This Question Paper consists of 36 questions including figures and printed pages + Graph sheet. ß Ÿ- òê apple 36 Ÿ ÃÕÊ ÁøòÊ fl ÈÁŒ à Îc U + ª Ê» ÊË U Ò Roll No. ŸÈ Ê Day and Date of Examination UˡÊÊ Ê ÁŒŸ fl ÁŒŸÊ MATHEMATICS (ªÁáÊÃ) () Code No. Êapple«U Ÿ.5/AS/ Set A Signature of Invigilators. ÁŸ UËˇÊ Êapple apple SÃÊˇÊ U. General Instructions :. Candidate must write his/her Roll Number on the first page of the Question Paper.. Please check the Question Paper to verify that the total pages and total number of questions contained in the Question Paper are the same as those printed on the top of the first page. Also check to see that the questions are in sequential order. 3. For the objective type of questions, you have to choose any one of the four alternatives given in the question i.e. (A), (B), (C) or (D) and indicate your correct answer in the Answer-Book given to you.. All the questions including objective type questions are to be answered within the allotted time and no separate time limit is fixed for answering objective type questions. 5. Making any identification mark in the Answer-Book or writing Roll Number anywhere other than the specified places will lead to disqualification of the candidate. 6. Write your Question Paper code No. 5/AS/-A on the Answer-Book. 7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can answer in any one of the languages listed below : (b) English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi, Oriya, Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi. You are required to indicate the language you have chosen to answer in the box provided in the Answer-Book. If you choose to write the answer in the language other than Hindi and English, the responsibility for any errors/mistakes in understanding the question will be yours only.!5/as/--a! [ Contd...
Ê Êãÿ ŸÈŒapple Ê. UˡÊÊÕË Ÿ òê apple apple Îc U U ŸÊ ŸÈ Ê fl ÿu Á πapple. Î ÿê Ÿ òê Êapple ÊÚ ø apple Á Ÿ òê apple È Îc UÊapple ÃÕÊ ŸÊapple Ë ÃŸË Ë ÅUÿÊ Ò Á ÃŸË Õ Îc apple apple U U Ë Ò ß ÊÃ Ë ÊÚ ø Ë U apple Á Ÿ Á UM apple Ò 3. flsãèáÿc U ŸÊapple apple Ê Êapple øê U Áfl À Êapple (A), (B), (C) ÃÕÊ (D) apple apple Êappleß ûê øèÿÿê Ò ÃÕÊ ŒË ªß ûê U- ÈÁSUÃ Ê apple Ê Ë ûê Á Áπ U. flsãèáÿc U ŸÊapple apple ÊÕ- ÊÕ Ë ŸÊapple apple ûê ÁŸœÊ Á Uà flᜠapple Ëà U Ë ŒappleŸapple Ò flsãèáÿc U ŸÊapple apple Á ª apple ÿ Ÿ Ë ÁŒÿÊ Ê ªÊ 5. ûê U- ÈÁSUÃ Ê apple øêÿ-áøq ŸÊŸapple ÕflÊ ÁŸÁŒ c U SÕÊŸÊapple apple ÁÃÁ UÄÃ Ë Ë ŸÈ Ê Á πÿapple U UˡÊÊÕË Êapple ÿêappleçÿ U UÊÿÊ ÊÿappleªÊ 6. ŸË ûê U- ÈÁSUÃ Ê U Ÿ òê Ë Êapple«U ÅÿÊ 5/AS/-A Á πapple 7. ( ) Ÿ òê apple fl Á ŒË/ ª apple Ë apple Ò Á» U Ë, ÿáœ Ê øê apple ÃÊapple ŸËøapple ŒË ªß Á Ë Ê Ê apple ûê Œapple Ãapple Ò ª apple Ë, Á ŒË, ŒÍ, Ê Ë, ª Ê, ÃÁ, ÿê, ãÿ«, Ãapple ȪÈ, UÊ UË, Á«ÿÊ, ªÈ UÊÃË, Êapple áêë, ÁáÊ È UË, Á ÿê, Ÿapple Ê Ë, Ë UË, S Î Ã ÊÒ U Á œë Î ÿê ûê U- ÈÁSÃ Ê apple ÁŒ ª ÊÚÄ apple Á πapple Á Ê Á Ê Ê apple ûê U Á π U apple Ò (π) ÿáœ Ê Á ŒË fl ª apple Ë apple ÁÃÁ UÄà Á Ë ãÿ Ê Ê apple ûê U Á πãapple Ò ÃÊapple Ÿ Êapple ÊŸapple apple ÊappleŸapple flê Ë òêèá UÿÊapple /ª ÁÃÿÊapple Ë Á ê appleuœê Ë apple fl Ê Ë ÊappleªË!5/AS/--A! [ Contd...
