Summative Assessment-I CLASS-10th GUESS PAPERS

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Grooming at the APEX INSTITUTE is done methodically focusing on understanding of the subject, tricks of tackling the questions and above all enthusing students with self confidence, ambition… Full description 

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Mathematics Question Bank

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Ch 8 _Trigonometry

Cbse Class 10th Sample Papers

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Sample Test Paper (for Summative Assessment-1 Class - X)

(Maths & Science)

New Batch Starts from first week of Oct

Master your semester with Scribd & The New York Times Special offer for students: Only $4.99/month.

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Ch 8 _Trigonometry


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SUMMATIVE ASSESSMENT-I 2014-15 Class-X MATHEMATICS TIME : 3 Hrs

Maximum Marks

Instructions:

General Instructions: Instructions: (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided into four sections A,B,C and D.

Section A comprises of 10 questions of 1 mark each. Section B comprises of 8 questions of 2 m each. Section C comprises of 10 questions of 3 marks each and section D comprises of 6 quest 4 marks each. (iii) Use of calculator is not permitted.

SECTION - A Question numbers 1 to 10 carry 1 mark each. For each of the questions fouralternative choices have been provided of which only one is correct. have to select the correct correc t choice.

1. If x2 + 2kx + 4 =0 has a root x=2, then the value of k is ? (A) -1 (B) - 2 (C) 2 2. Which term of the A.P. 92, 88, 84, 80, ..... is 0 ? (A) 23 (B) 32 (C) 22

Master your semester with Scribd & The New York Times

(D)

-4

(D) 24  Read Free Foron 30this Days Sign up to vote title

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Special offer Onlyand $4.99/month. 3.for If students: the height length of the shadow of a man are the same, then the angle of eleva

the sun is

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is. (A)

60 TT cm2

(B)

of 19


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68 TT cm2

Ch 8 _Trigonometry


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(C)

120 TT cm2

(D)

136 TT cm2

7. The length of the tangent drawn from a point 8 cm away from the centre of a circle, of 6 cm, is : (A) cm (B) cm (C) 10 cm (D) 5 cm

8. In Fig. 1, if from an external point T, TP and TQ are two tangents to a circle with with cen so that
(A) 60°

(B) 70°

(C) 80°

(D) 90°

9. In Fig, P divides AB internally in the ratio :

Master your semester with Scribd & The New York Times (A) : 4 (B) : 3 (C) 3 : 7 Special offer for3students: Only4$4.99/month.

(D) 4 : 7


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Ch 8 _Trigonometry


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12 . Find the common difference of an A.P. whose first term is write its 4th term.



and the 8th term is

13. A tower stands vertically on the ground. From a point on the ground which is 60 m from the foot of the tower, the angle of elevation of the top of the tower is found to be 60 Find the height of the tower.

14. In Fig, arcs are drawn by taking vertices A, B and C of an equilateral triangle of side1 to intersect the sides BC, CA and AB at their respective mid-points D, E and F. Find the of the shaded region (Use TT=3.14)

15. Prove that the line segment joining the points of contact of two parallel tangents to a is a diameter of the circle.OR In Fig. 4, 0 is the centre of a circle and BCD is tangent to i Prove that


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16. that the point P (-4, 2) lies on the line segment joining the points A (-4, 6) andB Special offer forShow students: Only $4.99/month. 6).

