2
0
sin sin cos 4
x (^) dx x x
p (^) p
4. Assertion (A):
2 2 4 0
d x dt x dx (^) t x
∫
Reason (R): (^) 2^ dx^ 2 1 tan^1 x^ c x a a^ a
= −^ ^ +
∫ +
5. Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b " a , b Î T. Then R is (1) reflexive but not transitive (2) transitive but not symmetric (3) equivalence relation (4) None of these 6. The area of the region bounded by the y -axis, y = cos x and y = sin x , 0 ≤ x ≤ p/2 is (1)^2 sq. units (2) ( 2 + 1 )sq. units (3) ( 2 - 1)sq. units (4) (2 2 - 1)sq. units 7. A ladder, 5 metre long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor
SAMPLE
Question Paper
2 OSWAAL CUET(UG) Sample Question Papers,^ MATHEMATICS/APP. MATH.
and the ladder is decreasing when lower end of ladder is 2 metre from the wall is :
(1)^1 10
radian/sec (2)
radian/sec
(3) 20 radian/sec (4) 10 radian/sec
8. If A and B are two events such that P ( A ) ≠ 0 and P(B|A) = 1, then (1) A ⊂ B (2) B ⊂ A (3) B = j (4) A = j 9. The value of sin–1^ cos^3 5
p (^) is
p 10 (2)^
p
(3) -^
p 10 (4)^
10. If P(A|B) > P (A), then which of the following is correct : (1) P(B|A) < P (B) (2) P(A ∩ B) < P (A) .P (B) (3) P(B|A) > P (B) (4) P(B|A) = P (B) 11. The equation of normal to the curve 3^ x^2^^ -^ y^2 =^8 which is parallel to the line x + 3 y = 8 is (1) (^) 3 x – y = 8 (2) (^) 3 x + y + 8 = 0 (3) (^) x + 3 y ± 8 = 0 (4) (^) x + 3 y = 0 12. Consider the non-empty set consisting of children
in a family and a relation R defined as aRb if a is brother of b. Then R is (1) symmetric but not transitive (2) transitive but not symmetric (3) neither symmetric nor transitive (4) both symmetric and transitive
13. The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is Z = 4 x + 3 y. Compare the quantity in Column A and Column B Column A Column B Maximum of Z 325 (1) The quantity in column A is greater. (2) The quantity in column B is greater. (3) The two quantities are equal. (4) The relationship cannot be determined on the basis of the information supplied. 14. The value of (^) //^22 ( x^3 x cos x tan 5 x 1 ) dx is (1) 0 (2) 2 (3) p (4) 1 15. Distance of the point (α, β, γ) from y -axis is (1) b (2) |b| (3) |b|+ |g| (4) (^) 2 ^2
Section - B
Mathematics
16. The value of sin cos 33 5
^
^
^
is
(1)^3
17. If y = log e^ x e
2 2
^
, then d y dx
2 2 equals
(1) - 1 x
(2) -^
x^2
(3)^22 x
(4) -^ x^22
18. If the curve ay^ +^ x^2 =^7 and x^3 = y , cut orthogonally at (1, 1), then the value of a is : (1) 1 (2) 0 (3) –6 (4) 6 19. Let A =
and B =
, then | AB |
is equal to (1) 460 (2) 2000 (3) 3000 (4) – 7000
20. If A and B are any two events such that P (A) + P (B) – P(A and B) = P (A), then (1) P(B|A) = 1 (2) P(A|B) = 1 (3) P(B|A) = 0 (4) P(B|A) = 0 21. The sine of the angle between the straight line x - (^2) = y - (^) = z - 3
and the plane 2 x – 2 y + z = 5 is
(1)^10
(2)^4
(3)^2
22. The area of the region bounded by the curve x^2 = 4 y and the straight-line x = 4 y – 2 is
(1)
sq. units (^) (2)^5 8
sq. units
(3)^7
sq. units (4)^9 8
sq. units
4 OSWAAL CUET(UG) Sample Question Papers,^ MATHEMATICS/APP. MATH.
41. The feasible solution for a LPP is shown in given figure. Let Z = 3 x – 4 y be the objective function Minimum of Z occurs at
42. Let
= (l – 2) a + b and
= (4l – 2) a + 3 b be two given vectors where a and b are non collinear. The
value of l for which vectors α^ ^ and β
are collinear, is : (1) –4 (2) – (3) 4 (4) 3
43. Let f x ( ) = |sin x |,then (1) f is everywhere differentiable (2) f is everywhere continuous but not differentiable at x = n p , n Î Z. (3) f is everywhere continuous but not differentiable at x = (2 n + 1) (^) , 2
(^) n Î Z.
