CBSE Board Exam is coming in February. So, I have brought CBSE Board Class 12 Math Important Questions 2024 which are being asked the same for last 3-4 years. Try to solve these questions for securing high marks in your board examinations.
You can also check the Important Questions for Physics, Chemistry, English and Other Subjects
CBSE Board Class 12 Math Important Questions 2024: Objective
1. Total number of possible matrices of order 3 × 3 with each entry 2 or o is.
(a) 9
(b) 27
(c) 81
(d) 512
2. If the area of a triangle ABC, with vertices A(1,3), B(0,0) and C(k, 0) is 3 sq. units, then the value of k is:
(a) 7
(b)3
(c) 4
(d) 5
3. If A is 3 x 3 matrix such that |A| = 8, then |34| equals:
(a) B
(b) 24
(c) 72
(d) 216
4. Let A be a non-singular square matrix of order 3 × 3. Then [adj A ] is equal to:
(a) |A|
(b) |A|2
(c) |A|3
(d) 3|A|
5.
6. If A is a square matrix of order 3, such that A(adj A) = 101, then adj A❘ is equal to:
(a) 1
(b) 10
(C) 100
(d) 101
7. The domain of the function cos-1(2x – 1) is
(a) [0,1]
(b) [-1,1]
(c) (-1,1)
(d) [0, π]
8. If set A = {1,2} and set B = {a,b}, then cartesian product of set A and set B is given by
(a) A × B = [(1, a), (1, b), (2, a), (2, b)}
(b) A x B = {(a, 1), (1, b), (2, a), (2, b)}
(c) A × B = {(a, 1), (b, 1), (2, a), (2, b)}
(d) A × B = {(a, 1), (b, 1), (2, a), (b, 2)}
9. If the relation R in the set {1,2,3,4} given by R = {(1,1), (1,2), (1,4), (3,1),(3,2), (4,3), (4,2)} then domain of R is given by
(a) domain (R) = {1,3,4}
(b) domain (R) = {1,2,3}
(c) domain(R) = {7,2,4}
(d) None of the above
10.
11. The relation R in the set {1,2,3} given by R = {(1,1), (2,2), (3,3), (1,2), (2,3)} is.
(a) reflexive but neither symmetric nor transitive
(b) reflexive, symmetric but not transitive
(c) symmetric but neither reflexive nor transitive
(d) an equivalence relation
12. The relation R in the set {1,2,3} given by R = {(1,1), (2,2), (3,3), (1,2), (2,3)} is.
(a) reflexive but neither symmetric nor transitive
(b) reflexive, symmetric but not transitive
(c) symmetric but neither reflexive nor transitive
(d) an equivalence relation
13. The relation R is the set of natural number N defined as R {(x, y): x + 4y = 10, x, y ∈ N} is
(a) an equivalence relation
(b) transitive but neither reflexive nor symmetric
(c) Reflexive, symmetric but nor transitive
(d) Reflexive but neither symmetric nor transitive
14. The relation R in the set of natural numbers N defined as R = {(x,y): y = x + 5 and x < 4} is.
(a) Reflexive
(b) symmetric
(c) transitive
(d) an equivalence relation
15. The function f: NN given by f(x) = 2x is
(a) Surjective
(b) bijective
(c) injective
(d) many-one
16. The function f: Z → Z defined by f (x) = x + 2 is.
(a) one-one
(b) onto
(c) bijective
(d) None of these
17. The function f(x) = 2×3 – 3x² – 12x + 4, has.
(a) two points of local maximum
(b) two points of local minimum
(c) one maxima and one minima
(d) neither maxima nor minima
18.
CBSE Board Class 12 Math Important Questions 2024
1. The equations of a line are 5x315y+7310z. Write the direction cosines of the line and find the coordinates of a point through which it passes.
2. Find the general solution of the differential equation ex tan y dx + (1-ex) sec² y dy = 0.
3. From a lot of 30 bulbs which include 6 defective bulbs, a sample of 2 bulbs is drawn at random one by one with replacement. Find the probability distribution of the number of defective bulbs and hence find the mean number of defective bulbs.
4. Nx N defined by (a, b) R (c, d), if ad(b + c) = b(a + d). Show toater is an equivalence relation.
5. Find the angle between the lines 2x3yz and 6xy42.
6. Also, a function f(x) is said to be differentiable at x = a if its L.H.D. and R.H.D. at x = a exist and both are equal.
7. State the two normal equations used in fitting a straight line.
8. Abhay bought a mobile phone for 30,000. The mobile phone is estimated to have a scrap value of ₹ 3,000 after [2] a span of 3 years. Using the linear depreciation method, find the book value of the mobile phone at the end of 2 years.
9. The rate at which radioactive substances decay is known to be proportional to the number of such nuclei that are present at the time in a given sample. If 100 grams of a radioactive substance is present 1 year after the substance was produced and 75 grams is present 2 years after the substance was produced, how much radioactive substance was produced?
10. A bond has issued with the face (Par) value of 1,000 at 10% coupon for three years The required rate of return is 8%. What is the value of the bond if the coupon amount is payable on half-yearly basis? Given (1.04) 0.79031
11. The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs
(i) none
(ii) not more than one
(iii) more than one
(iv) at least one will fuse after 150 days of use.
12. From a lot of 10 items containing 3 defectives, a sample of 4 items is drawn at random. Let the random variable X denote the number of defective items in the sample. If the sample is drawn randomly, find:
13. Following table shows the data on energy consumption and expenditure at Badarpur Thermal Power Station in [3] Delhi region. Construct an aggregative price index for the energy expenditure in year 2015 using Marshall-Edgewarth’s index number.
14. A company produces soft drinks that has a contract which requires that a minimum of 80 units of chemical A and 60 units of chemical B to go into each bottle of the drink. The chemicals are available in a prepared mix from two different suppliers. Supplier 5 has a mix of 4 units of A and 2 units of B that costs ₹10, the supplier T has a mix of 1 units of A and 1 unit of B that costs 74. How many mixes from S and T should the company purchase to honor contract requirements and yet minimize cost?
15. . An amount of Rs 5000 is put into three investments at the rate of interest of 6%, 7% and 8% per anmum respectively. The total annual income is Rs 358. If the combined income from the first two investments is Rs 70 more than the income from the third, find the amount of each investment by matrix method.