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Ch 8 _Trigonometry


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OR

Solve for x : 6 x2 + 7x - 10=0 20. How many terms of the A.P. 9, 17, 25, ..... , must be taken to get a sum of 450 ? 21. Draw a right triangle with sides of length 5 cm and 4 cm making an right angle. Construct another triangle whose sides are first triangle.

times the corresponding sides of the

22. A cylindrical pipe has inner diameter of 4 cm and water flows through it at the rate per minute. How long would it take to fill a conical tank, with with diameter of base as 80 depth 72 cm ? OR

A hemispherical hemispherical bowl bowl of internal internal diameter diameter 36 cm. cm. is full of of liquid. This liquid liquid is to be fil cylindrical bottles of radius 3 cm and height 6 cm. How many such bottles are required to empty the bowl ? 23. Find the probability that a non leap year chosen at random has (i) 52 Sundays (ii) 53 Sundays

24. All the face cards of spades are removed from a pack of 52 playing cards and then t pack is shuffled well. A card is then drawn at random from the remaining pack of card the probability of getting (i) a black face card, (ii) a queen. OR

An urn contains contains 8 red, red, 6 white, white, 4 black black balls. A ball is drawn drawn at random from from the urn. urn. Fin probability that the drawn ball is.  (i) red or white (ii) neither black nor white Read Free Foron 30this Days Sign up to vote title

Master your semester with Scribd & The25.New York Times In Fig.5, in ΔABC, D and E are the mid -points Special offer for students: Only $4.99/month.

the length of DE. Prove that DE=

AB.

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Useful  Not useful sides of the BC and AC respectively. Cancel anytime.

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Ch 8 _Trigonometry


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28. Find the area of the shaded region in Fig. 7 if BC=BD=8 cm, AC=AD=15 cm and 0 is centre of the circle. (Take TT=3.14)

SECTION - D Question numbers 9 to carry marks each.

Master your semester with Scribd  Read Free Foron 30this Days Sign up to vote title 29. The product of Tanay's age (in years) five years ago and his age ten year lateris & The16.Determine New York Times  Useful  Not useful Tanay's present age. Special offer for students: Only $4.99/month.

Cancel anytime.

30. In November 2009, the number of visitors to a zoo increased daily by 20. If a total of1

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Ch 8 _Trigonometry


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A solid is in the form form of a right right circular cylinder with hemispherical hemispherical ends. ends. The total heig the solid is 19 cm and the diameter of the cylinder and the hemispheres is7 cm. Find th volume and total surface area of the solid.

33. In Fig. 8, two circular flower beds have been shown on two sides of a square lawnA of side 56 m. If the centre of each circular flower bed is the point of intersection0 of the diagonals of the square lawn, find the sum of the areas of the lawn and flower beds

34. A tree is broken by the wind. The top struck the ground at an angle of 30 and at distance of 30 metres from its root. Find the whole height of the tree. (Use √3 =1.732) OR

Find the height of a mountain if the elevation of its top at an unknown distance from the is 60° and at a distance 10 km further off from the mountain, along the same line, the an elevation is 30° .



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Ch 8 _Trigonometry


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Maximum Marks

Instructions:

General Instructions: Instructions: (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided into four sections A,B,C and D.

Section A comprises of 10 questions of 1 mark each. Section B comprises of 8 questions of 2 m each. Section C comprises of 10 questions of 3 marks each and section D comprises of 6 quest 4 marks each. (iii) Use of calculator is not permitted.

SECTION - A

Question numbers 1 to 10 carry 1 mark each. For each question four choic provided of which only one is correct. You have to select the correct choice. 1. For

(A) 14

what (B)

value

of

(C)

Which of 2. (A) 13, 8, 3, -2, -7, -12

k

will

be

a

root

of

3 x 2

(D) -14 the

following

Master your semester with Scribd & The(C)New York Times (D) Special offer for students: Only $4.99/month.

3. If a pole of height 6 m casts a shadow

is not an (B) 10.8, 11.2, 11.6,  Read Free Foron 30this Days Sign up to vote title

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m long on the ground, then the sun's

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them (A) 105°

(B)

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65°


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(C)

Ch 8 _Trigonometry


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should 95°

(D)



75°

6. The angle of elevation of the top of a tower from a point on the ground is 45° observer is 42 m away from the foot of the tower, the height of the tow (A) 63 m (B) 21 m (C) 84 m (D) 42 m 7.

