MHT-CET-XII Maths Past Paper PDF 2024-25

MATRIX ACADEMY MHT-CET-XII - New Syllabus (MH) 2024-25 Time : 90 Min Maths : Groupwise Paper Marks : 100 01) The maximum value of (x  2y) under the questions in three hours, the linear constraints are...

MATRIX ACADEMY MHT-CET-XII - New Syllabus (MH) 2024-25 Time : 90 Min Maths : Groupwise Paper Marks : 100 01) The maximum value of (x  2y) under the questions in three hours, the linear constraints are constraints 2x  3y  6, x  4y  4, x, y  0 is x  0, y  0 , x  10, y  14 and 5x  10y  180. A) 4 Then the vertices of a feasible region are B) 3.2 A) (0, 18), (36, 0) C) 3 B) (10, 13), (8, 14) D) 2 C) (0, 18), (10, 13) D) (10, 13), (8, 14), (12, 12) 02) The incidence of occupational disease in an industry is such that the workmen have a 10% 07) The position of points O (0, 0) and P (2, - 2) in chance of suffering from it. The probability that out the region of graph of inequation 2x  3y  5 , will of 5 workmen, 3 or more will contract the disease be is A) O and P both inside A) 0.0856 B) O and P both outside B) 0.000856 C) O outside and P inside C) 0.0000856 D) O inside and P outside D) 0.00856 08) Find out maximum value of z=5x+7y subject 03) In binominal distribution if n = 25 E (X) = 10, to x  y  4, 3x  8y  24, 10x  7y  35, x, y  0. then var (X) =............... A) 42.8 A) 2/5 B) 24.6 B) 2 C) 24.8 C) 3 D) 48.2 D) 6 04) If a fair coin is tossed 8 times, then the 09) A vertex of the linear inequalities 2x  3y  6 , probability that it shows heads at least once is x  4y  4 and x, y  0 , is 3 A) (1, 0) A) 256 B) (1, 1) 1  2 12  B) C)  ,  256 5 5  85  12 2  C) D)  ,  256  5 5 255 D) 256 10) In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 05) The probability that a person who undergoes a eggs none are rotten, if the sampling is with kidney operation will recover is 0.7. If the six replacement, is patients who undergoes similar operations, then  9  5 the probability that half of them will recover is A)   A) 0.3704  10  5 B) 0.1852 1 C) 0.03704 B)   5 D) 0.01852 5 9 C)   06) In a test of Mathematics, there are two types of 5 questions to be answered-short answered and long 5 answered. The relevant data is given below  1  D)    10  11) In binomial probability distribution, mean is 3 and standard deviation is 3/2. Then the probability distribution is 6 The total marks is 100. Students can solve all the 1 3 A)    questions. To secure maximum marks, a student 4 4 solves x short answered and y long answered NEET, JEE-MAIN, MHT-CET, MHT-CET-XI  MSA 3 these ingredients and one kg of food B has 12, 4 1 3 B)    and 6 units respectively. The price of food A 4 4 is Rs.4 per kg and that of food B is Rs.3 per kg. 12 3 1 Find out minimum cost. C)    4 4 27 29 A) units of food A and units of food B, 9 25 12 3 1 D)    90 4 4 minimum cost is Rs. 11 12) The corner points of the feasible region 35 41 B) units of food A and units of food B, determined by the system of linear constraints are 22 11 (0,10), (5,5) (15,15), (0,20). Let z  px  qy , where 80 minimum cost is Rs. p, q > 0. Condition on p and q so that the 11 maximum of z occurs at both the points (15, 15) 35 41 C) units of food A and units of food B, and (0, 20) is 22 11 A) q = 3p 90 B) q = 2p minimum cost is Rs. C) p = 2q 11 D) p = q 6 11 D) units food A and units of food B, 5 10 13) If a fair coin is tossed 8 times, then the 81 probability that it shows heads exactly 5 times is minimum cost is Rs. 10 7 A) 16 18) If p.m.f. of r.v. X is x 4 x 5  4  5   4  B) P(X)        , x  0,1,2,3,4, then Var(X)= 16 x 9   9  5 A) 0.9768 C) 32 B) 0.09876 7 C) 0.9786 D) D) 0.9876 32 14) If for a binomial distribution X B (7, p) P (X 19) Inequations 3x  y  3 and 4x  y  4 = 1) = P ( X = 2), then p is............................... A) have solution