CBSE Class 12 Mathematics 2022

What 2022 actually asked, chapter by chapter

Marks we counted in the 2022 papers themselves. CBSE allocates marks per unit, not per chapter — this is what was observed, not an official CBSE weightage.

All 110 questions from 2022

• Q1Find: ∫ dx√4 x-x^22 mkasked 3×
• Q1Find the sum of the order and the degree of the differential equation: (x+(dy)/(dx))^2=((dy)/(dx))^2+12 mkasked 2×
• Q1Write the projection of the vector ( b+ c) on the vector a, where a= 2 i-2 j+ k, b= i+2 j-2 k and c=2 i- j+4 k.2 mkasked 3×
• Q1Find: ∫ dx/(x^2 - 6x + 13)2 mkasked 3×
• Q1The Cartesian equation of a line A B is: (2 x-1)/12=(y+2)/2=z-3/3 Find the direction cosines of a line parallel to line…2 mk
• Q1If /(d x)[ F(x)]=( sec^4 x)/(cosec^4 x) and F((π)/4)=(π)/4, then find F(x). OR Find: ∫ ( log x-3)/(( log x)^4) d x.2 mkasked 3×
• Q1Find the product of the order and the degree of the differential equation [ /(dx)(xy^2)] · (dy)/(dx)+y=0.2 mkasked 2×
• Q1Find the vector equation of a line passing through a point with position vector 2 i- j+ k and parallel to the line…2 mk
• Q1A bag contains 3 red and 4 white balls. Three balls are drawn at random, one-by-one without replacement from the bag.…2 mk
• Q2In a parallelogram PQRS, PQ=3 i-2 j+2 k and PS=- i-2 k. Find PR and QS.2 mkasked 2×
• Q2Find the general solution of the following differential equation: (d y)/(d x)=e^x-y+x^2 e^-y2 mkasked 3×
• Q2A coin is tossed twice. The following table shows the probability distribution of number of tails: Find the value of K.…2 mkasked 3×
• Q2Find the general solution of the differential equation: e^dy/dx = x^2.2 mk
• Q2Find the general solution of the differential equation: log ((dy)/(dx))=ax+by.2 mk
• Q2Find: ∫ ( sin 3 x)/( sin x) d x OR Evaluate: ∫ 0^1/2 log 3 e^xe^2 x+1 dx2 mkasked 2×
• Q3Three friends A, B and C got their photograph clicked. Find the probability that B is standing at the central position,…2 mk
• Q3Let X be a random variable which assumes values x 1, x 2, x 3, x 4 such that 2 P(X=x 1)=3 P(X=x 2)=P(X=x 3)=5 P(X=x 4).…2 mkasked 3×
• Q3Find the general solution of the differential equation: (dy)/(dx)=(3 e^2 x+3 e^4 x)/(e^x+e^-x)2 mk
• Q3The foot of a perpendicular drawn from the point (-2, -1, -3) on a plane is (1, - 3, 3). Find the equation of the plane.2 mkasked 3×
• Q3a and b are two unit vectors such that 2 a+3 b = 3 a-2 b. Find the angle between a and b.2 mkasked 3×
• Q4A pair of dice is thrown. It is given that the sum of numbers appearing on both dice is an even number. Find the…2 mkasked 3×
• Q4Let A and B be two events such that P =5/8, P =1/2 and P(A / B)=3/4. Find the value of P(B / A).2 mkasked 3×
• Q4If a × b ^2+ a · b ^2=400 and b =5, then find the value of a. OR Find all the possible vectors of magnitude 5 √3 which…2 mkasked 3×
• Q4If a= i+ j+ k, a · b=1 and a × b= j- k, then find b2 mkasked 3×
• Q5Find the values of λ, for which the distance of point (2,1, λ) from plane 3 x+5 y+ 4 z=11 is 2 √2 units.2 mkasked 3×
