Date: March 2022
General instructions:
- The question paper is divided into four sections:
- Section A: Question No. 1 contains 8 multiple choice type questions carrying two marks each. Question No. 2 contains 4 very short answer type questions carrying one mark each.
- Section B: Question No. 3 to Question No. 14 are 12 short answer-I type questions carrying two marks each. Attempt any eight questions.
- Section C: Question No. 15 to Question No. 26 are 12 short answer-II type questions carrying three marks each. Attempt any eight questions.
- Section D: Question No. 27 to Question No. 34 are 8 long answer type questions carrying four marks each. Attempt any five questions.
- Start each section on a new page.
- Figures to the right indicate full marks.
- For each MCQ, correct answer must be written along with its alphabet.
e.g., (a) ..... / (b ) .... / ( c ) .... / ( d) ..... Only first attempt will be considered for evaluation. - Use of graph paper is not necessary. Only rough sketch of graph is expected
- Use of log table is necessary. Use of calculator is not allowed.
If p → q is an implication, then the implication ∼ q → ∼ p is called its
Converse
Contrapositive
Inverse
Alternative
Chapter: [0.01] Mathematical Logic [0.01] Mathematical Logic [0.011000000000000001] Mathematical Logic
If `|bar("a")|` = 2, `|bar("b")|` = 5, and `bar("a")*bar("b")` = 8 then `|bar("a") - bar("b")|` = ______
13
12
`sqrt(13)`
`sqrt(21)`
Chapter: [0.015] Vectors
The displacement of a particle at time t is given by s = 2t3 – 5t2 + 4t – 3. The time when the acceleration is 14 ft/sec2, is
1 sec
2 sec
3 sec
4 sec
Chapter: [0.022000000000000002] Applications of Derivatives
If f(x) = logx (log x) then f'(e) is ______
1
e
`1/"e"`
0
Chapter: [0.021] Differentiation
The general solution of `("d"y)/("d"x)` = e−x is
y = ex + c
y = e–x + c
y = – e–x + c
y = e2x + c
Chapter: [0.026000000000000002] Differential Equations
If A = `[(4, -1),(-1, "k")]` such that A2 − 6A + 7I = 0, then K = ______
1
3
2
4
Chapter: [0.012] Matrics
The area bounded by the parabola y2 = x along the X-axis and the lines x = 0, x = 2 is ______ sq.units
`4/3`
`(4sqrt(2))/3`
`2/3`
`(2sqrt(2))/3`
Chapter: [0.025] Application of Definite Integration
The combined equation of the lines through origin and perpendicular to the pair of lines 3x2 + 4xy − 5y2 = 0 is ______
5x2 + 4xy − 3y2 = 0
3x2 + 4xy − 5y2 = 0
3x2 - 4xy + 5y2 = 0
5x2 + 4xy + 3y2 = 0
Chapter: [0.013999999999999999] Pair of Straight Lines
Evaluate: `int_(pi/6)^(pi/3) cosx "d"x`
Chapter: [0.024] Definite Integration
Find the distance from (4, −2, 6) to the XZ- plane
Chapter: [0.015] Vectors
Find the separate equation of the line represented by the following equation:
3y2 + 7xy = 0
Chapter: [0.013999999999999999] Pair of Straight Lines
Find the principal solutions of cosec x = 2
Chapter: [0.013000000000000001] Trigonometric Functions
Write the following compound statement symbolically.
Nagpur is in Maharashtra and Chennai is in Tamil Nadu.
