TBSE Class 11 Model Question Paper for 2021 Maths

Class - XI : Mathemaitcs : 80 Marks : 2020-2021
!Ó˲yàÈüÈܲ / ≤Ã!ï˛!ê˛ ≤Èϟ¿Ó˚ ÙylÈüÈ1 / 1 x 20 = 20
1. { x, y, z} ˆ§ê˛!ê˛Ó˚ âyï˛ ˆ§ê˛ ˆ°ˆÏáy–
2. Î!ò (x+3,5)=(6,2x+y) •Î˚ ï˛ˆÏÓ x G y !lî≈Î˚ ܲˆÏÓ˚y–
3. f : R → R, f(x)=x2+3 myÓ˚y ≤Ãò_ •ˆÏ° {x: f(x)=28} !lî≈Î˚ ܲˆÏÓ˚y–
4. §¡∫rô R ~Ó˚ ˆ«˛e ~ÓÇ ≤çyÓ˚ !lî≈Î˚ ܲˆÏÓ˚y ˆÎáyˆÏl R={(x+1, (x+5) : x ∈ (0,1,2,3,4,5,)} myÓ˚y §ÇK˛yï˛–
11π
5. Sin − ~Ó˚ Ùyl Ü˛ï˛ ⁄
3
6. Î!ò tan θ ~ÓÇ tan φ = •Î˚ ï˛ˆÏÓñ tan ( θ + φ ) ~Ó˚ Ùyl ܲï˛⁄
7. 5037 ′30′′ ˆÜ˛ ˆÓ˚!í˛Î˚yˆÏl ≤Ãܲy¢ ܲˆÏÓ˚y–
8. !òâyï˛§Ù#ܲÓ˚î x2+8=0 ~Ó˚ Ó#çà%ˆÏ°y ˆ°ˆÏáy–
9. 12i–5 ~Ó˚ Ù!í˛í˛z°y§ !lî≈Î˚ ܲˆÏÓ˚y–
10. §Ùyôyl ܲˆÏÓ˚y : 11x<10, x ~ܲ!ê˛ fl∫y˲y!Óܲ §Çáƒy–
11. 6!, 8!, 9!, ~ÓÇ 11! ~Ó˚ °§yà% !lî≈Î˚ ܲˆÏÓ˚y–
12. n ~Ó˚ Ùyl !lî≈Î˚ ܲˆÏÓ˚y Îál nC7=nC5 •Î˚–
13. (1+2x+x2)20 ~Ó˚ !Óhfl,Ï!ï˛ˆÏï˛ ˛õò§Çáƒy !lî≈Î˚Ü ˛ˆÏÓ˚y–
14. P(0,2) ~ÓÇ Q (1,5) !Ó®%mÎ˚ §ÇˆÏÎyçܲ ˆÓ˚áyÓ˚ l!ï˛ !lî≈Î˚ ܲˆÏÓ˚y–
15. x2= – 8y x!ôÓ,_!ê˛Ó˚ ly!˲Ó˚ fiÌylyAܲ !lî≈Î˚ ܲˆÏÓ˚y–
16. A(–2, 4, 1) ~ÓÇ B(1, 2, –5) ~Ó˚ ÙôƒÓï˛#≈ ò)Ó˚c !lî≈Î˚ ܲˆÏÓ˚y–
17. (a, 1, 3), (–2, b, –5) ~ÓÇ (4, 7, c) ¢#£Ï≈!Ó®% !Ó!¢T˛ !eË%˛ˆÏçÓ˚ ˲Ó˚ˆÏܲw Ù)°!Ó®% •ˆÏ° a, b, c !lî≈Î˚ ܲˆÏÓ˚y–
18. Ùyl !lî≈Î˚ ܲˆÏÓ˚y / lim
x→ 0 x2
19. ò%!ê˛ SÈE˛yˆÏܲ ~ܲ§yˆÏÌ ~ܲÓyÓ˚ ˆSÈyí˛¸y •ˆÏ° ≤ÃyÆ ˆÎyàÊ˛ˆÏ°Ó˚ Ùyl 10 ˆÌˆÏܲ ˆÓ!¢ ˛õí˛¸yÓ˚ §Ω˛yÓly Ü˛ï˛ ⁄
20. ò%!ê˛ Ù%oyˆÏ«˛˛õˆÏl í˛z˲Î˚•z ˆ•í‰˛ Óy í˛z˲Î˚•z ˆê˛° ˛õí˛¸yÓ˚ §Ω˛yÓly Ü˛ï˛ ⁄
!Ó˲yàÈüÈá / ≤Ã!ï˛!ê˛ ≤Èϟ¿Ó˚ Ùyl ÈüÈ 2 / 2x6=12
21. Ùyl !lî≈Î˚ ܲˆÏÓ˚y / Sin130 Cos1100+Cos1300Sin1100\
0