• Q5Two balls are drawn at random from a bag containing 2 red balls and 3 blue balls, without replacement. Let the variable…2 mkasked 3×
• Q5Probabilities of A and B solving a specific problem are 2/3 and 3/5, respectively. If both of them try independently to…2 mkasked 3×
• Q5If a line makes an angle α, β, γ with the coordinate axes, then find the value of cos 2 α+ cos 2 β+ cos 2 γ.2 mk
• Q5Find the general solution of the differential equation sec^2 x · tan y d x+ sec^2 y · tan x d y=0.2 mkasked 3×
• Q5Solve the differential equation: log ((dy)/(dx))=x-y.2 mk
• Q5Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability…2 mkasked 3×
• Q5If the distance of the point (1,1,1) from the plane x-y+z+λ=0 is 5/(√3), find the value (s) of λ.2 mkasked 3×
• Q6Events A and B are such that P( A)=1/2, P( B)=7/12 and P( A B)=1/4 Find whether the events A and B are independent or…2 mkasked 3×
• Q6There are two bags. Bag I contains 1 red and 3 white balls, and Bag II contains 3 red and 5 white balls. A bag is…2 mk
• Q6Find: ∫ (√ cot x)/( sin x cos x) d x OR Find: ∫ 1/(x(x^2+4)) d x2 mk
• Q6Write the cartesian equation of the line PQ passing through points P(2,2,1) and Q(5,1,-2). Hence, find the y-coordinate…2 mkasked 3×
• Q6If a=2 i+y j+ k and b= i+2 j+3 k are two vectors for which the vector ( a+ b) is perpendicular to the vector ( a- b),…2 mk
• Q6Evaluate: ∫ 0^1 x^2 e^x d x2 mkasked 3×
• Q6A pair of dice is thrown and the sum of the numbers appearing on the dice is observed to be 7. Find the probability…2 mkasked 3×
• Q6Find the particular solution of the differential equation (d y)/(d x)=2 y^2, given y=1 when x=1.2 mk
• Q7If a, b, c are three vectors such that a · b= a · c and a × b= a × c, a ≠ 0, then show that b= c. OR If a =3, b =5, c…3 mk
• Q7Evaluate: ∫ 0^2 π ( d x)/(1+e^ sin x)3 mk
• Q7If a and b are two vectors such that a+ b = b, then prove that ( a+2 b) is perpendicular to a. OR If a and b are unit…3 mkasked 2×
• Q7Find the shortest distance between the following lines: r=3 i+5 j+7 k+λ( i-2 j+ k) and r=(- i- j- k)+μ(7 i-6 j+ k).3 mk
• Q7ABCD is a parallelogram such that AC= i+ j and BD=2 i+ j+ k. Find AB and AD. Also, find the area of the parallelogram…3 mk
• Q7Find the area of the region (x, y): x^2 ≤ y ≤ x+2, using integration.3 mk
• Q7Using integration, find the area of the region (x, y): y^2 ≤ x ≤ y.3 mk
• Q7If a, b, c and d are four non-zero vectors such that a × b= c × d and a × c=4 b × d, then show that ( a-2 d) is…3 mkasked 3×
• Q7If the area of the region bounded by the line y=mx and the curve x^2=y is 32/3 sq. units, then find the positive value…3 mk
• Q7Evaluate: ∫ 0^π / 4 (d x)/(1+ tan x)3 mk
• Q8Find the equation of the plane passing through the line of intersection of the planes r ·( i+ j+ k)=10 and r ·(2 i+3 j-…3 mkasked 2×
• Q8Evaluate: ∫ 0^1 tan^-1 x d x OR Find: ∫ (2 x)/(x^2+3 x+2) d x3 mkasked 3×
• Q8Evaluate: ∫ -1^2 x^3-x d x3 mk
• Q8Find the general solution of the differential equation x (d y)/(d x)-y+x sin y/x=0.3 mk
• Q8If a=2 i- j+ k, b= i+ j-2 k and c= i+3 j- k and the projection of vector c+λ b on vector a is 2 √6, then find the value…3 mk
