Straight Line Distance Formula If two point A (x 1 , y 1 ) and B(x 2 , y 2 ) are given , The distance between them is Section Formula Consider two points A(x 1 , y 1 ) and B(x 2 , y 2 ) Case 1 : Let a point P(x,y) divides the segment AB internally in the ratio of m : n such that PA : PB = m : n The coordinates of point P(x,y) : Consider two points A(x 1 , y 1 ) and B(x 2 , y 2 ) Case 2 : Let a point P(x,y) divides the segment AB externally in the ratio of m : n such that PA : PB = m : n The coordinate of P (x,y) are : Mid point Formula If P(x,y) is the mid point of AB , then m:n = 1:1 , then the coordinate of point P : Area of triangle Consider a triangle with vertices A(x 1 ,y 1 ) , B(x 2 ,y 2 ) , C(x 3 ,y 3 ) Slope of a Line Slope of a line is defined as the tangent of tha angle θ which a line makes with +ve X-axis. It is denoted by m. m= tanθ Important Points : i) m can be defined as tanθ fo...

Practice question For Quadratic Equation 1. How many real solutions of the equation x 2 − 3 |x| + 2 = 0 exist ? 2. Find the value of ‘a’ for which one root of the quadratic equation (a 2 − 5a + 3) x 2 + (3a − 1) x + 2 = 0 is twice as large as the other. 3. If the roots of the quadratic equation x 2 + px + q = 0 are tan30° and tan15°, respectively then what is the value of 2 + q − p ? 4. The quadratic equations x 2 – 6x + a = 0 and x 2 – cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. what is the common root ? 5. Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation , what is the quadratic equation ? 6. If (1 – p) is a root of quadratic equation x 2 + px + (1− p) = 0 , what are its roots ? 7. If roots of the equation x 2 – bx + c = 0 be two consecutive integers, then What is the value b 2 – 4c ? 8. If both the...

Start the test Question no. 1 Let z, w be complex numbers such that z + i w =0 and arg zw =π . Then arg z equals   π/4   5π/4   3π/4   π/2 Question no. 2 If z and w are two non-zero complex number such that |zw|=1, and Arg (z)-Arg(w)=π/2 , then z¯w is equal to   1   -1   -i   i Question no. 3 If |z+4|<= 3, then the maximum value of |z+1| is   4   10   6   0 Question no. 4 The conjugate of complex number is 1/(i-1), then that complex number is   1/(i+1)   -1/(i+1)   1/(i-1)   -1/(i-1) Question no. 5 What are the square roots of -2i ?   ∓(1+i)   ∓(1-i)   ∓i   ∓1 Question no. 6 What is the value of the sum of   i   2i   -2i   1+i Question no. 7 What is the number of distinct solution of the equation z 2 + |z| = 0 (where z i...

Practice question For Complex Number 1.If w is a complex cube root of unity and x 2 = w 2 - w -2 , then what is the value of x 2 + 4x + 7 ? 2. If z is complex number such that z + z -1 = 1 , then what is the of z 99 + z -99 ? 3. If the point z 1 = 1 + i is the reflection of the point z 2 in the line i z - iz = 5 , what is the point z 2 ? 4. What is the real part of (sinx + icosx) 3 ? 5. If x = a + b , y = aα + bβ , z = aβ + bα , where α and β are complex cube root of unity , then show that xyz = a 3 + b 3 . 6. Let z be the complex number such that |z| + z = 3 + i , what is the value of |z| ? 7. Find the condition for which the complex number sinx + icos2x and cosx - isin2x are conjugate to each other ? 8. For all complex number z 1 , z 2 , satisfying |z 1 | = 12 and |z 2 - 3- 4i | = 5 , what is the minimum value of |z 1 - z 2 | ? 9. If iz 3 + z 2 -z + i = 0 , then show that |z| = 1. 10. If z 1 and z 2 are two non...

Chapter 2 What is polynomial ? "An expression that contains different power of same variable in algrebaic form " . Example : P(x) = 2x + 5 , P(y) = y 2 + 5y + 6 What is the Degree Of polynomial ? " Degree of polynomial is the highest power of variable in given polynomial. " For Example : P(x) = 2x + 5 has one as the highest power of x , so degree of polynomial is 1 similarly P(y) = y 2 + 5y + 6 is 2 as the highest power of y , degree polynomial. Linear Polynomial : Polynomial having degree '1' Quadratic Polynomial : Polynomial having degree '2' Cubic Polynomial : Polynomial having degree '3' Zeroes of a polynomial : A real number K is said to be zero of polynomial , If P(K) = 0 Example : P(x) = x + 5 For x = -5 ⇒ P(-5) = 0 So , -5 is the zero of the polynomial. Geometrical meaning Of zeroes : If we plot or draw any polynomial on x-y plane, and the curve cuts the x-axis at ...

Chapter 1 Euclid Division Algorithm: Given positive integers a and b , there exist unique integers q and r satisfying a = bq + r , 0 ≤ r < b How to find HCF and LCM using Euclid's Algorithm I) 135 and 225 let a = 225 , b = 135 Apply Euclid's Algorithm till remainder becomes zero , the corresponding divisor will be the HCF 225 = 135 × 1 + 90 135 = 90 × 1 + 45 90 = 45×2 + 0 So , HCF = 45 . I) 455 and 42 let a = 455 , b = 42 Apply Euclid's Algorithm till remainder becomes zero , the corresponding divisor will be the HCF 445 = 42 ×10 + 35 42 = 35 × 1 + 7 35 = 7×5 + 0 So , HCF = 7 . Fundamental theorem of Arithmetic: "Every Composite number can be expressed as a product of primes and this factorizaion is unique." Example : Let's take a composite number '12' It can be written as factorization of prime numbers. i.e. 12 = 2 ×2 ×3 and this factorization is unique. this is the fundamental the...

IIT JEE Examination In this article , you will get to know about the process of examination to get the admission in IIT(Indian Institute of Technology). Admission to various undergraduate programs across IITs is carried out through the Joint Entrance Examination (Advanced) [JEE (Advanced)]. At present, there are twenty three IITs across the country. Through JEE (Advanced), IITs offer admission into undergraduate courses leading to a Bachelors, Integrated Masters, Bachelor-Master Dual Degree in Engineering, Sciences, or Architecture. The Joint Entrance Examination (Advanced)[JEE (Advanced)] will be conducted by the seven Zonal Coordinating IITs under the guidance of the Joint Admission Board. Examination Pattern: The examination consists of two papers (Paper 1 and Paper 2) of three hours duration each. Note : i) Appearing in both the papers is compulsory ii) Candidate who wish to appear for JEE (Advanced) are required to write / have written the JEE (Main) of that year...