Chapter: [0.01] Mathematical Logic [0.01] Mathematical Logic [0.011000000000000001] Mathematical Logic
Find the Cartesian equation of the line passing through A(1, 2, 3) and B(2, 3, 4)
Chapter: [0.016] Line and Plane
Given X ~ B(n, p). If E(X) = 6, V(X) = 4.2, find n and p
Chapter: [0.027999999999999997] Binomial Distribution
If `bar("a")` and `bar("b")` are two vectors perpendicular each other, prove that `(bar("a") + bar("b"))^2 = (bar("a") - bar("b"))^2`
Chapter: [0.015] Vectors
Find the principal solutions of tan x = `-sqrt(3)`
Chapter: [0.013000000000000001] Trigonometric Functions
Find the adjoint of matrix A = `[(6, 5),(3, 4)]`
Chapter: [0.012] Matrics
The probability distribution of X is as follows:
| X | 0 | 1 | 2 | 3 | 4 |
| P(X = x) | 0.1 | k | 2k | 2k | k |
Find k and P[X < 2]
Chapter: [0.027000000000000003] Probability Distributions
Find the acute angle between the lines x = y, z = 0 and x = 0, z = 0
Chapter: [0.016] Line and Plane
Form the differential equation of y = (c1 + c2)ex
Chapter: [0.026000000000000002] Differential Equations
If A = `[(-1),(2),(3)]`, B = `[(3, 1, -2)]`, find B'A'
Chapter: [0.012] Matrics
Evaluate: `int_0^(pi/2) cos^3x "d"x`
Chapter: [0.024] Definite Integration
Find the area of the region bounded by the following curves, X-axis and the given lines : x = 0, x = 5, y = 0, y = 4
Chapter: [0.025] Application of Definite Integration
`int sin(logx) "d"x`
Chapter: [0.023] Indefinite Integration [0.15] Integration
Find acute angle between the lines `(x - 1)/1 = (y - 2)/(-1) = (z - 3)/2` and `(x - 1)/2 = (y - 1)/1 = (z - 3)/1`
Chapter: [0.016] Line and Plane
Prove that: `int_"a"^"b" "f"(x) "d"x = int_"a"^"c""f"(x) "d"x + int_"c"^"b" "f"(x) "d"x`, where a < c < b
Chapter: [0.024] Definite Integration
A spherical soap bubble is expanding so that its radius is increasing at the rate of 0.02 cm/sec. At what rate is the surface area is increasing, when its radius is 5 cm?
Chapter: [0.022000000000000002] Applications of Derivatives
Differentiate `cot^-1((cos x)/(1 + sinx))` w.r. to x
Chapter: [0.021] Differentiation
A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.
Chapter: [0.027000000000000003] Probability Distributions [0.19] Probability Distribution
Find the joint equation of pair of lines through the origin which is perpendicular to the lines represented by 5x2 + 2xy - 3y2 = 0
Chapter: [0.013999999999999999] Pair of Straight Lines [0.09] Line
Find the coordinates of the foot of perpendicular from the origin to the plane 2x + 6y − 3z = 63
Chapter: [0.016] Line and Plane
Prove that medians of a triangle are concurrent
Chapter: [0.015] Vectors [0.07] Vectors
`int (x^2 + x -1)/(x^2 + x - 6) "d"x`
Chapter: [0.023] Indefinite Integration [0.15] Integration
A fair coin is tossed 8 times. Find the probability that it shows heads exactly 5 times
Chapter: [0.027999999999999997] Binomial Distribution [0.2] Bernoulli Trials and Binomial Distribution
In ∆ABC, prove that `sin (("A" - "B")/2) = (("a" - "b")/"c") cos ("C"/2)`
Chapter: [0.013000000000000001] Trigonometric Functions [0.03] Trigonometric Functions
`int (x + sinx)/(1 - cosx) "d"x`
Chapter: [0.023] Indefinite Integration [0.15] Integration
Maximize z = 5x + 2y subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0
Chapter: [0.017] Linear Programming
Find the local maximum and local minimum value of f(x) = x3 − 3x2 − 24x + 5
Chapter: [0.022000000000000002] Applications of Derivatives [0.14] Applications of Derivative
If the population of a town increases at a rate proportional to the population at that time. If the population increases from 40 thousand to 60 thousand in 40 years, what will be the population in another 20 years? `("Given" sqrt(3/2) = 1.2247)`
Chapter: [0.026000000000000002] Differential Equations
Examine whether the statement pattern
[p → (∼q ˅ r)] ↔ ∼[p → (q → r)] is a tautology, contradiction or contingency.
Chapter: [0.011000000000000001] Mathematical Logic
Prove that `2 tan^-1 (1/8) + tan^-1 (1/7) + 2tan^-1 (1/5) = pi/4`
Chapter: [0.013000000000000001] Trigonometric Functions
If y = cos(m cos–1x), then show that `(1 - x^2) ("d"^2y)/("d"x^2) - x("d"y)/("d"x) + "m"^2y` = 0
Chapter: [0.021] Differentiation
Express `- hat"i" - 3hat"j" + 4hat"k"` as the linear combination of the vectors `2hat"i" + hat"j" - 4hat"k", 2hat"i" - hat"j" + 3hat"k"` and `3hat"i" + hat"j" - 2hat"k"`
Chapter: [0.015] Vectors
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Maharashtra State Board previous year question papers 12th Board Exam Mathematics and Statistics with solutions 2021 - 2022
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