• Q8Find the vector equation of the plane passing through the intersection of the planes r ·(2 i+2 j-3 k)=7 and r ·(2 i+5…3 mk
• Q8Find the co-ordinates of point where the line x-3/-1=(y+4)/1=(z+5)/6 crosses the plane passing through points (7/2,…3 mk
• Q8Find the particular solution of the differential equation x (dy)/(d x)-y=x^2 · e^x, given y(1)=0. OR Find the general…3 mkasked 3×
• Q8Find: ∫ 1e^x+1 dx OR Evaluate: ∫ 1^4 x + 3-x d x3 mkasked 3×
• Q9Evaluate: ∫ 1^3 √x√x+√4-x dx3 mk
• Q9If a, b and c are mutually perpendicular vectors of equal magnitude, then prove that the vector (2 a+ b+2 c) is equally…3 mk
• Q9The two adjacent sides of a parallelogram are represented by vectors 2 i-4 j+ 5 k and i-2 j-3 k. Find the unit vector…3 mkasked 2×
• Q9Find: ∫ (x^3+x)/(x^4-9) d x. OR Evaluate, using properties: ∫ -π^π(3 sin x-2)^2 d x3 mk
• Q9Let a= i+ j, b= i- j and c= i+ j+ k. If n is a unit vector such that a. n=0 and b. n=0, then find c. n. OR If a and b…3 mk
• Q9Solve the differential equation: (dy)/(dx)=(x^2+y^2)/(x y).3 mk
• Q9Show that the lines: 1-x/2=y-3/4=z/-1 and x-4/3=(2 y-2)/-4=z-1 are coplanar.3 mkasked 2×
• Q9Solve the following differential equation: (1+e^y / x) d y+e^y / x(1-y/x) d x=03 mk
• Q9Find the particular solution of the differential equation (y+3 x^2) (d x)/(d y)=x, given that y=1, when x=1.3 mk
• Q9Find: ∫ (d x)/(√x+√[3]x). OR Evaluate: ∫ 0^π / 2 ( cos x)/((1+ sin x)(4+ sin x)) d x.3 mkasked 2×
• Q10Using vectors, find the value of 'b' if the points A(-1, -1, 2), B(2, b, 5) and C(3, 11, 6) are collinear. Also,…3 mk
• Q10Find the equation of the plane passing through points (2, 1, 0), (3, -2, -2) and (1, 1, -7). Also, obtain its distance…3 mkasked 3×
• Q10If a and b are two vectors of equal magnitude and α is the angle between them, then prove that a+ b a- b = cot ((α)/2).3 mk
• Q10If a line makes 60° and 45° angles with the positive directions of x-axis and z-axis respectively, then find the angle…3 mkasked 3×
• Q10Find the co-ordinates of the point on the line (x+2)/3=(y+1)/2=(z-3)/2 which is at a distance of 5 units from the point…3 mk
• Q10Find the distance of the point (2, 3, 4) measured along the line (x-4)/3=(y+5)/6=(z+1)/2 from the plane 3 x+2 y+2…3 mk
• Q10Find: ∫ e^x · sin 2 x d x OR Find: ∫ (2 x)/((x^2+1)(x^2+2)) d x3 mkasked 3×
• Q10Evaluate: ∫ (-π)/2^(π)/2( sin x + cos x ) d x3 mk
• Q10If a and b are two vectors such that a= i- j+ k and b=2 i- j-3 k, then find the vector c, given that a × c= b and a ·…3 mk
• Q10Evaluate: ∫ 0^π / 2 1/(1+( tan x)^2 / 3) d x3 mk
• Q10Find the particular solution of the differential equation x (dy)/(dx)+x cos^2((y)/x)=y; given that when x=1, y=(π)/4.3 mkasked 2×
• Q11Using integration, find the area of the smaller region enclosed by the curve 4 x^2+4 y^2=9 and the line 2 x+2 y=3. OR…4 mkasked 3×
• Q11Find the equations of the planes passing through the line of intersection of the planes r ·( i+3 j)=6 and r ·(3 i- j-4…4 mkasked 3×
• Q11Find the area of the region bounded by curve 4 x^2=y and the line y=8 x+12, using integration.4 mk
