Start the test Question no. 1 If the n th term of an A.P. is 2n-1, what is the sum of upto n terms ?   n 2   n 2 -1   n 2 +1   0.5n(n+1) Question no. 2 If the three observation are 3,-6 and -6. Then what is their harmonic mean?   0   -3   -0.5   ∞ Question no. 3 If the number of terms of an A.P. is (2n+1), then what is the ratio of the sum of odd terms to the even terms?   n/(n+1)   n 2 /(n+1)   (n+1)/n   (n+1)/2n Question no. 4 If the sum of terms of an A.P. is n 2 -2n , then what is the n th term?   3n-n 2   2n-3   2n+3   2n-5 Question no. 5 If the AM and GM of two numbers are 5 and 4 respectively, then what is the HM of those numbers?   5/4   16/5   9/2   9 Question no. 6 If x 2 , y 2 , z 2 are in A.P., then y+z, z+x, x+y are in   AP   GP   HP   None of these Question no. ...

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...