22. ˆÏܲ a+ib xyܲyˆÏÓ˚ ≤Ãܲy¢ ܲˆÏÓ˚y–
7
23. − ~Ó˚ !Óhfl,Ï!ï˛ˆÏï˛ ˆ¢£Ï !òܲ ˆÌˆÏܲ ã˛ï%˛Ì≈˛õò!ê˛ !lî≈Î˚ ܲˆÏÓ˚y–
x2 6
24. x2+4y2+2x+16y+13=0 í˛z˛õÓ,_!ê˛Ó˚ í˛z͈Ïܲwï˛y !lî≈Î˚ ܲˆÏÓ˚y–
25. Î!ò f(x) xˆÏ˛õ«˛Ü˛!ê˛Ó˚ çlƒ lim = π !§Âô •Î˚ñ ï˛ˆÏÓ lim f ( x ) !lî≈Î˚ ܲˆÏÓ˚y–
x →1 x2 − 1 x →1

3
26. A, B, C •° ~ܲ!ê˛ §Ù§Ω˛Ó ˛õÓ˚#«˛yÓ˚ !ï˛l!ê˛ ˛õÓ˚flõÓ˚ ˛õ,Ìܲ ~ÓÇ §¡õ)î≈ âê˛ly– Î!ò P(B)= P(A) ~ÓÇ 2P(C)=P(B)
2
•Î˚ñ ï˛ˆÏÓ P(A) !lî≈Î˚ ܲˆÏÓ˚y–
!Ó˲yàÈüÈà / Each Question Carries 4 Marks / 4x6=24
27. Î!ò A G B ò%!ê˛ ˆ§ê˛ ∪ ~ܲ!ê˛ §y!Ó≈ܲ ˆ§ê˛ ~Ó˚)˛õ •Î˚ ˆÎ n( ∪ )=1000, n(A)=300, n(B)=400 ~ÓÇ
n(A ∩ B)=200, ï˛ˆÏÓ A xÌÓy B ˆÜ˛yˆÏly!ê˛ˆÏï˛•z ˆl•z ~Ó˚)˛õ ˆÙyê˛ ˛õò§Çáƒy !lî≈Î˚ܲˆÏÓ˚y–
28. ÓyhflÏÓ xˆÏ˛õ«˛Ü˛ f ~Ó˚ ˆ«˛e G ≤çyÓ˚ !lî≈Î˚ ܲˆÏÓ˚y ˆÎáyˆÏl f(x) = myÓ˚y xˆÏ˛õ«˛Ü˛!ê˛ §ÇK˛yï˛–
x−4
D xÌÓy
Î!ò f(x)=ax+b ˆÎáyˆÏl a G b xáu˛ §Çáƒyñ f(–1)=–5 ~ÓÇ f(3)=3 •Î˚ñ ï˛ˆÏÓ a G b !lî≈Î˚ ܲˆÏÓ˚y–
29. 2z = |z|+2i §Ù#ܲÓ˚î!ê˛Ó˚ §Ùyôyl ܲˆÏÓ˚y–
30. §Ùyôyl ܲˆÏÓ˚y 1 ≤ |x–2| ≤ 3
D xÌÓy
˜Ï°!áܲÓ˚)ˆÏ˛õ §Ùyôyl ܲˆÏÓ˚y / 2x+y ≥ 4, x+y ≤ 3 ~ÓÇ 2x–3y ≤ 6
1 1 1
31. Î!ò Ù)° !Ó®% ˆÌˆÏܲ bx+ay=ab ˆÓ˚áyÓ˚ °¡∫ ò)Ó˚c p •Î˚ñ ï˛ˆÏÓ ˆòáyG ˆÎ 2