• Q11Using integration, find the area of the region (x, y): 4 x^2+9 y^2 ≤ 36., 2 x+3 y ≥ 6. OR Using integration, find the…4 mkasked 2×
• Q11Find the distance of the point (-1, -5, -10) from the point of intersection of the line (x-2)/3=(y+1)/4=(z-2)/12 and…4 mkasked 2×
• Q11Three persons A, B and C apply for a job of manager in a private company. Chances of their selection are in the ratio…4 mk
• Q11Evaluate: ∫ -3^3 (x^4)/(1+e^x) d x4 mk
• Q12A man is known to speak truth 7 out of 10 times. He threw a pair of dice and reports that doublet appeared. Find the…4 mk
• Q12Find: ∫ (x^2)/((x^2+1)(3 x^2+4)) d x OR Evaluate: ∫ -2^1 √5-4 x-x^2 d x4 mkasked 3×
• Q12Find the particular solution of the differential equation x (d y)/(d x)+y+1/(1+x^2)=0, given that y(1)=0. OR Find the…4 mkasked 3×
• Q12Evaluate: ∫ 0^π x/(9 sin^2 x+16 cos^2 x) d x4 mk
• Q12Evaluate: ∫ 0^1 x(1-x)^n d x4 mkasked 2×
• Q12Using integration, find the area of the region bounded by the curves x^2+y^2=4, x=√3 y and x -axis lying in the first…4 mk
• Q12Find the area bounded by the curves y= x-1 and y=1, using integration.4 mkasked 3×
• Q12A card from a pack of 52 playing cards is lost. From the remaining cards, 2 cards are drawn at random without…4 mkasked 2×
• Q13Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the zx-plane. Case-Study Based…4 mk
• Q13Solve the following differential equation: (y- sin^2 x) d x+ tan x d y=0 OR Find the general solution of the…4 mkasked 3×
• Q13In a factory, machine A produces 30% of total output, machine B produces 25% and the machine C produces the remaining…4 mk
• Q13Evaluate: ∫ 0^π / 2 x/( sin x+ cos x) d x Case-Study Based Question4 mk
• Q13Evaluate: ∫ 0^π x/(1+ sin x) d x4 mk
• Q13There are two boxes, namely box-I and box-II. Box-I contains 3 red and 6 black balls. Box-II contains 5 red and 5 black…4 mk
• Q13Using integration, find the area of the region enclosed by the curve y=x^2, the x -axis and the ordinates x=-2 and x=1.…4 mk
• Q13Find the area of the region enclosed by the curves y^2=x, x=1/4, y=0 and x=1, using integration. Case Study Problem:4 mk
• Q13Evaluate: ∫ 0^π / 2(2 log cos x- log sin 2 x) d x Case-Study Based Question4 mk
• Q13Find the distance of the point (1, -2, 9) from the point of intersection of the line r=4 i+2 j+7 k+λ(3 i+4 j+2 k) and…4 mkasked 3×
• Q14A shopkeeper sells three types of flower seeds A1, A2, A3. They are sold in the form of a mixture, where the…4 mkasked 3×
• Q14At the start of a cricket match, a coin is tossed and the team winning the toss has the opportunity to choose to bat or…4 mkasked 3×
• Q14Electrical transmission wires which are laid down in winters are stretched tightly to accommodate expansion in summers.…4 mkasked 3×
• Q14In a game of Archery, each ring of the Archery target is valued. The centremost ring is worth 10 points and rest of the…4 mkasked 3×
• Q14Two motorcycles A and B are running at the speed more than the allowed speed on the roads represented by the lines r=λ(…4 mkasked 3×