Class 12 CBSE Sample Question Paper 2024 - 1
SECTION – A
Q1. One type of liquid contains 20% water and the second type of liquid contains 35% of water. A glass is filled with 10 parts of first liquid and 4 parts of second liquid. The water in the new mixture in the glass is
(a) 12(1/7)%
(b) 24(2/7)%
(c) 37%
(d) 46%
Q2. Pipes A and B can fill a tank in 15 and 12 min, respectively. Pipe C empties the tank at the rate of 2 L/min. If all the pipes are opened at the same time, then the tank
is filled in 8(4/7) min. The capacity of tank is
(a) 80 L
(b) 75 L
(c) 60 L
(d) 90 L
Q3.
If X is a Poisson variable such that P(X=K) = P(X = K + 1), then variance of
X is
(a) K-1
(b) K
(c) K+1
(d) K + 2
Q4. A member of the population is called
(a) data
(b) element
(c) family
(d) group
Q5. In a 100 m race, Aman runs at the speed of 4 km/h. Aman gives Atul a start of 4 m and still beats him by 15 s. The speed of Atul is
(a) 3.89 km/h
(b) 3.54 km/h
(c) 3 km/h
(d) 3.29 km/h
Q6. If 
then,
(a) x=1,y=2
(b) x=-1,y=-2
(c) x=1,y=-2
(d) x=1,y=4
Q7. Evaluate (57-42) mod 11 is
(a) 3
(b) 5
(c) 9
(d) 4
Q8.
The equation of normal at (1, 2) to the
curve y2 = 4x is
(a) 4x - y = 2
(b) x + y - 3=0
(c) y - x - 1
(d) None of these
Q9.
The best fitting trend is one in which the sum of squares of residuals is
(a) maximum
(b) zero
(c) minimal
(d) None of these
Q10.
The general pattern of increases or decreases in economics or social phenomena is known by
(a) irregular trend
(b) secular trend
(c) seasonal trend
(d) cylic trend
Q11.
The interval in which f(x)= x4-2x2 is
increasing is
(a) (-1,0)
(b) (1,∞)
(c) (0, 1)
(d) (-1, 0)U(1,∞)
Q12. The value of 
is
(a) log(2/3)
(b) log(2/5)
(c) log(5/2)
(d) log(4/5)
Q13. The relation between 'Marginal Cost' and 'Average Cost' of producing 'x' unit of a product is
Q14. If the demand is 150 during April 2017, 250 in may, 350 in June, 450 in July, then the 4 month simple moving average for August 2017 is
(a) 400
(b) 300
(c) 500
(d) 600
Q15. The supply function of a producer is given
by P = 3/5 e3x, where x denotes thousands units. If sales are 4000 units, then producer's surplus (PS) is
Q16. Seasonal variations are
(a) short term
(b) long term
(c) sudden
(d) None of these
Q17. The income of a group of 10000 persons was found to be normally distributed with mean Rs 1750 per month and standard deviation Rs 50. The percentage of persons having income exceeding Rs 1668 is
(a) 90%
(b) 92%
(c) 89%
(d) 95%
Q18. The probability distribution of a discrete random variable X is given below :
then E(X) is equal to
(a) 6
(b) 4
(c) 3
(d) -5
For questions 19 and 20, two statements are given – one labelled Assertion(A) and the other labelled
Reason (R). Select the correct answer to these questions from the codes (i), (ii), (iii) and (iv) as given
below:
(i) Both A and R are true and R is the correct explanation of the assertion
(ii) Both A and R are true but R is not the correct explanation of the assertion
(iii) A is true, but R is false
(iv) A is false, but R is true
(i) Both A and R are true and R is the correct explanation of the assertion
(ii) Both A and R are true but R is not the correct explanation of the assertion
(iii) A is true, but R is false
(iv) A is false, but R is true
Q19.
Assertion (A) - The points A(a, b+c), B(b, c + a), C (c, a + b) are collinear
Reason (R) Area of triangle with three collinear points are zero.
Q20.
Assertion (A) The marginal cost of a total cost function (x) = x3/3
+3x2-7x+16 at
x=2 is Rs 10.