MATHEMATICS (ªÁáÊÃ) () Time : ½ Hours ] [ Maximum Marks : 85 ÿ ½ ÉÊá appleu ] [ ÍáÊÊZ 85 Instructions : () Question Numbers ( - 0) are Multiple Choice Questions. Each question carries one mark. For each question, four alternative choices A, B, C and D are provided, of which only one is correct. You have to select the correct alternative and indicate it in the answer-book provided to you by writing (A), (B), (C) or (D) as the case may be. Q. No. to 5 also carry one mark each. () Question Numbers (6-5) carry marks each. (3) Question Numbers (6-33) carry marks each. () Question Numbers (3-36) carry 6 marks each. (5) All questions are compulsory. ÁŸŒapple Ê () Ÿ ÅÿÊ ( - 0) à ÈÁfl À Ë Ÿ (Multiple Choice Questions) Ò àÿapple Ÿ Ê Ò àÿapple Ÿ apple øê U Áfl À A, B, C ÃÕÊ D ÁŒÿapple ªÿapple Ò, Á Ÿ apple apple apple fl Ë Ò Ê Êapple Ë Áfl À øèÿÿê Ò ÃÕÊ àÿapple Ÿ apple ûê U ŸË ûê U ÈÁSÃ Ê apple (A), (B), (C) ÕflÊ (D) Ò Ë Ë ÁSÕÁà Êapple, Á π U Œ ÊÊ ŸÊ Ò Ÿ ÅÿÊ apple 5 Ë Ê Ò () Ÿ ÅÿÊ (6-5) à àÿapple Ÿ apple Ò (3) Ÿ ÅÿÊ (6-33) à àÿapple Ÿ apple Ò () Ÿ ÅÿÊ (3-36) à àÿapple Ÿ apple 6 Ò (5) Ë Ÿ ÁŸflÊÿ Ò 3!5/AS/--A! [ Contd...
. Which of the following is not a rational number? ÁŸêŸÁ Áπà apple apple ÊÒŸ Á U appleÿ ÅÿÊ Ÿ Ë Ò? (A) 5 (B) 3 5 (C) 5 (D) ( 3). If x= is a zero of the polynomial f (x)=x 5x+k, then the value of k is : ÿᜠx= È Œ f (x)=x 5x+k Ê ÊÍãÿ Ò, ÃÊapple k ÊŸ Ò (A) 6 (B) (C) (D) 6 3. HCF of two numbers is 3 and their LCM is. If one number is 7, the other number is : ŒÊapple ÅÿÊ Êapple Ê.. 3 Ò ÊÒ U Ÿ Ê.. Ò ÿᜠÅÿÊ 7 Ò, ÃÊapple ŒÍ UË ÅÿÊ Ò (A) (B) 3 (C) 7 (D) 9. 5% of a number is 70, the number is : ÅÿÊ Ê 5% ÿᜠ70 Ò, ÃÊapple ÅÿÊ Ò (A) 500 (B) 800 (C) 00 (D) 700 5. In a plane the point equidistant from vertices of a triangle is called its : (A) Centroid (B) Incentre (C) Circumcentre (D) Orthocentre à apple ÁòÊ È apple ÃËŸÊapple ÊË ÊappleZ apple ŒÍ USÕ Á ŒÈ ÊÃÊ Ò (A) apple 㜠(B) à apple 㜠(C) Á U apple 㜠(D) apple ãœ!5/as/--a! [ Contd...
