CBSE Class 11 Sample Papers, Syllabus, Test Papers & NCERT Solutions

Maths Class 11
English Class 11
Hindi Class 11
Accounts Class 11
Chemistry Class 11
Biology Class 11
Cconomics Class 11
Geography Class 11
History Class 11
Political Science Class 11
Sociology Class 11

Limits and Derivatives, Class 11 Mathematics R.D Sharma Question Answer

LIMITS Page 29.11 Ex 29.1 Q1. Answer : limx→0 xx Left hand limit: limx→0- xx Let x=0-h, where h→0.⇒limh→0 0-h0-h=limh→0 -hh=-1 Right hand limit: limx→0+ xxLet x=0+h, where h→0.limh→0 0+h0+h=limh→0 hh=1 Left hand limit ≠ Right hand limit Thus,lim x→0 xx does not exist. Q2. Answer : fx=2x+3,x≤2x+k,x>2Left hand limit:limx→2- fx=limx→2- 2x+3Let x=2-h, where h→0.limh→0 […]

Conic Sections, Class 11 Mathematics R.D Sharma Question Answer

CIRCLES Page 24.16 Ex 24.1 Q1. Answer : Let (h, k) be the centre of a circle with radius a. Thus, its equation will be x-h2+y-k2=a2. (i) Here, h = −2, k = 3 and a = 4 ∴ Required equation of the circle: x+22+y-32=42 ⇒x+22+y-32=16 (ii) Here, h = a, k = b and radius […]

Binomial Theorem, Class 11 Mathematics R.D Sharma Question Answer

Page 18.11 Ex 18.1 Q1. Answer : (i) (2x + 3y)5 =C05(2x)5(3y)0+C15(2x)4(3y)1+C25(2x)3(3y)2+C35(2x)2(3y)3+C45(2x)1(3y)4+C55(2x)0(3y)5 =32×5+5×16×4×3y+10×8×3×9y2+10×4×2×27y3+5×2x×81y4+243y5=32×5+240x4y+720x3y2+1080x2y3+810xy4+243y5 (ii) (2x − 3y)4 =C04(2x)4(3y)0-C14(2x)3(3y)1+C24(2x)2(3y)2-C34(2x)1(3y)3+C44(2x)0(3y)4=16×4-4×8×3×3y+6×4×2×9y2-4×2x×27y3+81y4=16×4-96x3y+216x2y2-216xy3+81y4 (iii) x-1×6=C06 x61x0-C16 x51x1+C26 x41x2-C36 x31x3+C46 x21x4-6C5 x11x5+C66 x01x6=x6-6 x5×1x+15 x4×1×2-20×3×1×3+15×2×1×4-6 x×1×5+1×6=x6-6×4+15×2-20+15×2-6×4+1×6 (iv) (1 − 3x)7 =C07(3x)0-C17(3x)1+C27(3x)2-C37(3x)3+C47(3x)4-C57(3x)5+C67(3x)6-C77(3x)7=1-7×3x+21×9×2-35×27×3+35×81×4-21×243×5+7×729×6-2187×7=1-21x+189×2-945×3+2835×4-5103×5+5103×6-2187×7 (v) (ax-bx)6=C06(ax)6(bx)0-C16(ax)5(bx)1+C26(ax)4(bx)2-C36(ax)3(bx)3+C46(ax)2(bx)4-C56(ax)1(bx)5+C66(ax)0(bx)6 =a6x6-6a5x5×bx+15a4x4×b2x2-20a3b3×b3x3+15a2x2×b4x4-6ax×b5x5+b6x6=a6x6-6a5x4b+15a4x2b2-20a3b3+15a2b4x2-6ab5x4+b6x6 (vi) xa-ax6=C06xa6ax0-C16xa5ax1+C26xa4ax2-C36xa3ax3+C46xa2ax4-C56xa1ax5+C66xa0ax6=x3a3-6x2a2+15xa-20+15ax-6a2x2+a3x3 (vii) x3-a36=C06(x3)6(a3)0-C16(x3)5(a3)1+C26(x3)4(a3)2-C36(x3)3(a3)3+C46(x3)2(a3)4-C56(x3)1(a3)5+C66(x3)0(a3)6=x2-6×5/3a1/3+15×4/3a2/3-20xa+15×2/3a4/3-6×1/3a5/3+a2 (viii) (1+2x-3×2)5Consider 1-2x and 3×2 as two separate entities and apply the binomial […]

Probability, Class 11 Mathematics R.D Sharma Question Answer

Probability Page No.33.6 Ex.33.1 Q1. Answer : If a coin is tossed once, the possible outcomes are a head (H) and tail (T). Therefore, the sample space of this experiment is S = { H, T}. Q2. Answer : If a coin is tossed twice, the possible outcomes are HH, HT, TH, TT. Therefore, the […]