Reason (R) Marginal cost (MC)= d/dx(C(x))
SECTION – B
Q21. A Lenevo computer, whose cost is
Rs 600000 will depreciate to a scrap value of Rs 60000 in 5 yr. Using linear method of depreciation, find the book value of the computer at the end of third year.
Q22. A furniture dealer deals in only two items-tables and chairs. He has Rs 50000 to invest and has storage space of at most 60 pieces. A table costs Rs 2500 and a chair Rs 500. Then, find the constraints of the above problem (where, x is number of tables and y is number of chairs).
Q23. A bag contains 2 white and 4 black balls. A ball is drawn 5 times with replacement. Find the probability that atleast 4 of the balls drawn are white.
OR
There are 50 telephone lines in an exchange. The probability that any one of them will be busy is 0.1. Find the probability that all the lines are busy.
Q24. A pipe can fill a cistern in 6 h. Due to a leak in its bottom, it is filled in 7 h. If the cistern is full, then find the time will it be emptied by the leak.
Q25. If A =
, then find |adj(A)|
OR
If X= 
then satisfy the equation AX=B then the matrix A is equal to
SECTION-C
Q26. Find the maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24x - 18x2, is
Q27. If A = 
and A-1 = 
then find the value of x + y
Q28. Determine the maximum value of Z=11x+7y, subject to the constraints are 2x + y ≤6, x≤2 and x, y ≥0.
Q29. Two batches of the same product are tested for their mean life. Assuming that, the lives of the product follow a normal distribution with an unknown variance, test the hypothesis that the mean life is the same for both the branches, given the following information.
OR
The Educational Testing Service conducted a study to investigate difference between the scores of male and female students on the Scholastic Aptitude Test. The study identified a random sample of 562 female and 852 male students, who had achieved the same high score on the mathematics portion of the test. That is, female and male students were viewed as having similarly high abilities in mathematics.
Q30. Find the probability distribution of a random variable X is given as under
where n is a constant.
OR
If a die is thrown 5 times, then find the probability that an odd number will come up exactly three times.
Q31.
A firm anticipates an expenditure of Rs 500000 for plant modernisation at the end of 10 yr from now. How much should the company deposit at the end of each year into a sinking fund earning interest 5% per annum. [use (1.05)10 = 1.629]
SECTION-D
Q32.
A manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of first machine is 12 h and that of second machine is 9 h per day.
Each unit of product A requires 3 h on both machines and each unit of product B requires 2 h on first machine and 1 h on second machine. Each unit of product A is sold at a profit of ₹ 7 and B at a profit of ₹ 4. Find the production level per day for maximum profit graphically.
Q33. Fit a straight line trend for the following data and find the trend values. Estimate the sales for 2018.
Q34. Two containers of equal capacity are full
of mixture of oil and water. In the first, the ratio of oil to water is 4: 7 and in the second, it is 7:11. Now, both the mixtures are mixed in a bigger container. Find the resulting ratio of oil to water.
OR
Two pipes A and B can fill a tank in 24 min and 32 min, respectively. If both the pipes are opened together, then after how much time pipe B should be closed so that the tank is full in 9 min?
Q35. Rohit has taken a loan of
Rs 600000 with
interest rate 10% for the period of 12 yr. Find (reducing) EMI for the above data. [given (1.0083)12 = 1.1043]
OR
What nominal rate compounded quarterly will be equivalent to 12% compounded continuously? [given e0.12 = 1.1274]
SECTION-E
CASE STUDY – I
Q36. If 
Based on the above information answer the following questions
(i) If y = (x+3)(4x-5) then find dy/dx
(ii) If y = xex then find dy/dx
(iii) If y = (log x)(x2+2) then find dy/dx
CASE STUDY – II
Q37. Let X be the random variable which count the number of hours a student of class XI studies.
X has a probability distribution P(X) of the following form:
Based on the above information answer the following questions
(i) What is the value of k ?
(ii) The value of P(X<2) is
(iii) (a) The value of P(X ≤ 2) is
(b) The value of P(0 ≤ X < 4) is
CASE STUDY – III
