10th Surface area and volume practice paper for CBSE Exam 2013

1. A solid iron rectangular block of dimensions 4.4 m, 2.6m, and 1m is cast into a hollow cylindrical pipe of internal radius 30cm and thickness 5cm. Find the length of the pipe. (Use Π = 22/7)   (Ans = 112m)

2. A well with inside diameter 7m, has been dug 22.5m deep and the earth dug our is used to form an embankment around it. If the height of the embankment is 1.5m, find the width of the embankment.  (Ans = 10.5m)

3. Water is flowing at the rate of 7m/ sec through a circular pipe whose internal diameter is 2cm, into a cylindrical tank of radius 40cm. Find the increase in water level in ½ hour.     (Ans = 7.875m)

4. Water is flowing at 5km/hr through a pipe of diameter 14cm into a rectangular tank which is 50m long and 44m wide. Find the time in which the water level in the tank rises by 7cm.   (Ans = 2 hours)

5. Water flows @ 10 m/ min through a cylindrical pipe having its diameter as 5mm. How much time will it take to fill a conical vessel whose diameter of base is 40cm and depth 24cm?    (Ans = 51min 12sec)

6. The radii of the internal and external surfaces of a metallic spherical shell are 3cm and 5cm respectively. It is melted and recast into a solid right circular cylinder of height 32/3 cm. Find the diameter of the base of the cylinder.                                                (Ans = 7cm)

7. The radius of a solid iron sphere is 8cm. 8 rings of iron plate of external radius 20/3 cm and

the thickness 3cm are made by melting this sphere. Find the internal diameter of each ring.   (Ans = 8cm)

8. A tent of height 77dm is in the form of a right circular cylinder of diameter 36m and height 44dm surmounted by a right circular cone. Find the cost of canvas at Rs 3.50/m2  (Ans = Rs. 5365.80)

9. A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of hemisphere is 4.2cm and the total height of the toy is 10.2cm, find the volume of the wooden toy. (Ans = 266.11cm3)

10. A cylindrical container of radius 6cm & height 15cm is filled with ice-cream. The whole ice cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is 4 times the radius of its base, find the radius of the cone.       (Ans = 3cm)

11. A solid is composed of a cylinder with hemispherical ends. If whole length of the solid is  98cm and diameter of cylinder is 8cm, find the total surface area & volume of the given solid .         

(Ans = 8624cm2 , 54618.67cm3)

12. A right triangle whose sides are 15cm and 20cm, is made to revolve about its hypotenuse. Find the volume and total surface area of the double cone so formed. (Use   Π = 3.14).  

(Ans 3768cm3, 318.8cm2)

13. A cylindrical road roller made of iron is 1m long. Its internal diameter is 54cm and the thickness of iron sheet used in making the roller is 9cm. find the mass of the roller, if 1cm3 of iron has 8gm mass.         (Ans = 1425.6kg) 

14. The difference between outside and inside surface areas of a metallic cylindrical pipe 14cm long is 44cm2  if the pipe is made of 99cm3 of metal, find the outer and inner radii of the pipe.   (Ans = 2.5cm, 2cm)

15. A bucket is in the form of a frustum of a cone and holds 28.49 litres of water. The radii of the top and bottom are 28cm, 21cm respectively. Find the height of the bucket.     (Ans = 15cm)

16. The perimeters of ends of a frustum are 48cm & 36cm, if height of frustum be 11cm, find its

volume.                    (Ans = 1554cm3)

17. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base.If its volume be 1/27 of the volume of the given cone, at what height above the base is the section made?  (Ans = 20cm)

18. A tent is made in form of a conic frustum surmounted by a cone. The diameters of base and top of frustum are 20m & 6m respectively and height is 24m. If height of the tent is 28m, find the area of the canvas cloth required. (Ans = 340Πm2)

19. A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface area of the remainder is 8/9 of the curved surface of the whole cone, find the ratio of the line segments into which the cone’s altitude is divided by the plane (Ans = 1:2)

20.A cylinder and a cone have equal bases and equal heights. If their curved surfaces are in the ratio 8:5, determine the ratio of the radius of the base to the height of either of them  (Ans = 3:4)

21.Lead spheres of diameter 6cm are dropped into a cylindrical beaker containing some water and are completely submerged. If the diameter is 18cm and the water rises by 40cm, find the number of lead spheres dropped in the  water (Ans = 90) 

