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Karnataka Secondary Education Examination Board came into existence in the year 1966. It conducts examinations for class 10th of affiliated schools and 12 other examinations like Karnataka open school, Diploma in Education, Music etc. The Board has Bangalore as its headquarters. Examination related issues pertaining to four educational divisions are addressed by divisional secretaries or ex-officio Joint Directors of the Board at Belguam, Kalaburgi and Mysore. KSEEB headquarters is at Malleshwaram, Bangalore which houses the Secretary’s office for Bangalore educational division also..
Every year nearly 8.5 lakh students appear for the SSLC (Secondary School Leaving Certificate) examination which will be conducted in March/April of every year. The Board reconducts the same examination in the month of June for the benefit of the students who fail in main examinations. Nearly 2.20 lac students take the supplementary examination.
To save fuel, to avoid air pollution and for good health two persons A and B ride bicycle for a distance of 12 km to reach their office everyday. As the cycling speed of B is 2 km/h more than that of A, B takes 30 minutes less than that of A to reach the office. Find the time taken by A and B to reach the office.
𝐈𝐟 𝒙=𝒑 𝒕𝒂𝒏 𝜽+𝒒 𝒔𝒆𝒄 𝜽 𝒂𝒏𝒅 𝒚=𝒑𝒔𝒆𝒄 𝜽+𝒒 𝒕𝒂𝒏 𝜽 𝒕𝒉𝒆𝒏
𝒑𝒓𝒐𝒗𝒆 𝒕𝒉𝒂𝒕 𝒙^𝟐−𝒚^𝟐=𝒒^𝟐−𝒑^𝟐
𝐏𝐫𝐨𝐯𝐞 𝐭𝐡𝐚𝐭 (〖𝒄𝒐𝒕〗^𝟐 (〖𝟗𝟎〗^𝟎−𝜽))/(〖𝒕𝒂𝒏〗^𝟐 𝜽−𝟏)+(〖𝒄𝒐𝒔𝒆𝒄〗^𝟐 𝜽)/(〖𝒔𝒆𝒄〗^𝟐 𝜽−〖𝒄𝒐𝒔𝒆𝒄〗^𝟐 𝜽)=𝟏/(〖𝒔𝒊𝒏〗^𝟐 𝜽−〖𝒄𝒐𝒔〗^𝟐 𝜽)
Calculate the median of the following frequency distribution table :
Find the mode of the following data :
The following table gives the information of daily income of 50 workers of a factory. Draw a ‘less than type ogive’ for the given data.
A bag contains 3 red balls, 5 white balls and 8 blue balls. One ball is taken out of the bag at random. Find the probability that the ball taken out is (a) a red ball, (b) not a white ball.
Prove that “the lengths of tangents drawn from an external point to a circle are equal”.
Construct a triangle ABC with sides BC = 3 cm, AB = 6 cm and AC = 4·5 cm. Then construct a triangle whose sides are 𝟒/𝟑 of the corresponding sides of the triangle ABC.
ABCD is a rectangle of length 20 cm and breadth 10 cm. OAPB is a sector of a circle of radius 𝟏𝟎√𝟐 cm. Calculate the area of the shaded region. [ Take π = 3·14 ]
A hand fan is made up of cloth fixed in between the metallic wires. It is in the shape of a sector of a circle of radius 21 cm and of angle 120° as shown in the figure. Calculate the area of the cloth used and also find the total length of the metallic wire required to make such a fan.
Find the solution of the following pairs of linear equation by the graphical method :
x + y = 7
3x – y = 1
There are five terms in an Arithmetic Progression. The sum of these terms is 55, and the fourth term is five more than the sum of the first two terms. Find the terms of the Arithmetic progression.
In an Arithmetic Progression sixth term is one more than twice the third term. The sum of the fourth and fifth terms is five times the second term. Find the tenth term of the Arithmetic Progression.
A tower and a pole stand vertically on the same level ground. It is observed that the angles of depression of top and foot of the pole from the top of the tower of height 60 m is 30° and 60° respectively. Find the height of the pole.
A container opened from the top is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the milk which can completely fill the container at the rate of Rs. 20 per litre. [ Take π = 3·14 ]
State and prove Pythagoras theorem.