Mathematical Reasoning, Class 11 Mathematics R.D Sharma Question Answer

Mathematical Reasoning Page No.31.4 Ex.31.1 Q1. Answer : (i) Listen to me, Ravi! It is an exclamatory sentence. Therefore, it is not a statement. (ii) Every set is a finite set. It is a false assertive sentence because there are some sets that are infinite like the set of all real numbers. Therefore, it is […]

Straight Lines, Class 11 Mathematics R.D Sharma Question Answer

Page 23.13 Ex 23.1 Q1. Answer : (i) θ=-π4 ∴ Slope of the line=m=tanθ⇒Slope of the line=tan-π4=-tanπ4=-1 Hence, the slope of the line is -1. (ii) θ=2π3 ∴ Slope of the line=m=tanθ⇒Slope of the line=tan2π3=-tanπ3=-3 Hence, the slope of the line is -3. (iii) θ=3π4 ∴ Slope of the line=m=tanθ⇒Slope of the line=tan3π4=-tanπ4=-1 Hence, the […]

Permutations & Combinations, Class 11 Mathematics R.D Sharma Question Answer

PERMUTATIONS Page. 16.4 Ex 16.1 Q1. Answer : (i) 30!28! = 30×29×28!28! ∵ n!= n(n-1)! =30×29 = 870 (ii) 11!-10!9!=11×10×9! – 10×9!9! ∵ n! =n(n-1)! =9!(110-10)9! =100 (iii) LCM of (6!,7! and 8!): n! = n(n-1)! Therefore, (6!,7! and 8!) can be rewritten as: 8! = 8×7×6! 7! = 7×6! 6! = 6! ∴ LCM […]

Linear Inqualities, Class 11 Mathematics R.D Sharma Question Answer

Page 15.10 Ex 15.1 Q1. Answer : We have, 12x<50⇒x<5012 Dividing both the sides by 12⇒x<256(i) x∈RThen, the solution of the given inequation is -∞,256.(ii) x∈ZThen, the solution of the given inequation is ……….-3, -2, -1, 0, 1, 2, 3, 4.(iii) x∈NThen, the solution of the given inequation is 1, 2, 3, 4. Q2. Answer […]

Complex Numbers & Quadratic Equations, Class 11 Mathematics R.D Sharma Question Answer

COMPLEX NUMBERS Page 13.1 Ex – 13.1 Q1. Answer : i i457 =i4×114+1 =i4114×i =i ∵i4=1ii i528 =i4×132 =i4132 =1 ∵i4=1iii 1i58=1i4×14+2 =1i414×i2 =1i2 ∵i4=1 =-1 ∵i2=-1iv i37+1i67=i4×9+1+1i4×16+3 =i49×i+1i416×i3 =i-1i ∵i3=-i =i-1i×ii =i-ii2 =i–i ∵i2=-1 =2i v i41+1i2579 =i4×10+1+1i4×64+19 =i410×i+1i464×i9 =i+1i9 ∵ i4=1 =i+ii29 =i-i9 ∵i2=-1=0 vi i77+i70+i87+i4143=i4×19+1+i4×17+2+i4×21+3+i4×103+23 =i419×i+i417×i2+i421×i3+i4103×i2 =i-1-i-13 ∵i4=1,i3=-i and i2=-1 =-23 =-8vii i30+i40+i60=i4×7+2+i4×10+i4×15 […]

Maths Trigonometric Functions, Class 11 R.D Sharma Question Answer

 1. MEASUREMENT OF ANGLES Page 4.12 Ex – 4.1 Q1. Answer : We have:π rad =180°∴1 rad=180π° i 18π5=180π×9π5° =36×9° =324° ii-5π6=180π×-5π6° =-30×5° =-150° iii 18π5c=180π×18π5° =36×18° =648° iv -3c=180π×-3° =18022×7×-3° =-378022° =-1711822° =-171°1822×60′ =-171°49111′ =-171°49’111×60” =-171°49’5.45” ≈-171°49’5” (v) 11c=180π×11° =18022×7×11° =630° vi 1c=180π×1° =18022×7×1° =63011° =57311° =57°311×60′ =57°16411′ =57°16’411×60” =57°16’21.81”≈57°16’22” Q2. Answer : We have:180°=π rad∴1°=π180 […]

Sets, Class 11 Mathematics R.D Sharma Question Answer

Page 1.2 Ex – 1.1 Q1. Answer : Well-defined collections are sets. Example: The collection of good teachers in a school is not a set, It is a collection. Thus, we can say that every set is a collection, but every collection is not necessarily a set. The collection of vowels in English alphabets is a set. […]