22. A circus tent is cylindrical to a height of 3m and conical above it. If its diameter is 105m and the slant height of the conical portion is 53m, calculate the length of the canvas cloth 5m wide required to make the tent.(Ans = 1947m)

23.  A cone, a hemi-sphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes as well the ratio of their total surface areas  (Ans = 1:2:3, (√2 + 1):3:4)

24.  A cone of radius 10cm is divided into two parts by drawing a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of the two parts of the cone (Ans = 1:7)

25. A building is in the shape of a cylinder surmounted by a hemi-spherical vaulted dome. The internal diameter of the building is equal to the total height of the building. If the volume of air space inside the building is 880/21 m3, find the height of the crown of the vault above the floor.             (Ans = 4m)

26. An inverted cone of vertical height 12cm and radius of the base 9cm has water to a depth of 4cm. Find the area of the internal surface of the cone not in contact with water.    (Ans = 376.8cm2)

27. The mass of a spherical iron shot-put 12cm in diameter is 5kg. Find the mass of a hollow cylindrical pipe 12cm long (made of the same metal), if it’s internal and external diameters are 20cm and 22cm, respectively.                                                                (Ans = 4.375kg)

Math Adda: Sample Question Paper Class 10 SA-1 -2012-2013

Sample Question Paper Class 10 Mathematics SA-1 -2012-2013

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10th Math Sample paper 1st Term (24)

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Sample Question Paper Class 10 Science Sample SA-1 -2012-2013

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10th Sample paper-2013 (26)

10th Science SA-1 Assignments 2012-13 (1)

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X guess question for CBSE 2012 Mathematics

By JSUNIL TUTORIAL CBSE MATHS & SCIENCE     Class-X Quadratic Equations

Q1. Solve 36x²-12ax+(a²-b²)=0

Q2. Solve 1/a+b+x=⅟a+⅟b+⅟x

[x≠0,x≠-(a+b)]

Q3. Solve 5^(x+I) +5^(2-x)=5³+1

Q4. If -4 is a root of the equation x²+px-4=0 and the equation x²+px+q=0 has equal roots.

Find the values of p&q. [Ans. P=3,q=9/4]

Q5. For what values of ‘k’,the given equation hai real and equal roots,

(k-12)x²+2(k-12)x+2=0 [Ans. K=12,14]

Q6. Rs.250 was divided equally among a certain number of children,each would have received 50 paise less.Find the no. of children.[ans.100]

Q7. The sum of ages of a man and his son is 45 years.Five years ago,the product of their ages was four times the man’s age at that time.Find their present ages.  [36yrs.,9yrs.]

Q8. The difference of two numbers is 5 and the difference of their reciprocals is ⅟10.Find the numbers. [Ans.10,5 &-5,-10]

Q9. A train covers a distance of 90km. at uniform speed.If the speed of the train is increased by 15km an hour,the journey would have taken 30 minutes less.Find the original speed of the train.     [45km/hr.]

Arithmetic Progession

Q1. Find the 105^th term of the A.P.

4,4¹/₂,5,5¹/₂,… [Ans.56]

Q2. Is 51 a term of  A.P.

5,8,11,14?

Q3. Which term of an A.P. 24,21,18,15,---- is the first negative term?

Q4. If the p^th,q^th & r^th terms of an A.P. be a,b,c respectively,then show that a(q-r)+b(r-p)+c(p-q)=0

Q5. If the n^th term of a progression be a linear expression in n, then prove that this progression is an A.P.

Q6. The first and the last terms of an A.P. are a and l respectively.Show that the sum of the n^th term from 
the beginning and the n^th term from the end is (a+l).

Q7. Divide 24 into three parts such that they are in A.P. and their product is 440. (5,8,11)

Q8.Find the sum of all three digit natural numbers which are multiples of 7 [Ans.70336]

Q9. The sum of n terms of an A.P. is (5n²-3n). Find the A.P. Hence,find its 10^th term. [Ans.T₁₀=92]

Q10. If the sum of first n,2n and 3n terms of an A.P. be S₁,S₂ and S₃ respectively,then prove that S₃=2(S₂-S₁).

