Chapter 10Straight Lines Class 11 NotesQ. Radius of the circle is 5 cm. find the equation of the tangent linex cosω + y sinω = px cos600 + y sin600 = 5x .1/2 + y. √3/2 = 5x+ √3 y = 10General equation of a lineThe general equation of a line is Ax + By + C = 0Slope = (-A)/Bx intercept = (-C)/Ay intercept = (-C)/BQ. Find the slope, x intercept and y intercept of the line 2x+3y – 4 = 0Slope = (-A)/B= (-2)/3x intercept = (-C )/A = 4/2 = 2y intercept = (-C)/B = 4/3Q. Find the equation of a line perpendicular to x – 7y +5 = 0 and having x intercept 3Slope of the

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# Straight Lines class 11 Chapter 10

Chapter 10 Straight Lines What is a Straight Line? Lines can be parallel, perpendicular, intersecting, or concurrent. A straight line is the set of all points between and extending beyond two points. In Euclidean geometry, the two properties of straight lines are that they have only one dimension, length, and they forever continue in two directions. Different Types of Formula Distance formula Distance between (x1,y1) and (x2,y2) is Section Formula i) Internal Division ii) External Division Mid point = Area of a triangle (x1,y1) , (x2,y2) and (x3,y3) are three vertices of a triangle Area =[x1(y2-y3) + x2(y3-y1)+ x3(y1 – y2)] Slope of a line Slope , m = tanθ where θ is the angle which the line makes with positive direction of X- axis in anti clockwise direction [00 ≤

# Sequence and series Class 11

Chapter 9Sequence and seriesQ. Let the sequence an be defined by a1 = 1, an = an-1 +2 for n ≥ 2. Write first 3 termsa1 = 1an = an-1 +2a2 = a2-1 +2 = a1 + 2 = 1 + 2 = 3a3 = a3-1 +2 = a2 + 2 = 3 + 2 = 5d = a2 – a1If a, b and c are three consecutive terms of an A.P, 2b = a + can = a + (n-1)da2 = a + da3 = a + 2da4 = a + 3dn = ((a_(n- ) a_1)/d) + 1Sn = n/2(2a+(n-1)d) = n/2(a1+an)If a, b and c are three consecutive terms of an A.P, then b

# Introduction to Three Dimensional Geometry

Chapter 12 Introduction to Three Dimensional Geometry x- axis : (x,0,0) y- axis : (0,y,0) z- axis : (0,0,z) XY-plane : (x,y,0) YZ-plane : (0,y,z) ZX-plane : (x,0,z) + + + : I - + + : II - - + : III + - + : IV + + - : V - + - : VI - - - : VII + - - : VIII Q. (4,-2,3) IV XOYIZ Q. (-4,2,5) II XIOYZ The distance of the point (a,b,c) from x-axis The distance of the point (a,b,c) from y-axis The distance of the point (a,b,c) from z-axis Q. Find the distance of the point (2,3,4) from y-axis The image of (a,b,c) w.r.to XY-plane : (a,b,-c) The image of (a,b,c) w.r.to YZ-plane : (-a,b,c) The image of (a,b,c) w.r.to ZX-plane : (a,-b,c) Q. Find the image of (2,-3,-4) w.r.to XY-plane (2,-3,4) Distance formula Q. Using distance formula show

# Mathematical Reasoning Class 11

Chapter 14Mathematical ReasoningA sentence is called mathematically acceptable statement if it is either true or false not bothStatements:Two plus two equals four8 is less than sixThe sum of all interior angles of a triangle is 1800The product of -1 and 8 is 8Not a statement:Mathematics is difficultThe sides of a quadrilateral have equal lengthAnswer this questionToday is a windy dayHe is a mathematics graduateKashmir is far from hereOpen the doorWhile dealing with statements,we usually denote them by small letters p,q,r…P: fire is always hotQ: All real numbers are complex numbersNegation of a statementThe denial of a statement is called its nagationChennai is a cityChennai is not a cityIt is false that Chennai is a cityIt is not the case that

# Probability Class 11

Chapter 16ProbabilityIn earlier class, we have already studied about the concept of probability. We have defined the probability of an event as the ratio of number of outcomes favorable to the event, to the total number of outcomes.Random experiments In our day today life, there are so many experimental activities, the results may not be same when they are repeated under same conditions. Consider the following experimentsTossing a coinThrowing a dieWe know the results of these experiments. But we are not sure which one of these results will come when it is executed. These kinds of experiments are called random experimentsThe results of a random experiments are called outcomesThe set of all possible outcomes of a random experiment is called sample

# Binomial Theorem class 11

Chapter 8Binomial TheoremBinomial theorem for any positive integer n(a+b)n = nC0 an + nC1 an-1 b + nC2 an-2 b2 + … + nCn bn = an + nC1 an-1 b + nC2 an-2 b2 + … + bnQ. Expand= x8 + 4.x6.() + 6.x4. + 4.x2. += x8 + 12x5 + 54x2 +Q. (97)3(97)3 = (100-3)3= 1003 – 3C1(100)2.3 + 3C2(100)(3)2 – 33= 1000000 – 3.10000.3 + 3. 100.9 – 27= 1000000 – 90000 + 2700 – 27= 912673 Note: 102 = 100+20.99 = 1- 0.01Q. Find (a+b)4 – (a-b)4. Hence evaluate(a+b)4 = a4 + 4C1 a3 b + 4C2 a2 b2 + 4C3 a b3 + b4= a4 + 4a3b + 6a2b2 + 4ab3 + b4(a-b)4 = a4 - 4a3b +

# Permutations and Combinations Class 11

Chapter 7Permutations and CombinationsFundamental principle of counting If an event can occur in m different ways, following which another event can occur in n different ways, then the total number of occurrence of the events in the given order is m×n.1. How many three digit numbers can be formed using the digits 1,2,3,4,5 ifa) repetition of the digits is allowedb) repetition of the digits is not allowed a) 5×5×5 = 125b) 5×4×3 = 602. How many three digit numbers can be formed using the digits 1,2,3,4,5,6 ifa) repetition of the digits is allowedb) repetition of the digits is not alloweda) 6 ×6 ×3 =108b) 4 ×5 ×3= 603. How many 5 digit telephone numbers can be constructed if each number starts with 67

# Complex Numbers Class 11

Chapter 5 Complex Numbers In earlier classes, we have studied second degree equations. We have seen that if the b 2 -4ac is less than 0, then the second degree equation has no solution. What is the reason? Negative real numbers has no real root. So we need to extend the real number system to a larger number system so that negative real number has also a square root. In fact, the main objective is to solve a second degree equation in the case when the discriminant is a negative real number which is not possible in the system of real numbers. For this we have to study a new type of numbers called imaginary numbers. Let us start……. Welcome all Imaginary number An

# Relations and Functions Class 11

Chapter 2 Relations and Functions Class 11 Ordered pair A pair having an order is called ordered pair Consider (a,b). a is called first component and b is called second component. If (a,b) = (c,d), the a = c and b = d Eg : If (2x-3, 3y+1) = (5,7), find x and y Ans: Equating the first component 2x-3 = 5 2x = 5 + 3 = 8 x = 8/2 = 4 equating the second component 3y+1 = 7 3y = 7-1 = 6 y = 6/3 = 2 Also Read: Trigonometry Equations Cross product (Cartesian Product) Q. A × B is the set of all ordered pairs in which first element is from A and second element from B 1. Let A = {1,2,3} and B = {4,5}, write A×B and B×A? Ans: A×B = {(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)} B×A = {(4,1),(4,2),(4,3),(5,1),(5,2),(5,3)} Note