27th December 2021
Q. 1 What is the HCF of two consecutive even numbers?
Sol.
1
Q.2 if the sum of the zeros of the polynomial P(x) = kx² + 2x + 3k is equal to their product then find the values of k.
Sol.
Sum of zeros = product of zeros
–b/a = c/a
–b = a
–k = 2
k = –2
Q. 3 for what value of k do the equation 3 x – y + 8 = 0 and 6 x – ky = – 16 represent coincident lines.
Sol.
Since it represent coincident lines
3/6 = –1/–k = 8/–16
–1/–k = 8/–16
–1/–k = –1/2
k=–2
Q.4 Find the quadratic equation whose roots are twice the roots of the 2x² – 5 x + 2 = 0.
Sol.
Q. 5 Write the discriminant of the quadratic equation.
Sol.
Q. 6. find the 6th term of an AP 17, 11, 14, .......….
Sol.
Q. 7 If the numbers (x – 2) (5x – 1) ,(5x + 2) are in AP. Find x
Sol.
Q. 8 A cone , a hemisphere and a cylinder stand on equal basis and have the same height. Find the ratio of their volumes.
Sol.
Q. 9 Find the common difference of the AP.
Sol.
Q. 10. Write the statement of the fundamental theorem of arithmetic.
Sol. The Fundamental Theorem of Arithmetic states that Every composite number can be expressed (factorised) as a product of primes, and this factorisatin is unique, apart from the order in which the prime factors occur.
Q. 11. Write down the formula showing the relationship between three measures of Central tendency.
Sol. Empirical relationship between three measurements of the central tendency
Mode = 3 Median – 2 Mean
Q. 12. In a ∆ ABC DE || BC and AD = (x + 3), DB = (3x + 19), AE = x and CE = (3x + 4), then find x.
Sol.
Q. 13. Someone is asked to choose a number between 1 to 100. Find the probability that the chosen number is prime.
Sol. Prime numbers between 1 to 100 are
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97, i.e 25 outcome.
n(S) = 100
n(E) = 25
P(E) = n(E)/n(S)
P(E) = 25/100
= 1/4
Q. 14. if x = sin 45° cos 45°+ sin 30°, then find the value of x
Sol.
Q. 15. If three different coins are tossed together then find the probability of getting two heads.
Sol.
Q. 16. What is the probability of an impossible event?
Sol. The probability of an impossible event is
= 1
SECTION – II
Q. 17. CASE STUDY 1 (CAMPAIGN AGAINST PUBG GAME)
Using of mobile screen for long hours, it make lazy, affect your eyesight and give you hadache. Those who are addicted to playing PUBG can get easily stressed out or face any issue in public, due to the lack of social interaction.
social awareness about ill effects of PUBG, a school decided to start "BAN PUBG" campaign, students are asked to prepare campaign board in the shape of a rectangle.(as shown in the figure)
Q. 18
Sol.
Q. 19.
Sol.
Q. 20
Sol.
PART B
Q. 21. If HCF (54, 81) = 27, then find LCM (54, 81)
Sol.
Q. 22. prove that the length of the tangents drawn from the external point to a circle are equal.
Sol.
Q. 23. Find the ratio in which the line segment joining the points (1, –3) and (4, 5) is divided by x-axis.
Sol.
Q. 24. show that √3 is an irrational number.
Sol.
Q. 25. Find a quadratic polynomial whose zeroes are (5 – 3√2) and (5 + 3√2)
Sol.
Q.26. If tan A = 3/4 then find the value of 1 / sin A + 1 / cos A.
Sol.
Q. 27. State and Prove the basic proportionality theorem.
Sol.
Q. 28. If sin (A + 2B) = 1 / 2 and cos (A + 4 B) = 1 /√2, A > B then find A and B.
Sol.
Q. 29. In figure OACB is a quadrant of a circle with centre O and radius 3.5cm. If OD is 2 cm find the area of (i) quadrant OACB (ii) Shaded region.
Sol.
Q. 30.
Sol.
Q.31. A card is drawn at random from a well shuffled pack of 52 cards. Find the probability that the drawn card is
(i) A card of spade
(ii) Either a king or queen
(iii) Neither a Jack nor a king
Sol.
Q. 32. Find the 31st term of an AP whose 11th term is 38 and 16th term is 73.
Sol.
Q. 33. In figure the line segment XY is parallel to side AC of ∆ABC and it divides the triangle into two parts of equal areas. Find the ratio AX/AB.
Sol.
Q.34 A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it can go 40 km upstream and 55 km downstream dot determine the speed of the stream and that of the boat in still water.
Sol.
Q. 35. Two hoardings of cleanliness are put on a 80m wide road on two poles which are on opposite sides of road and are of same height. The angle of the elevation of the both poles from a point on the road is 60° and 30°. Find the height of poles and distance of the pole from the that point.
Sol.
Q. 36 A hemispherical tank full of water is emptied by a pipe at the rate of 25 / 7 litre per second. How much time will it take to empty half the tank if its three is diameter? (Ļ = 22/7).
Sol.
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