Areas related to circles

Q1. Three horses are tied with 7m. long ropes at three corners of triangular field having sides 20m.,34m,42m.Find the area of the plot,which remains ungrazed.  [Ans. 77m²,259m²]

Q2.The minute hand of a clock is 12cm. long.Find the area of the face of the clock described by the minute hand in 35 minutes.  [Ans. 264m2]

Q3. The perimeter of a sector of a circle of radius 5.6cm is 27.2cm.Find the area of the sector. [Ans.44.8cm2]

Q4. Three circles,each of radius 6cm touches the other two. Find the area enclosed between them. [π=3.14,√3=1.732]  [Ans.5.76cm2]

Coordinate Geometry

Q1. Show that the points A(1,2),B(5),C(3,8) and D(-1,6) are the vertices of a square.

Q2. Find the coordinates of the circumcentre of a triangle,whose vertices are A(4,6),B(0,4) and C(6,2).Also find the circumcentre. [Ans. (3,3) and r=√10 units.]

Q3.Find the lengths of the medians of a triangle ABC,having vertices at A(0,-1),B(2,1) and C(0,3).

Q4. Find the coordinates of the centroid of a triangle ABC whose vertices are (6,-2),B(4,-3),C(-1,-4)  [Ans. G(3,-3)]

Q5. Find the area of the rhombus whose vertices taken in order are the points A(3,0),B(4,5),C(-1,4) and D(-2,-1)          [Ans. 24sq. units]

Probability

Q1. A box contains 19 balls bearing numbers 1,2,3 ----- 19 respectively.A ball is drawn at random from the box.Find the probability that the number on the ball is:

(i.)A prime number

(ii.)Divisible by 3 or 5

(iii.)Neither divisible by 5 nor by 10

(iv.)An even number

Q2. Tickets numbered 2,3,4,5----100,101 are placed in a box and mixed thoroughly.One ticket is drawn at random from the box.Find the probability that the number on the ticket is:

(i.)   An even number

(ii.)   A number less than 16

(iii.)  A number which is a perfect square.

(iv.)  A prime number less than 40.

Q3. One card is drawn from a well shuffled deck of 52 cards. Find the probability of drawing:

(i.)   An ace

(ii.)  A  ‘4’ of spades

(iii.)  A ‘9’ of black suit

(iv.)  A red king

Q4. Find the probability of getting 53 Fridays in a leap year.

Q5. The king,the queen,the jack and 10,all of spades are lost from a pack of 52 playing cards. A card is drawn at random from the remaining well shuffled pack. Find the probability of getting:

(i.)        Red card

(ii.)       King

(iii.)      Black card

Area related to circles(02-01-2012)

Surface areas and Volumes(02-01-2012)

Mathematics Assignment - Arithmetic Progression(11-11-11)

Mathematics Assignment Chapter: Introduction to Trignometric

Maths Assignment: Chapter - Application of trignometric

Maths Assignment: Chapter - Quadratic Equations Part 1

Maths Assignment: Chapter - Quadratic Equations Part 2

Thanks to http://www.hansrajmodelschool.org

CBSE Ch:Probability X Mathematics Assignments

 X Mathematics Assignments Chapter: probability

Directions for 1 – 4: State true or false

1. If the probability of a candidate winning an election is 80%, then the probability of the opponent winning the election is also 80%.

2. If two dice are thrown simultaneously then the total number of outcomes is 12.

3. A throws a coin twice and ‘B’ throws a similar coin thrice, the possibility of getting ‘all heads’ is more for ‘B’ than ‘A’.

4. The sum of the probability of an event happening and the same not happening is always the same.

1. F                2. F                3. F                            4. F

5. An unbiased die is thrown. What is the probability of getting?

(i) an even number?  (ii) a multiple of 5? (iii) an even number or a multiple of 3? (iv) a multiple of 2 and 3?

6. Two unbiased coins are tossed simultaneously. What is the probability of getting(i) all heads? (ii) at least one head?  (iii) at the most one tail? (iv) at least one head and one tail?

7. Two dice are thrown simultaneously. What is the probability of getting?

(i) an odd number as the sum? (ii) a total of at least 10? (iii) the same number on both dice? (iv) a sum greater then 10?

8. Find that the probability of a leap year selected at random will contain 53 Mondays.

9. One card is drawn from a pack of 52 cards. What is the probability of getting

(i) an ace or a king? (ii) a red card and a king? (iii) a face card? (iv) a king or a queen or a jack?