In the figure, if the semiperimeter of .:ΔABC= 23 cm then AF+BD+CE

(A) 46 cm

(B) 11.5 cm

(C) 23 cm

(D) 34.5 cm

8. In the figure, PT is a tangent to the circle with centre O. If PT=30 cm and diameter is 32 cm, then length of line segment 0P will will

(A) 68 cm

(B) 34 cm

(C) 17 cm

(D) 34.8 cm

Master your semester with Scribd 9. The circumference of a circle is 100 cm. & The New York Times (A) cm (B) cm Special offer for students: Only $4.99/month.

(C)

(D)

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Foron 30 Days The sideRead of aupFree square inscribed Sign to vote this title in the

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12. Find

the

sum

of

of 19

the


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first

23

Ch 8 _Trigonometry


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terms

of

the

A.P

:

7,

10

2

,

14,

long just reaches the top of a vertical wall. If the ladder makes an a 13 . A ladder 15 m long 60 with the wall, find the height of the

swept by the minute hand 14. The minute hand of a clock is 21 cm long. Find the area swept face of the clock from 7.00 am to 7.05

15. Prove that the tangents drawn at the ends - points of a diameter of a circle are parall OR

In the figure, a quadrilateral ABCD is drawn to circumscribe a circle. Prove thatAB+CD=AD+BC.

16. Find the value of x, if the distance between the points (x, -1) and (3, -2) is x+5.

17. If the point C (-1, 2) divides internally the line segment joining A (2, 5) and B (x, y) in ratio 3 : 4, then find the coordinates of B.  Read Free Foron 30this Days Sign up to vote title  and a  cone in the ratio o 18. The radii of the circular bases of a right circular cylinder Not are useful  Useful Cancel anytime. and their heights are in the ratio of 2 : 3. What is the ratio of their volumes ?


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20. Determine 'a' so that 2a+1, a2+a+1 and 3a2-3a+3 are consecutive terms of an A.P.

21. Draw a pair of tangents to a circle of radius 3.5 cm which are perpendicular to each o 22. Show that the points (7, 3), (3, 0), (0, -4) and (4, -1) are the vertices of a rhombus. 23. Find the area of .:lABC whose vertices are A (4, 4), B (0, 0) and C (6, 2).

has a die whose six six faces show show the letters letters as given below below : 24. A child has A B C D E A The die is thrown at random once. What is the probability of getting (i) A (ii) E. 25. Three coins are tossed together. Find the probability of getting at least two heads.

26. A solid metallic sphere of diameter 21 cm is melted and recast into a number of sma cones, each of diameter 7 cm and height 3 cm. Find the number of of cones so formed.

27. A piece of wire that has been bent in the form of a semicircle including the bounding diameter is straightened and then bent in the form of a square. The diameter of the sem is 14 cm. Which has a larger area, the semi-circle or the square. Also find the difference between them. OR

In the figure, ABC is a triangle right angled at A. Semicircles are drawn on AB, ACand ACand diameters. Find the area of the shaded region.



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Special offer forProve students: Onlythe $4.99/month. that parallelogram circumscribing a circle is rhombus. 28.

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

In the figure PO ? QO . The tangents to the circle with centre 0 at P and Q intersect at a T. Prove that PQ and 0T are right bisectors of each other.

SECTION - D Question numbers 29 to 34 carry 4 marks each.

which is 100 m wide. The 29. Two pillars of equal heights are on either side of a road, which of elevation of the top of the pillars are 60 and 30 at a point on the road between the Find the position of the point between the pillars on the road and the height of the pillars OR

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

30. For what value of n, the nth terms of the A.P. 63, 65, 67, .......... and 3, 10, 17, ......... equal ? Also find that term. OR

A ladder has has rungs 25 cm apart. apart. The rungs rungs decrease decrease uniformly uniformly in length length from from 45 cm at bottom to 25 cm at the top (see figure). If the top and bottom rungs are 2.5 m apart, wh the length of the wood required for the rungs ?



