Q1. If one zero of the quadratic polynomial x2+ 3x + k is 2, then the value of ‘k’ is
Q2. If sinθ + cosθ = p and secθ + cosecθ = q, show that q (p2 – 1) = 2p.
Q3.Show that is irrational Number
Q4.A carton consists of 60 shirts of which 48 are good, 8 have major defects and 4 have minor defects. Nigam, a trader, will accept the shirts which are good but Anmol, another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. Find the probability that it is acceptable to Anmol.
Q5. Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.
Q6.A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamun, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.
Q7. Find the value of x for which DE ∥ AB in the given figure.
Q8. Find the coordinates of the points of trisection of the line segment joining (4, –1) and (–2, –3).
Q9. Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ.
Q10. In a two digit number the sum of the two digits is 8. If 18 is added to the number its digits are reversed. Find the number. .
Q11.Solve graphically: x-y+2=0 and 4x-y-4=0.Also find the area of the triangle thus formed.
Q12. In a circle of radius 21 cm, an arc subtends an angle of 60o at the center. Find: the length of the arc. area of the sector formed by the arc. area of the segment formed by the corresponding chord
Q13. An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Q14.Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of △PQR (see figure). Show that △ABC∼△PQR.
Q15.State and proof Basic Proportionality theorem.
Q16.To conduct Sports Day activities in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each, 100 flower pots have been placed at a distance of 1 m from each other along AD as shown in figure. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 th the distance AD on the 8 th line and posts a red flag. On the basis of above information, answer the following questions.
(i) Write the coordinates of green flag. (ii) Write the coordinates of red flag. (iii) Find the distance between both the flags. Or If Rashmi has to post a blue flag exactly half way between the line segment joining the flags, then find the coordinates of that point.
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