6. Which of the following statements in not true? (A) (B) (C) (D) all rectangles are squares rhombus is a parallelogram sum of interior angles of a quadrilateral is 360 square is a rhombus ÁŸêŸÁ Áπà ՟Êapple apple apple ÊÒŸ- Ê ÕŸ àÿ Ÿ Ë Ò? (A) (B) (C) (D) Ë Êÿà flª ÊappleÃapple Ò øãè È Ê Ã U øãè È ÊappleÃÊ Ò øãè È apple ãã ÊappleáÊÊapple Ê ÿêappleª 360 ÊappleÃÊ Ò flª øãè È ÊappleÃÊ Ò 7. Number of tangents drawn to a circle from an external point is : Á Ë Ês Á ãœè apple flîûê U πë øë ÊŸapple flê Ë S Ê appleuπê Êapple Ë ÅÿÊ Ò (A) 0 (B) (C) (D) 3 8. One side of a parallelogram is 5 cm and its corresponding altitude is 5 cm. Area (in cm ) of the parallelogram is : Á Ë Êãà U øãè È Ë È Ê 5 apple. Ë. ÃÕÊ ªÃ ÊË 5 apple. Ë. Ò ß Êãà U øãè È Ê ˇÊappleòÊ» (flª apple. Ë. apple ) ÒÒ (A) 75 (B) 37.5 (C) 0 (D) 0 5!5/AS/--A! [ Contd...
9. In the figure given below, ABC is right angled at B. Which of the following is true? ŸËøapple ŒË Ê Î ÁûÊ apple, ABC apple ÊappleáÊ B ÊappleáÊ Ò ÁŸêŸÁ Áπà apple apple ÊÒŸ Ê àÿ Ò? (A) 5 sin C = (B) 7 sin C = 7 5 (C) sin C = (D) 5 sin C = 7 0. If sin (A+36 )=cos A, where (A+36 ) is an acute angle, then value of A is : ÿᜠsin (A+36 )=cos A, Á (A+36 ) ãÿíÿ ÊappleáÊ Ò, ÃÊapple A Ê ÊŸ Ò (A) 5 (B) 7 (C) (D) 8. If 9 x+ 3 3 3 3 3 3 =, Find the value of x. ÿᜠ9 x+ 3 3 3 3 3 3 =, ÃÊapple x Ê ÊŸ ôêêã ËÁ. Write 0.06 as a percent. 0.06 Êapple Áà Êà apple M apple Á Áπ 3. In the figure given below, find x. ŸËøapple ŒË Ê Î ÁûÊ apple x Ê ÊŸ ôêêã ËÁ A 658 B x 358 C 6!5/AS/--A! [ Contd...
. In the figure given below, AB is the diameter of a circle with centre O. Find BDC. ŸËøapple ŒË Ê Î Áà apple, AB flîûê Ê ÿê Ò Á Ê apple 㜠O U Ò BDC ôêêã ËÁ 5. Find the volume of a hemisphere of radius cm. apple. Ë. ÁòÊíÿÊ apple œ ªÊapple apple Ê Êÿß ôêêã ËÁ 6. The first term and common difference of a A.P. are 5 and respectively. Find the sum of the first 0 terms of the A.P. Êãà U üêapple Ë Ê Õ Œ fl Êfl ãã U Ê 5 ÊÒ U Ò ß Ê Ã U üêapple Ë apple Õ 0 ŒÊapple Ê ÿêappleª ôêêã ËÁ 7. A retailer buys a cooler for ` 3,800 and spends ` 00 on its transport. If he sells the cooler for `,00, determine his profit percent.»è U U Áfl apple ÃÊ Í U ` 3,800 apple π UËŒÃÊ Ò ÊÒ U ß apple ÊŸapple apple Á ` 00 Ê Ê«apple apple M apple πø UÃÊ Ò ÿᜠfl Í U Êapple `,00 apple appleøãê Ò, ÃÊapple Ê Ê Áà Êà ôêêã ËÁ 8. In the figure given below, if AP=x+, BP=x+, CP=x and DP=x+, find the value of x. ŸËøapple ŒË Ê Î Áà apple, ÿᜠAP=x+, BP=x+, CP=x ÊÒ U DP=x+, ÃÊapple x Ê ÊŸ ôêêã ËÁ 7!5/AS/--A! [ Contd...