+ 2 = 2
a b p
D xÌÓy
x + 3 y + 5 = 0 §Ó˚°ˆÏÓ˚áyÓ˚ §yˆÏÌ 600 ˆÜ˛yˆÏî lï˛ ~ÓÇ Ù)°!Ó®%àyÙ# §Ó˚°ˆÏÓ˚áyÓ˚ §Ù#ܲÓ˚î !lî≈Î˚ ܲˆÏÓ˚y–
32. ≤ÃyÌ!Ùܲ ï˛_¥yl%ÎyÎ˚# cos(x2+1) ~ÓÇ x ~Ó˚ §yˆÏ˛õˆÏ«˛ xÓܲ° §•à !lî≈Î˚ ܲˆÏÓ˚y–
!Ó˲yàÈüÈâ / ≤Ã!ï˛!ê˛ ≤Èϟ¿Ó˚ Ùyl 6 / 6 x 4 = 24
2b
33. Î!ò a cos 2θ + bsin 2θ = c ~Ó˚ ò%!ê˛ Ó#ç α ~ÓÇ β •Î˚ ï˛ˆÏÓ ≤ÃÙyî ܲˆÏÓ˚y tan α + tan β =
a+c
xÌÓy
π 3π 5π 7π
Ùyl !lî≈Î˚ ܲˆÏÓ˚y cos 4 + cos 4 + cos 4 + cos 4
8 8 8 8
34.10 çl ˛õ%Ó˚%£Ï ~ÓÇ 7 çl Ù!•°yÓ˚ ÙˆÏôƒ ˆÌˆÏܲ 6 çˆÏlÓ˚ ~ܲ!ê˛ Ü˛!Ù!ê˛ àë˛l ܲÓ˚y •ˆÏÓ ÎyˆÏï˛ xhs˝ï˛ 3çl ˛õ%Ó˚%£Ï ~ÓÇ 2 çl
Ù!•°y ÌyܲˆÏÓl– Î!ò !ӈϢ£Ï ò%•zçl Ù!•°y ~ܲ•z ܲ!Ù!ê˛ˆÏï˛ ÌyܲˆÏï˛ x§¡øï˛ •lñ ï˛ˆÏÓ Ü˛ï˛ !Ó!˲ߨ í˛z˛õyˆÏÎ˚ ~Ó˚)˛õ ܲ!Ù!ê˛ àë˛l ܲÓ˚y
ÎyˆÏÓ⁄
9
35. (1+x+2x ) x −
2
~Ó˚ !Óhfl,Ï!ï˛ˆÏï˛ x !lÓ˚ˆÏ˛õ«˛ ˛õò!ê˛ !lî≈Î˚ ܲˆÏÓ˚y–
xÌÓy
2n
1 1 × 3 × 5 × ...... × (2n − 1)
ˆòáyG ˆÎñ x − ~Ó˚ !Óhfl,Ï!ï˛Ó˚ Ùôƒ˛õò!ê˛ •° × ( −2)n
x n!
36. ~ܲ!ê˛ ÓƒyˆÏà 8!ê˛ °y° Ó° ~ÓÇ 5!ê˛ §yòy Ó° xyˆÏSÈ– í˛zˆÏj¢ƒ•#l˲yˆÏÓ ï˛y ˆÌˆÏܲ !ï˛l!ê˛ Ó° ˆï˛y°y •°–
(i) !ï˛l!ê˛ Ó°•z §yòy (ii) !ï˛l!ê˛ Ó°•z °y° (iii) ~ܲ!ê˛ Ó° °y° ~ÓÇ ò%!ê˛ Ó° §yòy û •GÎ˚yÓ˚ §Ω˛yÓly !lî≈Î˚ ܲˆÏÓ˚y–