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building is in the form of a right circular cylinder cylinder surmounte surmounted d by a hemispherica hemispherica 32. A building both having the same base radii. The base diameter of the dome is equal to height of the building. Find the height of the building, if it contains

of the

m 3 of air.

OR

A well whose whose diameter diameter is 7 m has been been dug 22.5 22.5 m deep and the earth earth dugout dugout is used used an embankment around it. If the height of the embankment is 1.5 m. Find the width embankment.

33. A shuttle cock used for playing Badminton has the shape of a frustum of a cone mou on a hemisphere (see figure). The diameters of the ends of of the frustrum are 5 cm cm and2 the height of the entire shuttle cock is 7 cm. Find the external surface area.

34. Prove that the tangents to a circle from an external point are equal.



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Ch 8 _Trigonometry


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Maximum Marks

Instructions:

General Instructions: Instructions: (i) All questions are compulsory.

(ii) The question paper consists of 34 questions divided into four sections A,B,C and D. Section comprises of 10 questions of 1 mark each. Section B comprises of 8 questions of 2 marks each. Section C comprises of 10 questions of 3 marks each and section D comprises of 6 questions o marks each. (iii) Use of calculator is not permitted.

SECTION - A

Questions number 1 to 10 carry 1 mark each. For each of the questions 1 to 10 fo alternative choices are given, of which only one is correct. Select the correct cho 2 1. One of the roots of the quadratic equation 6 x - x - 2=0 is :

(A)

(B)

(C)

(D) -1

2. Which term of the A.P. 100, 90, 80, . . . . . . . is zero ? (A) 5th (B) 6th (C) 10th (D) 11th  Read Free Foron 30this Days Sign up to vote title  0, if  AB=7 cm, BC=5 cm, A 3. In Fig. 1, AQ, AR and BC are tangents to circle with centre Not useful  Useful Cancel anytime. cm, length of the tangent AQ is : Special offer for then students: Only $4.99/month.


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(A) 5 cm

(B) 7 cm

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(C) 8.5 cm

Ch 8 _Trigonometry


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(D) 17 cm

4. In Fig. 2, AP and AQ are tangents to the circle with centre 0, from an external point A. APQ is equal equal to : ∠PAQ = 70° then ∠

(A) 35°

(B) 55°

(C) 110°

(D) 125°

5. The angle between two tangents drawn from an external point to a circle is 110°. The subtended at the centre by the segments joining the points of contact to the centre of cir (A) 70° (B) 110° (C) 90° (D) 55°  Read Free Foron 30this Days Sign up to vote title

Master your semester with Scribd  & The6.New York Times Useful Not useful   The angle of depression from the top of a tower 12 m high, at a point on the ground is Special offer for students: The distanceOnly of $4.99/month. the point from the top of the tower is :

(A) 12 m

(B) 6 m

(C)

m

(D) 24 m

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AB'= 10. Given a triangle with side AB=8 cm. To get a line segment AB'= divide the line segment AB in the ratio : (A) 3 : 4 (B) 4 : 3 (C) 1 : 3 (D) 3 : 1

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of AB, it is require

SECTION - B Questions number 11 to 18 carry 2 marks each.

11. Find the values of k for which the following quadratic equation has two equal roots.2 + 3=0 12. Find the sum of first twelve multiples of 7.

a 13. Prove that the tangents drawn at the end points of a chord of a circle make equal an with the chord. 14. Two coins are tossed together. Find the probability of getting at least one tail.

15. The points A (3, 2) and B (2, -3) are equidistant from a point P(x, y). Find the relation between x and y. 16. Find the value of k for which the points A (7, -2), B (5, 1) and C (3, k) are collinear. OR

In what ratio is the line segment joining the points P (-2, -3) and Q (3, 7) divided by the ?