9. In a ABC, AB=AC and AD is the altitude from A to BC. Prove that BD=DC. ÁòÊ È ABC apple, AB=AC ÃÕÊ AD, A apple BC U «UÊ Ê ªÿÊ ÊË Ò Á h ËÁ Á BD=DC. 0. Find the co-ordinates of the point which divides the line segment joining the points (, 3) and (5, 6) in the ratio : internally. apple apple Á ãœè apple ÁŸŒapple ÊÊ ôêêã ËÁ Êapple Á ãœè Êapple (, 3) ÊÒ U (5, 6) Êapple Á ÊŸapple flê apple appleuπêπ «U Êapple : apple ãã ŸÈ Êà apple Áfl ÊÁ à UÃÊ Ò. Find the perimeter and area of the sector of a circle of radius cm and central angle 30. apple apple ÁòÊíÿπ «U Ê Á U Ê ÊÒ U ˇÊappleòÊ» ôêêã ËÁ Êapple apple. Ë. ÁòÊíÿÊ apple flîûê apple ŸÊ È Ê Ò ÊÒ U Á Ê apple 㜠Ëÿ ÊappleáÊ 30 Ò. Prove that : Á h ËÁ Á cos A sin A= sin A. 3. Evaluate : ÊŸ ôêêã ËÁ tan7. tan3. tan67. tan83 sec 5. If the data 50,, 35, x+0, x, 8,, is written in descending order of magnitude and its median is 5, find the value of x. ÿáœ Ê «apple 50,, 35, x+0, x, 8,, fl UÊapple Ë apple Á πapple È Ò ÊÒ U ߟ Ê Êäÿ 5 Ò, ÃÊapple x Ê ÊŸ ôêêã ËÁ 8!5/AS/--A! [ Contd...
5. Construct a frequency distribution table from the following data : x i cumulative frequency 0-0 3 0-0 5 0-30 5 30-0 7 0-50 ÁŸêŸÁ ÁπÃ Ê «Êapple apple Ê U Ê UÃÊ UŸ Ê UáÊË Ë UøŸÊ ËÁ x i øÿë Ê U Ê UÃÊ 0-0 3 0-0 5 0-30 5 30-0 7 0-50 6. Solve the following system of linear equations graphically. ÁŸêŸÁ Áπà ÒUÁπ Ë UáÊ ÁŸ Êÿ Êapple Ê appleπëÿ ÁflÁœ apple ËÁ x y=7, x+y=5 OR/ ÕflÊ (For visually impaired learners only) ( apple fl ŒÎÁc UU Áfl Ê ª ÁfllÊÁÕ ÿêapple apple Á ) Solve the following system of linear equations. ÁŸêŸÁ Áπà ÒUÁπ Ë UáÊ ÁŸ Êÿ Êapple ËÁ x y=7, 3x+y=35 7. Simplify the following into the lowest form : ÁŸêŸÁ Áπà Êapple ãÿíÿã M apple U ËÁ 3 x++ x x x 9 x x+ 3 9!5/AS/--A! [ Contd...
8. A washing machine is available for ` 5000 cash or ` 50 cash down payment followed by two equal half yearly instalments. If the interest charged under this instalment plan is 8% per annum compounded half yearly, find the amount of each instalment. «apple œêappleÿapple Ë ÊËŸ ` 5000 Ÿ Œ ȪÃÊŸ ÕflÊ ` 50 ÃÈ Uà ȪÃÊŸ ÊÒ U ß apple ÊÕ ŒÊapple ÊŸ œ flêá Á ÃÊapple apple éœ Ò ÿáœ ß Á à ÿêapple ŸÊ apple ã㪠à Á ÊŸapple flê apple éÿê Ë Œ U 8% flêá ÊÒ U éÿê Áà U Ê Ë ÿêappleá à ÊappleÃÊ Ò, ÃÊapple àÿapple Á Ã Ë UÊÁ Ê ôêêã ËÁ 9. ABC is an acute angled triangle. If AD BC, prove that AB =AC +BC BC.DC. ABC ãÿíÿ ÊappleáÊ ÁòÊ È Ò ÿᜠAD BC, ÃÊapple Á h ËÁ Á AB =AC +BC BC.DC. 30. Construct a ABC, in which BC= cm, B=60 and AB AC=. cm ABC Ë UøŸÊ ËÁ Á apple BC= apple. Ë. B=60 ÊÒ U AB AC=. apple. Ë. OR/ ÕflÊ (For Visually Impaired learners only) ( apple fl ŒÎÁc U Áfl Ê ª ÁfllÊÁÕ ÿêapple apple Á ) Write the steps of construction to construct a pair of tangents to a circle of radius 3 cm from a point P outside the circle at a distance of 6 cm from the centre O of the circle. 