Question 4:- If Re(z-1/2z+i) = 1, where z = x + iy, then the point (x, y) lies on a : (A) Straight line whose slope is -2/3 (B) Straight line whose slope 3/2 (C) Circle whose diameter is √5/2 (D) Circle whose centre is at (-1/2, -3/2) Solution:- Since, z = x + iy … Read more
Question 3:- If w = α + iβ where β ≠ 0 and z ≠ 1 satisfies that condition that is purely real, then the set of values of z is (a) |z| = 1, z ≠ 2 (b) |z| = 1 and z ≠ 1 (c) … Read more
Question 2:- Let complex numbers α and lies on circles and , respectively. If satisfies the equation , then |α| is equal to (2013 Adv.) Solution:- Intersection of circles, the basic concept is to equations simultaneously and using properties of modulus of complex numbers. We know that, and Here, and could be written as and … Read more
Question 1:- If z is complex number such that |z| ≥ 2 . then the minimum value of |z + 1/2|. (a) is equal to 5/2 (b) lies int interval (1, 2) (c) is strictly greater than 5/2 (d) is strictly greater than 3/2 but less than 5/2 … Read more
Question 6:- In a hotel four rooms are available Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons . Then the number of all possible ways in which this can be done is ______ Solution:- Let … Read more
Question 5:- From a library containing 5 identical physics books, 4 identical chemistry books & 6 identical maths books. Find the number of ways in which we can select (a) At least one book (b) At least one book of each subject (c) At least 2 books (d) At least 2 book of each subject. … Read more
Question 4:- Assuming cricket wordcup-2023 is played 10 teams. How many total matches are played in the league stage if each team plays with every other team exactly once Solution:- Number of team = 10 Selection of 2 team from 10 team if each team plays with every other team exactly once = 45 Question … Read more
Question 3:- 2n chairs are arranged symmetrically around a table. there are 2n people including A and B, whose wish to occupy the chair. Find the number of seating arrangements if:- (i) A and B are next to each (ii) A and B are diametrical Solution:- (i) If A and B sit together then, number … Read more
Question 2:- How many ways 6 Boys & 6 Girls batch students can be seated around a circular table such that no two boys are together. Solution:- If one boys sit in the circle then the other student sit like a in linear then, Number of arrangement of 6 Boys in circle = (6-1)! = … Read more
UK Board UBSE 10th & 12th Result 2025 – Key Highlights. The Uttarakhand Board of School Education (UBSE) is all set to declare the Class 10 and Class 12 results for 2025. Students who appeared for the exams can access their results through the official websites — ubse.uk.gov.in and uaresults.nic.in. More than 2.23 lakh students … Read more