(4) none of these
44. The integrating factor of differential equation cos x dy sin dx
y x 1 is (1) cos x (2) tan x (3) sec x (4) sin x
45. If the direction cosines of a line are k , k , k , then (1) k > 0 (2) 0 < k < 1
(3) k = 1 (4) k^ =^
or -^
46. The area of a triangle with vertices (–3, 0), (3, 0) and (0, k ) is 9 sq. units. Then, the value of k will be (1) 9 (2) 3 (3) –9 (4) 6 47. Refer to Q. 41 maximum of Z occurs at (1) (5, 0) (2) (6, 5) (3) (6, 8) (4) (4, 10) Read the following text and answer the following questions on the basis of the same: On her birthday, Seema decided to donate some money to children of an orphanage home. If there were 8 children less, everyone would have got 10 more. However, if there were 16 children more, everyone would have got10 less. Let the number of children be x and the amount distributed by Seema for one child be y (in `). 48. The equations in terms of x and y are (1) 5 x – 4 y = 40 (2) 5 x – 4 y = 40 5 x – 8 y = –80 5 x – 8 y = 80 (3) 5 x – 4 y = 40 (4) 5 x + 4 y = 40 5 x + 8 y = –80 5 x – 8 y = – 49. Which of the following matrix equations represent the information given above?
(1)
^
x y
(2)
x y
(3)
^
x y
(4)
^
x y
50. The number of children who were given some money by Seema, is (1) 30 (2) 40 (3) 23 (4) 32
Section - B
Applied Mathematics
16. If a ≡ b (mod n ), then (1) n | a and n | b (2) n | b only (3) n |( a – b ) (4) None of these 17. Evaluate: (9 + 23) mod 12 = ....... (1) 2 (2) 8 (3) 32 (4) 12 18. If B > A , then which expression will have the highest value, given that A and B are positive integers. (1) A – B (2) A × B (3) A + B (4) Can't say 19. Tea worth 126 per kg and 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture
Sample Question Papers 5
per kg will be: (1) 169.50 **(2)** 170 (3) 175.50 **(4)** 180
20. A = [ a (^) if ] m (^) × n is a square matrix, if
(1) m < n (2) m > n (3) m = n (4) None of these
21. If A is a square matrix such that A^2 = A , then (I + A )³ – 7 A is equal to (1) A (2) I – A (3) I (4) 3A 22. Which of the given values of x and y make the following pair of matrices equal 3 7 5 1 2 3
x y x
(1) x^ = y
, (^7) (2) Not possible to find
(3) y^ =^ x =
7 −^2
, (^) (4) x = −^1 y = − 3
23. Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k, respectively. The restriction on n, k and p so that PY + WY will be defined are: (1) k = 3, p = n (2) k is arbitrary, p = 2 (3) p is arbitrary, k = 3 (4) k = 2, p = 3 24. If A and B are symmetric matrices of same order, AB – BA is a: (1) Skew-symmetric matrix (2) Symmetric matrix (3) Zero matrix (4) Identity matrix 25. The function f x ( ) =^^2 x^^^3 −^3 x^^^2 −^12 x +^4 , has
(1) two points of local maximum (2) two points of local minimum (3) one maxima and one minima (4) no maxima or minima
26. The total revenue in Rupees received from the sale of x units of a product is given by R ( x ) = 3 x^2 + 26 x + 15. The marginal revenue, when x = 15 is : (1) 100 **(2)** 116 (3) ` 123 (4) None 27. The maximum profit that a company can make, if the profit function is given by p x ( )^ =^41 −^72 x^^ −^18 x^2 is : (1) 111 (2) 112 (3) 113 (4) 114 28. If y = x^3 log x , then d y dx
4 4 is :
(1) 6 x (2)
x (3) x 6 (4)^ log 6
29. If x is real, the minimum value of x^2 – 8 x + 17 is (1) –1 (2) 0 (3) 1 (4) 2 30. A candidate claims 70% of the people in her constituency would vote for her. If 1,20,000 valid votes are polled, then the number of votes she expects from her constituency is (1) 100000 (2) 84000 (3) 56000 (4) 36000 31. Given that x = at^2 and y = 2 at then d y dx
2 2 is (1) (^) – 2 at^3
2 at^2
(3)^12 t
(4) –2 a t
32. The expectation of a random variable X (continuous or discrete) is given by.......... (1) ∑ X f(x), ∫ X f(X) (2) ∑ X^2 f(X), ∫ X^2 f(X) (3) ∑ f(X), ∫ f(X) (4) ∑ X f(X^2 ), ∫ X f(X^2 ) 33. Mean of a constant ‘ a ’ is ............... (1) 0 (2) a (3) a/2 (4) 1 34. Find the expectation of a random variable X. X 0 1 2 3
f(X)^1 6
35. Skewness of Normal distribution is ......... (1) Negative (2) Positive (3) 0 (4) Undefined 36. Which of the following values is used as a summary measure for a sample, such as a sample mean? (1) Population Parameter (2) Sample Parameter (3) Sample Statistic (4) Population mean 37. A simple random sample consist of four observation 1, 3, 5, 7. What is the point estimate of population standard deviation? (1) 2.3 (2) 2. (3) 0.36 (4) 0. 38. A price index which is based on the prices of the items in the composite, weighted by their relative index is called: (1) price relatives (2) Consumer price index (3) Weighted aggregative price index (4) Simple aggregative index 39. Which of the following is an example of line series problem? (i) Estimating numbers of hotel rooms booking in next 6 months. (ii) Estimating the total sales in next 3 years of an insurance company. (iii) Estimating the number of calls for the next one week. (1) Only (iii) (2) (i) and (ii) (3) (i), (ii) and (iii) (4) (ii) and (iii)