3 apple. Ë. ÁòÊíÿÊ apple flîûê U, flîûê apple Ê U apple apple 㜠Á ãœè O apple 6 apple. Ë. Ë ŒÍ UË U ÁSÕà Á ãœè P apple, ŒÊapple S Ê appleuπê Êapple Ë UøŸÊ apple Á, UøŸÊ apple Œ Á Áπ 3. The angle of elevation of the top of a building from the foot of a tower is 30 and the angle of elevation of the top of the tower from the foot of the building is 60. If the tower is 50 m high, find the height of the building. ËŸÊ U apple ÊŒ apple flÿ apple Á Êπ U Ê ÛÊÿŸ ÊappleáÊ 30 Ò ÃÕÊ flÿ apple ÊŒ apple ËŸÊ U apple Á Êπ U Ê ÛÊÿŸ ÊappleáÊ 60 Ò ÿáœ ËŸÊ U Ë øêß 50 Ë U U Ò, ÃÊapple flÿ Ë øêß ôêêã ËÁ 3. Find the mean of the following data : Class 50-60 60-70 70-80 80-90 90-00 Frequency 5 8 5 0 ÁŸêŸ Ê «Êapple Ê Êäÿ ôêêã ËÁ flª 50-60 60-70 70-80 80-90 90-00 Ê Uï Ê UÃÊ 5 8 5 0 0!5/AS/--A! [ Contd...
33. A bag contains cards which are numbered from to 90. A card is drawn at random from the bag. Find the probability that it bears : (i) (ii) a two digit number a number which is a perfect square Òª apple Ê«U Ò Á Ÿ U apple 90 à ÅÿÊ Á Ã Ò Òª apple apple Ê«U ÿêœîë UÿÊ ÁŸ Ê Ê ÊÃÊ Ò ÊÁÿ ÃÊ ôêêã ËÁ Á ÁŸ Ê apple ª Ê«U U (i) (ii) ŒÊapple Êapple Ë ÅÿÊ Á à Ò, ÍáÊ flª ÅÿÊ Á Ã Ò 3. A girl is twice as old as her sister. Four years hence, the product of their ages (in years) will be 60; find their present ages. «Ë Ë ÊÿÈ ŸË Ÿ Ë ÊÿÈ apple ŒÈªŸË Ò øê U fl øêã Ÿ Ë ÊÿÈ Ê ªÈáÊŸ» (fl ÊappleZ apple ) 60 ÊappleªÊ ŒÊappleŸÊapple Ë flã ÊŸ ÊÿÈ ôêêã ËÁ 6 35. If two sides of a triangle are unequal, then prove that the longer side has the greater angle opposite to it. ÿᜠÁ Ë ÁòÊ È Ë ŒÊapple È Ê ÊŸ Ò; ÃÊapple Á h ËÁ Á «Ë È Ê apple Ê Ÿapple Ê ÊappleáÊ, UÊapple UË È Ê apple Ê Ÿapple apple ÊappleáÊ apple «Ê ÊappleÃÊ Ò 6 36. External radius of a hollow right circular cylindrical pipe is 9 cm and its length is cm. If the volume of the metal used to make the pipe is 78 cm 3, find the thickness of the metal. π =. 7 flîûêëÿ apple ŸÊ Ê U πêappleπ apple Êß Ë Ês ÁòÊíÿÊ 9 apple. Ë. Ò ÊÒ U Ë ê Êß apple. Ë. Ò ÿáœ ß Êß Êapple ŸÊŸapple apple Á ÿêappleª Ë ªß œêãè Ê Êÿß 78 ÉÊŸ apple. Ë. Ò, ÃÊapple œêãè Ë Êapple UÊß ôêêã ËÁ π = 7 6 - o O o -!5/AS/--A! [ Contd...