10. All the face cards are removed from a pack of 52 cards and are then shuffled well. One card is selected from the remaining cards. What is the probability of

(i) getting an ace? (ii) getting a red card? (iii) getting 10 of spade? (iv) getting a number less than 5?

11. A bag contains five red balls and some white balls. If the probability of drawing a white ball is double that of a red ball, find the number of white balls in the bag.

12. A bag contains 20 balls out of which ‘x’ are red.

(i) If one ball is drawn at random, what is the probability that it will not be a white ball?

(ii) If five more red balls are added, the probability of drawing a red ball will become 40%. Find the number of balls which are not red.

13. 1000 tickets of a lottery were sold and there are three prizes in the lottery. If Sachin has purchased one ticket, what is the probability of his winning a prize?

14. 26 cards marked with English letters A to Z (one letter on each card) are shuffled well. If one card is selected at random, what is the probability of getting?

(i) a vowel?    (ii) a letter in the word PROBABILITY?

50 Mohan and Salim are friends. What is the probability that both will have

(i) the same birthday?     (ii) different birthdays?

(iii) their birthday on the same weekday?

15. A jar contains 24 marbles. Some are blue and the others are green. If a marble is drawn at random, the probability that it is green is 3/2 . Find the number of blue marbles in the jar.

52. What is the probability that a number selected at random from the numbers 10, 20, 20, 30, 30, 30, 40, 40, 40, 40 will be their mean?

16. A game consists of tossing a coin three times and noting the outcome each time. If one gets the same outcome in all the three tosses, then he wins. What is the probability of a participant winning the game?

16. While shuffling a pack of 52 cards, Khushi dropped one card by mistake. What is the probability of the dropped card being a red queen?

17. A die is numbered in such a way that its faces show the numbers 1,2,2, 3, 3, 6. It is thrown twice and the total score in two throws is noted. Find the sample space of the experiment. What is the probability that the total score  (i) is even?  (ii) is odd? (iii) is at least 5?

18. A circle of diameter 7 cm is drawn inside A rectangle of dimensions 15 cm × 7 cm . If a coin is dropped randomly inside the rectangle, what is the probability that the coin lands inside the  circle?

19. A piggy bank contains one hundred 50 p coins, fifty Re 1 coins, twenty Re 2 coins and ten Re 5 coins. If it is turned upside down one coin will fall. When Gautam turned it up side down for the first time, he got a Rs 2 coin. If he turns it upside down for a second time, what is the probability of getting

(i) an amount more than Re 1? (ii) a Rs 5 coin?(iii) a 50 p coin or Re 1 coin? (iv) at least one rupee?

20. In a game, Raju asks his friend Karan to write down a two-digit number secretly. What is the probability that Karan will write a doublet? What is the probability that Karan’s number is divisible by 2, 3 and 5?

21. Two customers, Mohan and Nishu are visiting a shop in the same week (Sunday to Saturday). Each is likely to visit the shop on any day as on any other day. What is the probability that both will visit the shop on (i) the same day? (ii) Consecutive days?

ASSIGNMENT CLASS X APPLICATIONS OF TRIGONOMETRY

1. A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 10 m. Find the height of the tree before it was broken.

2. From the top of a building 60 m high the angles of depressions of the top and the bottom of a tower are observed to be 30° and 60°. Find the height of the tower.

3. From a point on the ground the angles of elevation of the bottom and top of a water tank kept at the top of 20 m high tower are 45° and 60°. Find the height of the water tank.

4. A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 40 meters away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and the width of the river.

5. The angle of elevation of the top of a tower from a point A on the ground is 30°. On moving a distance of 20 metres towards the foot of the tower to a point B, the angle of elevation increases to 60°.Find the height of the tower and the distance of the tower from the point A.

6. A flagstaff stands on the top of a 5 m high tower. From a point on the ground, the angle of elevation of the top of the flag-staff is 60° and from the same point, the angle of elevation of the top of the tower is 45°. Find the height of the flag-staff.

7. The shadow of a tower, when the angle of elevation of the sun is 45°, is found to be 10 m longer than when it was 60°. Find the height of the tower.

8. On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are60° and 30° respectively. Find the height of the tower and the flag pole mounted on it.

9. A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elevation of 30°. A girl standing on the roof of 20 metre high building, finds the angle of elevation of the same bird to be 45°. Both the boy and the girl are on opposite sides of the bird. Find the distance of bird from the girl.