for all x A) 2/3 B) have solution for all y B) 1/4 C) have solution for positive x and y C) 1/6 D) have no solution for positive x and y D) 1/2 20) The values of x and y for which the objection 15) An urn contains 4 white and 3 red balls. If 3 function z = 3x + 4y under the constraints balls are drawn one by one with replacement and y  x  2,4x  3y  12, x  0, y  0 is maximum are probability of getting exactly two red ball is......... a  3 / b  , then a+b is............. 3 A) x=4 and y=0 B) x=3, and y=0 A) 8 C) x=0 and y=2 B) 11 D) x=6/7 and y=20/7 C) 10 D) 9 21) Shaded region is represented by 16) The points which provides the solution to the linear programming problem: Max P  2x  3y subject to constraints: x  0, y  0 , 2x  2y  9, 2x  y  7 , x  2y  8 is A) (1, 3.5) B) (2, 2.5) C) (2, 3.5) D) (3, 2.5) 17) Two different kinds of food A and B are being A) 2x  5y  80, x  y  20, x  0, y  0 considered to form a weekly diet. The minimum weekly requirement for fats. carbohydrates and B) 2x  5y  80, x  y  20, x  0, y  0 proteins are 18, 24 and 16 units respectively. One C) 2x  5y  80, x  y  20, x  0, y  0 kg of food A has 4, 16 and 8 units respectively of D) 2x  5y  80, x  y  20, x  0, y  0 NEET, JEE-MAIN, MHT-CET, MHT-CET-XI  MSA x  0, y  0 obtained, is 22) An insurance agent insures lives of 5 men, all A) (0, 0) having same age and good health. The probability B) (0, 2) that a man of this age will survive the next 30 C) (2, 0) 2 D) (1.5, 1.5) years is known to be. What is the probability 3 that in the next 30 years almost 3 men will 27) For a bionomial distribution X B (n, p) if survive? n=5 and P(X = 1) = 8P (X = 3), then mean of the 163 distribution is............ A) 1 243 A) 80 5 B) B) 1 243 32 C) 1/5 C) D) 0 243 131 28) The minimum value of objective function D) 243 c  2x  2y in the given feasible region, is 23) One coin is thrown 100 times, then the probability of getting head in odd number is 1 A) 2 1 B) 5 A) 38 3 B) 40 C) 8 C) 80 1 D) 134 D) 8 29) A die is thrown 6 times. If "getting an odd number" is a success, then the probability of 24) An experiment succeeds twice as often as it getting 5 successes is............. fails. Find the probability that in 4 trials there will A) 1/64 be at least three success. B) 31/32 24 C) 3/32 A) 27 D) 3/64 16 B) 30) The common solution set of the constraints 27 8 x y C)   2, x  0, and y  0 is....................... 27 2 3 4 D) 27 25) For an L.P.P. the feasible region is shown shaded in the figure. Find the maximum value of the objective function z  5x  7y A) A) 15 B) 21 C) 24 D) 25 B) 26) The point at which, the maximum value of (3x + 2y) subject to the constraints x  y  2 , NEET, JEE-MAIN, MHT-CET, MHT-CET-XI  MSA other from the box. The first bulb after selection being put back in the box before making the second selection. The probability that both the bulbs are without defect is 9 A) 25 4 B) 5 16 C) 25 C) 8 D) 25 35) 8 coins are tossed simultaneously. The probability of getting at least 6 heads is 7 A) 64 37 B) 256 57 C) D) 64 229 D) 31) The vertices of the feasible region for the 256 constraints x  y  4, x  2, y  1, x  y  1, x  0, y  0 are.................... 36) To maximize the objective function z  2x  3y A) (0, 1), (2, 1), (2, 2), (0, 4) under the constraints x  y  30, x  y  0, y  12, B) (2, 0), (4, 0), (3, 1), (2, 1) x  20, y  3 and x, y  0 C) (1, 0), (2, 0), (2, 1), (0, 1) D) (0, 0), (2, 0), (2, 1), (0, 1) A) x  20, y  10 B) x  12, y  12 32) An urn contains 25 balls of which 10 balls are C) x  18, y  12 red and remaining 15 balls are black in colour. A ball is drawn at random from the urn and its D) x  12, y  18 colour is noted and it is replaced. If 6 balls are drawn in this way. The probability that the number 37) A retailer deals in two items namely item A and