17. In Fig. 3 the chord AB of a circle of radius 10 cm subtends an angle of 90° at the cen Find the area of the segment ACBA. (Take π=3.14)



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19. Solve for x : a(a 2 + b2)x2 + b2x - a=0 OR

A two digit digit number is is such that that the product product of of the digits digits is 18. When 63 is subtracte subtracted d fro number, the digits interchange their places. Find the numbers. 20. Solve for x :

21. Construct an isosceles triangle ABC with Base BC=6cm, AB=AC and4 ∠ A =90°. D

another similar triangle whose sides are

of the sides of ΔABC.

22. Prove that the parallelogram circumscribing a circle is a rhombus. 23. An electric pole is 10 m high. If its shadow is of the sun at that time.

m in length. Find the angle of

OR

A circus artist artist is climbing climbing a rope rope 12 m long long which is tightly stretched and tied from the t vertical pole to the ground. Find the height of the pole if the angle made by the rope wit ground is 30°.

24. Cards numbered from 1 to 64 are placed in a box. A card is drawn at random from th Find the probability that the card number on the card drawn is a perfect cube.

25. Find the area of the rhombus ABCD whose vertices are A(3, 0), B (4, 5), C (-1, 4) an 2, -1).

26. Find the area of the triangle formed by the mid points of the sides of the triangle ABC whose vertices are A (0, -1), B (2, 1) and C (0, 3).  Read Free Foron 30this Days Sign up to vote title

Master your semester with Scribd  & The27.New Times useful  Useful  Not In Fig.York 4, a circle of radius 7 cm is inscribed in a square. Find the area of the shaded Special offer for students: Only $4.99/month. region.

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form of a cone cone of radius radius 3.5 cm surmounted surmounted on a hemisphere hemisphere of same 28. A toy is in the form radius. The total height of the toy is 15.5 cm. Find the total surface area of of the toy. OR

How many solid spheres of diameter 6 cm are required to be melted to form a solid me cylinder of height 45 cm and diameter 4 cm ? SECTION - D Questions 9 to carry 4 marks each. 29. Solve the following equation for x. 9x2 - 9(a+b)x + (2a 2 + 5ab + 2b 2)=0 OR

The sum of the squares of two consecutive odd natural numbers is 130. Find the numb whose nth term is given by 3 + 30. Find the sum of the first 31 terms of an A.P. whose

n

OR

The sum of the third and seventh term of an A.P. is 6 and their product is 8. Find the su the first sixteen terms of the A.P.

31. Prove that tangent at any point of a circle is perpendicular to the radius through the p contact.

sphere of radius radius 3 cm is melted and drawn drawn into a long long wire wire of uniform uniform circula 32. A solid sphere

Master your semester Scribd cross-section. If the length with of the wire is 36 m, find its radius.  Read Free Foron 30this Days Sign up to vote title  & The33.New York Times Useful  Not useful  An An aeroplane aeroplane at an an altitude altitude of 200 m observes observes the angles angles of depressio depression n of two oppos Cancel anytime.

Special offer for students: Only $4.99/month. points on two banks of the river to be 45° and 60°. Find, in metres, the width of the rive

=1.732)

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Our Result reflects our excellence and credibility Dhwani Jain

AIR-427(GE)

AIR 1823(GE)

AIR-521(GE)

Dhwani Jain is Studying in N.U.S.(National Univ. of Singapore) Ranked 2nd University in Asia.She was our Two year classroom program Student.

S

National University of Singapore

IIT-JEE Shubham Mukherjee

IIT-JEE Prerna Kashyap

Siddhant Rathore Siddhant Rathore

Score

206

Score

159

158

Score

Score

158

Student of Three year IIT-Advanced classroom Programme

AIR 5982 219 BITS Score: 329 IIT-Main Score: 219

VIT Rank : 14 Score

154

Pranit Kaul

Score

154

Abhik Setia

Dravin Verma

Lakshay Gupta

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Rishabh Gupta Roll No. 5655367

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Siddhant Rathore Roll No. 5654166

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