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 […]

# CBSE Class 11th Maths, NCERT & R.D Sharma Solutions & Sample Papers

## Straight Lines, Class 11 Mathematics R.D Sharma Solutions

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 […]

## Sequence and Series, Class 11 Mathematics R.D Sharma Solutions

ARITHMETIC PROGRESSION Page 19.4 Ex 19.1 Q1. Answer : Given : an = n2-n+1For n=1, a1 = 12-1+1 = 1For n=2, a2 = 22-2+1 = 3For n=3, a3 = 32-3+1 = 7For n=4, a4 = 42-4+1 =13For n=5, a5 = 52-5+1 = 21 Thus, the first five terms of the sequence are 1, 3, 7, […]

## Permutations & Combinations, Class 11 Mathematics R.D Sharma Solutions

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 Solutions

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 Solutions

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 […]

## Mathematical Induction, Class 11 Mathematics R.D Sharma Solutions

Page 12.2 Ex – 12.1 Q1. Answer : We have: P(n): n(n + 1) is even. Now, P(3) = 3(3 + 1) = 12 (Even) Therefore, P(3) is even. Page 12.3 Ex – 12.1 Q2. Answer : We have: P(n): n3+n is divisible by 3.Thus, we have:P(3) =33+3 =27+3=30 It is divisible by 3.Hence, P(3) is […]

## Trigonometric Functions, Class 11 Mathematics R.D Sharma Solutions

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 […]

## Relations & Functions, Class 11 Mathematics R.D Sharma Solutions

Page 2.8 Ex – 2.1 Q1. Answer : (i) a3+1, b-23=53, 13 By the definition of equality of ordered pairs, we have: a3+1, b-23=53, 13 ⇒a3+1 = 53 and b-23=13⇒a3= 53-1 and b = 13+23⇒a3=23 and b = 1⇒a = 2 and b = 1 (ii) (x + 1, 1) = (3, y − 2) By the […]

## Sets, Class 11 Mathematics R.D Sharma Solutions

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. […]

## Axiomatic Probability, Class 11 Mathematics NCERT Solutions

1. There will be total 10 MCQ in this test. 2. Please keep a pen and paper ready for rough work but keep your books away. 3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number. 4. No negative […]

## Problems on Probability, Class 11 Mathematics NCERT Solutions

1. There will be total 10 MCQ in this test. 2. Please keep a pen and paper ready for rough work but keep your books away. 3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number. 4. No negative […]

## Introduction to Probability, Class 11 Mathematics NCERT Solutions

1. There will be total 10 MCQ in this test. 2. Please keep a pen and paper ready for rough work but keep your books away. 3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number. 4. No negative […]

## Variance and Standard Deviation, Class 11 Mathematics NCERT Solutions

## Mean Deviation, Class 11 Mathematics NCERT Solutions

## Mathematical Statements, Class 11 Mathematics NCERT Solutions

## Implications and Validating of Statements, Class 11 Mathematics NCERT Solutions

## Logarithmic and Exponential Limits, Class 11 Mathematics NCERT Solutions

1. There will be total 10 MCQ in this test. 2. Please keep a pen and paper ready for rough work but keep your books away. 3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number. 4. No […]