of red ball and number of black balls will be equal item B. He has 50, 000 to invest and a space to is...................... store at the most 60 pieces. An item A costs him A) 8/125 Rs.2500 and B costs him Rs.500. A net profit to B) 864/3125 him on item A is Rs.500 and on item B is Rs.150. C) 27/125 Calulate how should he invest his amount so that D) 216/15625 he can get maximum profit? A) Maximum profit  Rs.12,500, when 10 units of 33) The feasible region for the following constraints item A and 50 units of item B L1  0, L2  0, L3  0, x  0, y  0 in the diagram B) Maximum profit  Rs.12,500, when 11 units of shown is item A and 55 units of item B C) Maximum profit  Rs.11,500, when 10 units of item A and 50 units of item B D) None of these 38) A company manufacture two types of bags, hand bangs and shoulder bags. The raw material and labour available per day is given in the table below: A) Area AHC B) Area DHF C) Line segment GI D) Line segment EG If profit on a should bag is Rs. 100 and that on a 34) In a box of 10 electric bulbs, two are defective. hand bag is Rs. 200, evaluate the number of Two bulbs are selected at random one after the shoulder bags and hand bags should be NEET, JEE-MAIN, MHT-CET, MHT-CET-XI  MSA manufactured so that the income is maximum? C) 18 (Assume that both types of bags can be sold.) D) 9 A) 4 hand bags and 10 shoulder bags B) 10 hand bags and no shoulder bag 45) If (0, 0), (20, 0) and (0, 20) are the vertices of C) 15 hand bags and no shoulder bag the feasible region of the L.P.P, maximize: z = 30x + D) No hand bag and 15 shoulder bags 20y subject to x  y  20,3x  y  60 and x  0, y  0, then z max  ? 39) If the probability that a student is not a A) 60 swimmer is 1/5, then the probability that out of 5 B) 400 students one is swimmer is 4 C) 600 5 4 1 D) 0 A) C1     5 5 5 46) Let a random variable X has a Binomial 4 1 distribution with mean 8 and variance 4. If B) 5     5 5 k 4 P  X  2  16 , then k is equal to 41 2 C) 5  5  A) 121 4 B) 137 5  4  1  C) 1 D) C1      5  5  D) 17 40) A shopkeeper wants to purchase two articles A 47) In a binomial distribution, the probability of and B of cost price Rs. 4 and 3 respectively. He getting failure is 3/4, and standard deviation if 3, thought that he may earn 30 paise by selling then its mean is......... article A and 10 paise by selling article B. He has A) 18 not to purchase total article worth more than Rs. B) 10 24. If he purchases the number of articles of A and C) 12 B, x and y respectively, the linear constraints are D) 8 x  0, y  0, 4x  3y  24. Then, the iso-profit line is 48) Max value of z equals 3x  2y subject to A) 4x  3y  24 x  y  3 , x  2 , 2x  y  1 , x  0, y  0 is B) 3x  y  20 A) 2 C) x  3y  20 B) 6 D) 3x  y  30 C) 8 D) 10 41) For the L.P. problem Max z  3x1  2x2 such 49) A machine has 14 identical component that that 2x1  x2  2 , x1  2x2  8 and x1, x2  0 , function independently. It will stop working if 3 or z more components fail. If the probability that a A) 40 component fails is 0.1, then what will be the B) 36 probability that the machine works? C) 24 D) 12 (298)(9)12 A) (10)14 42) For X B (n,p), if E(X) = 6, Var(X) = 4.2, then 14 n=  9  B) (298)   A) 40  10  B) 20  9  12 C) 10 C) (298)   D) 15  10  (149 )(9)12 43) Maximum value z  3x1  4x2 , if possible, D) (10)14 Subject to the constraints x1  x2  1,  x1  x2  0; x1, x2  0 is 50) The records of a hospital show that 10% of A) 105 the cases of certain disease are fatal. If six patients B) 100 are suffering from the disease, then the probability C) 156 that only 3 will die is D) Does not exist A) 1458  106 44) The mean and variance of a binomial B) 8748  105 distribution are 6 and 4. The parameter n is C) 41  106 A) 10 D) 1458  105 B) 12 NEET, JEE-MAIN, MHT-CET, MHT-CET-XI