10. From the top of a building 15 m high the angle of elevation of the top of a tower is found to be 30°.From the bottom of the same building, the angle of elevation of the top of the tower is found to be 60°.Find the height of the tower and the distance between the tower and the building.

11.At a point on the level ground the angle of elevation of a vertical tower is found to be such that its tangent is 5/12. On walking 192 m towards the tower, the tangent of the angle is found to be3/4 . Find the height of the tower.

12. Two men on either side of a cliff 80 m high observe the angles of elevation of top of the cliff to be 30° and 60° respectively. Find the distance between the two men.

13. An aeroplane, when 1500 m high passes vertically above another aeroplane at an instance when the angles of the two aeroplanes from the same point on the ground are 60° and 45° respectively. Find the vertical distance between the two aeroplanes.

14. The angles of elevation of the top of a tower from two points on the ground at distances 9m and 4m from the base of the tower are in same straight line with it are complementary. Find height of the tower.

15. The horizontal distance between two towers is 140 m. 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 60 m, find the height of the first tower.

CBSE Class X Self Evaluation Tests For Maths : Real Numbers

1. The values of the remainder r, when a positive integer a is divided by 3 are 0 and 1 only. Justify your answer

No. According to Euclid’s division lemma,

a = 3q + r, where 0 ≤ r < 3 and r is an integer. Therefore, the values of r can be 0, 1 or 2.

2. Can the number 6n, n being a natural number, end with the digit 5? Give reasons.

 No, because 6ⁿ = (2 × 3)ⁿ = 2ⁿ × 3ⁿ, so the only primes in the factorization of 6ⁿ are 2 and 3, and not 5. Hence, it cannot end with the digit 5.

3. Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.

No, because an integer can be written in the form 4q, 4q+1, 4q+2, 4q+3.

4. “The product of two consecutive positive integers is divisible by 2”. Is this statement true or false? Give reasons.

True, because n (n+1) will always be even, as one out of n or (n+1) must be even

5. “The product of three consecutive positive integers is divisible by 6”. Is this statement true or false”? Justify your answer.

True, because n (n+1) (n+2) will always be divisible by 6, as at least one of the factors will be divisible by 2 and at least one of the factors will be divisible by 3.

6. Write whether the square of any positive integer can be of the form 3m + 2, where m is a natural number. Justify your answer.

No. Since any positive integer can be written as 3q, 3q+1, 3q+2,

therefore, square will be 9q2 = 3m, 9q2 + 6q + 1 = 3 (3q2 + 2q) + 1 = 3m + 1, 9q2 + 12q + 3 + 1 = 3m + 1.

7. A positive integer is of the form 3q + 1, q being a natural number. Can you write its square in any form other than 3m + 1, i.e., 3m or 3m + 2 for some integer m? Justify your answer.

No. (3q + 1)2 = 9q2 + 6q + 1 = 3 (3q2 + 2q) = 3m + 1.

8. The numbers 525 and 3000 are both divisible only by 3, 5, 15, 25 and 75. What is HCF (525, 3000)? Justify your answer.

HCF = 75, as HCF is the highest common factor

9. Explain why 3 × 5 × 7 + 7 is a composite number.

3×5×7+7 = 7 (3×5 + 1) = 7 (16), which has more than two factors

10. Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.

No, because HCF (18) does not divide LCM (380).

11. Without actually performing the long division, find if 987/10500 will have terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer.

Terminating decimal expansion, because 987/ 10500 = 47/ 500  and 500 =5³ 2²

12. A rational number in its decimal expansion is 327/7081. What can you say about the prime factors of q, when this number is expressed in the form p/q ? Give reasons.

Since 327.7081 is a terminating decimal number, so q must be of the form 2^m.5ⁿ;m, n are natural numbers

Self Evaluation Tests Paper For Maths : Real Numbers-2

CBSE TEST PAPER MATHEMATICS (Class-10) SIMILAR TRIANGLE

1. In an equilateral Δ ABC, the side BC is trisected at D. Prove that 9AD2 = 7AB2

2.  P and Q are points on sides AB and AC respectively, of ΔABC. If AP = 3 cm,PB = 6 cm, AQ = 5 cm and QC = 10 cm, show that BC = 3 PQ.

3. The image of a tree on the film of a camera is of length 35 mm, the distance from the lens to the film is 42 mm and the distance from the lens to the tree is 6 m. How tall is the portion of the tree being photographed?