D x!ï˛!Ó˚=˛ ≤ß¿yÓ°#

Class - XI : Mathematics : 80 Marks : 2020-2021
Section-A : Each Question Carries 1 Mark : 1 x 20 = 20
1. Write the power set of the set { x, y, z}.
2. Find x and y, if (x+3, 5)=(6, 2x+y)
3. let f : R → R, be given by f(x)=x2+3, find {x: f(x)=28} .
4. Determine the domain and range of the relation R defined by R={(x+1, (x+5) : x ∈ (0,1,2,3,4,5,)}
11π
5. Find the value of Sin − .
3
6. If tan θ = and tan φ = then what is the value of tan ( θ + φ )˛⁄
7. Express 5037 ′30′′ in radians.
8. Write the roots of the quadratic equation x2+8=0 .
9. Find the modulus of 12i–5 .
10. Solve : 11x<10, when x in a natural number.
11. Find the LCM of 6!, 8!, 9! and 11!
12. Find n if nC7=nC5 .
13. Find the number of terms in the expansion of (1+2x+x2)20 .
14. Find the slope of the line passing through the points P(0,2) and Q (1,5) .
15. Find the Co-ordinate of the focus of the parabola x2 = – 8y
16. Find the distance between the points A(–2, 4, 1) and B(1, 2, –5) .
17. Centroid of a triangle with vertices (a, 1, 3), (–2, b, –5) and (4, 7, c) is at origin. Find the values
of a, b, c .
18. Evaluate / lim
x→ 0 x2
19. Find the probability of getting a total more than 10 in a single throw of two dice.
20. In a throw of two coins, find the probability of getting both heads or both tails.
Section B : Each Question Carries 2 Marks : 2x6=12
21. Evaluate / Sin1300 Cos1100+Cos1300Sin1100

22. Express in the form of a+ib .
7
23. Find the 4th term from the end in the expansion of 2 − .
x 6
24. Find the eccentricity of the ellipse x2+4y2+2x+16y+13=0 .
25. If the function f(x) satisfics lim = π , Evaluate lim f ( x) .
x →1 x2 − 1 x →1

26. A, B, C are three mutually exclusive and exhaustive events associated with a random experi
3
ment. Find P(A) if P(B)= P(A) and 2P(C)=P(B)
2
Section-C : Each Question Carries 4 Marks : 4x6=24
27. If A and B are two sets and˛ ∪ is a universal set such that n( ∪ )=1000, n(A)=300, n(B)=400 and
n(A ∩ B)=200, Find the total number of elements which neither belong to A nor to B.
28. Find the domain and range of the real function f defined by f(x) = .
x−4
* OR
If f(x)=ax+b, where a and b are integers, f (–1)= –5 and f(3)=3 then find a and b .
29. Solve the equation 2z = |z|+2i .
30. Solve : 1 ≤ |x–2| ≤ 3
* OR
Solve graphically / 2x+y ≥ 4, x+y ≤ 3 and 2x–3y ≤ 6
31. If p be the length of the prependicular drawn from the origin to the line bx+ay=ab. Show that
1 1 1
2
+ 2+ 2
a b p
* OR
Find the equation of a line which passes through origin and making an angle 600 with the
line x + 3 y + 5 = 0 .
32. Differentiate cos(x2+1) with respect to x using first principle.
Section-D : Each Question Carries 6 Marks : 6x4=24
2b
33. If acos 2θ + bsin 2θ = c has α and β as its roots, then prove that tan α + tan β =
a+c
* OR
4 π 3π 5π 7π
Find the value of cos + cos 4
+ cos 4 + cos 4
8 8 8 8
34. A committee of 6 is to be chosen from 10 men and 7 women so as to contain at least 3 men and
2 women. In how many different ways can this be done, if two particular woman refuse to serve
on the same committee ?
9
35. Find the term independent of x in the expansion of (1+x+2x ) x − 2
.
* OR
2n
1 1 × 3 × 5 × ...... × (2n − 1)
Show that the middle term in the expansion of x− is × ( −2)n
x n!
36. A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the probability
that
(i) all the three balls are white.
(ii) all the three balls are red.
(ii) one ball is red and two balls are white.

* Additional Questions