28/11/23
1) If tanx = a/b, then which of the following is the value of (a sinx + b cosx)/+a sinx + b cosx).
a) (a²+ b²)/(a²- b²)
b) a/√(a²- b²)
c) b/(a²- b²)
d) √(a²+ b²)
2) Evaluate: (sinx + cosex)²+ (cosx + Secx)²= tan²x + cot²x +7.
3) If cosecx + cotx = y, find the value of cosx.
4) Eliminate k
x= a seck, y= b tank.
5) If the points (a,0),(0,b) and (1,1) are collinear, then show that 1/a + 1/b =1.
6) A number is chosen at random from the numbers 1,2,...,15. Find the probabilities that the chosen number is
a) even
b) multiple of 3
c) multiple of 4
d) multiple of 3 but not 4
e) multiple of both 3 and 4.
7) In the figure BC= 5cm,
8) The wheel of a cart is making 5 revolution per second. If the diameter of the wheel is 84cm, find its speed in kmph. Give your answer, correct to nearest km.
9) The inner dimensions of a closed wooden box are 2m, 1.2m and 0.75m. The thickness of the wood is 2.5cm. find the cost of wood required to make the box if 1 m³ of wood cost &5400.
10) 3) A cylinder is surmounted by a cone at one end and a hemisphere at the other end, Given that common radius=3.5 cm, the height of the cylinder is 6.5 cm and the total height 12.8cm, calculate the volume of the solid correct to the nearest integer. 376 cm³
27/11/23
1) x takes 3 hours more than y to walk 30 km. If x doubles his pace, he is ahead of y by 3/2 hours. Find their speeds of walking. 10/3,5 kmph
2) In a cyclic quadrilateral ABCD, angle A= (2x+4)°, angle B= (y+3)°, angle C= (2y +10)°, angle D= (4x -5)°. Find the four angles. 70,53,110,127
3) 2x+ 3y=7; (k+1)x + (2k -1)y = 4k +1. Find the value of k for which system of equations have infinitely many solution. 5
4) Solve for x,y: a/x - b/y =0; ab²/x + a²b/y = a²+ b², where x,y≠0. a,b
5) Solve: abx²+ (b²- ac)x - BC= 0. c/b, -b/a
6) if the equation (1+ m²)x²+ 2mcx + (c²- a²)=0 has equal roots, prove that c²= a²(1+ m²).
7) The length of a hall is 5m more than its breadth . If the area of the floor of the hall is 84 m², what are the length and breadth of the hall ? 7, 12
8) Find the sum of the first 25 terms of an AP, whose nth term is given by aₙ= 7 - 3n. - 800
9) In figure AB diameter and AC is a chord of a circle such that angle BAC =30°. The tangent at C intersects AB produced in D. Prove that BC= BD.
10) Two chords AB and CD of a circle intersect each other at P outside the circle. If AB =5cm, BP= 3cm and PD =2 cm, find CD. 10cm
11) if x is an acute angle and tanx + cotx=2, find the value tan⁷x + cot⁷x.
12) If A and B are complementary angles, prove that (sinA+ sinB)²= 1+ 2 sinA cosA.
13) A bag contains 5 red balls , 8 white balls, 4 green balls and 7 black balls . If one ball is drawn at random , find the probability that it is
a) black.
b) red
c) not green
14) What is the probability that a leap year has 53 Sunday and 53 Mondays ?
15) If r₁ and r₂ be the radii of two solid metallic spheres and if they are melted into one solid sphere, prove that the radius of the new Sphere is (r₁³ + r₂³)¹⁾³.
25/11/23
1) The vertical and slant height of a cone are 24cm and 25cm. Calculate (i) curved surface (ii) volume of the cone.
2) The diameter of an iron sphere is 18cm. The sphere is melted and is drawn into a long wire of uniform cross section. If the length of the wire is 108m. Find its diameter.
3) Find the value of m if (x - m) is a factor of 3x³ + 2x² - 19x + 3m.
4) simplify:2tan 40/cot 50 - cosec 61/sec 29
5) Solve: 4x² - 4ax +(a² - b²) = 0
6) The horizontal distance between two towers is 140m. The angle of elevation of the top of the first tower when seen from the top of the second tower is 30°. If the height of the second tower is 60m. Find the height of the first tower.
7) Prove:
(1+cosA)/(1-cosA) = (cosecA + cotA)²
8) Find the sum of all multiples of 11 between 100 and 400. 6831
9) How many terms of the series {27+24+21+...} must be added to get the sum 132? 8 or 11
10) Of the point (x,y) be equidistant from the points (a+ b, b - a) and (a - b, a+ b), show that bx = ay.
11) Show (1+ Secx + tanx)(1- cosecx + cotx)= 2.
12) In the figure BOA is a diameter of a circle and the tangent at a point P meets BA extended at T.
13) In the figure O is the centre of a circle of radius 5cm,
10) Using step deviation method, Calculate the mean of the following frequency distribution:
Class. Frequency
50-60 9
60-70 11
70-80 10
80-90 14
90-100 8
100- 110 12
110-120 11
12) Draw a histogram and hence estimate the mode for the following frequency distribution:
CLASS- interval. Frequency
0-10 2
10-20 8
20-30 10
30-40 5
40-50 4
50-60 3
) The marks scored by 40 pupils of a class in a test were as follows:
CLASS: 0 1 2 3 4 5
No. of pupils: 2 4 5 14 11 4
Calculate the mean mark.
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