4. . Prove that in any triangle the sum of the squares of any two sides is equal to twice the square of half of the third side together with twice the square of the median, which bisects the third side.

5.  If a straight line is drawn parallel to one side of a triangle intersecting the othertwo sides, then it divides the two sides in the same ratio.

6. If ABC is an obtuse angled triangle, obtuse angled at B and if AD ^ CB Prove that  AC²=AB²+ BC²+2 BC x BD

7. If a straight line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side.

8. ABCD is a quadrilateral with AB =AD. If AE and AF are internal bisectors of ΔABC, D and E are points on AB and AC respectively such that AD/ DB = AEC/EC and ΔABC is isosceles.

9. In a ΔABC, points D, E and F are taken on the sides AB, BC and CA respectively such that DE IIAC and FE II AB.

10. . Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle.

11. If a perpendicular is drawn from the vertex of a right angled triangle to its hypotenuse, then the triangles on each side of the perpendicular are similar to the whole triangle.

12. A man sees the top of a tower in a mirror which is at a distance of 87.6 m from the tower. The mirror is on the ground, facing upward. The man is 0.4 m away from the mirror, and the distance of his eye level from the ground is 1.5 m. How tall is the tower? (The foot of man, the mirror and the foot of the tower lie along a straight line).

13. In a right Δ ABC, right angled at C, P and Q are points of the sides CA and CB respectively, which divide these sides in the ratio 2: 1. Prove that

(I) 9AQ²= 9AC²+4BC² (II) 9 BP²= 9 BC²+ 4AC² (III) 9 (AQ²+BP²) = 13AB²

14. ABC is a triangle. PQ is the line segment intersecting AB in P and AC in Q such that PQ parallel to BC and divides Δ ABC into two parts equal in area. Find BP: AB.

15. P and Q are the mid points on the sides CA and CB respectively of triangle ABC right angled at C. Prove that4(AQ²+BP²) = 5 AB²

CBSE CLASS 10 MCQ TRIGONOMETRY

1. If cos A = 4/5 , then the value of tan A is

(A) 3/5             (B)3/4              (C)4/3              (D)5/3

2. If sin A = 1/2 , then the value of cot A is

(A) 3                (B) 1/3             (C) 3/2             (D) 1

3. The value of the expression [cosec (75° + q) – sec (15° – q – tan (55° + q+ cot (35° – q)] is

(A) – 1             (B) 0                (C) 1                (D) 3/2

4. Given that sinq= a/b , then cosq is equal to



5. If cos (a + b) = 0, then sin (a - b) can be reduced to

(A) cos b                     (B) cos 2b                   (C) sin α                      (D) sin 2a

6. The value of (tan1° tan 2° tan3° ... tan 89°) is

(A) 0                (B) 1                (C) 2                            (D)1 / 2

7. If cos 9a= sinα and 9a < 90°, then the value of tan5a is

(A) 1/√3                       (B) √ 3                         (C) 1                (D) 0

8. If DABC is right angled at C, then the value of cos (A+B) is

(A) 0                (B) 1                            (C) 1/2                         (D)√3/2

9. If sinA + sin²A = 1, then the value of the expression (cos²A + cos⁴A) is

(A) 1                (B) 1/2                         (C) 2                            (D) 3

10. Given that sina= 1/2 and cosb =1/2 , then the value of (a + b) is

(A) 0°                           (B) 30°                         (C) 60°            (D) 90°

11. The value of the expression [sin² 22⁰ sin² 68⁰ / cos² 22⁰ cos² 68⁰       +  sin ² 63⁰ cos  63⁰ sin 27⁰ ]   is         

(A) 3                (B) 2                (C) 1                            (D) 0

12. If 4 tanq = 3, then [4sinq - cosq ] / [4sinq + cos q ] is equal to

(A) 2/3                                     (B) 1/3                         (C) 1/2             (D) 3/4

13. If sinq – cosq = 0, then the value of (sin⁴q + cos⁴qθ) is

(A) 1                (B) 3/4                         (C) 1/2                         (D) 1/4

14. sin (45° + q) – cos (45° – q) is equal to

(A) 2cosq                    (B) 0                (C) 2 sin q                   (D) 1

15. A pole 6 m high casts a shadow 2 √3m long on the ground, then the Sun’s elevation is

(A\) 60°                        (B) 45°                         (C) 30°                        (D) 90°