PRACTICE ASSIGNMENT CLASS: XI SUB. MATHEMATICS



Sspawarmentors for maths.Sspawarmentors for maths.Sspawar mentors for maths.2011PRACTICE ASSIGNMENT CLASS: XI SUB. MATHEMATICS SECOND TERM Satvinder singh MATHEMATICS CLASSES LADWA MOB: 09729064004, EMAIL:MATHHELP.SS@Q1. Simplify : (a) -16 . -4(b) -45 + -36-121 . Q2. Evaluate: (a) i9+i19 (b) 2i225+3i227 +4i229+5i231(c) i-25+i70 + i90+16 i101Q3. Express the following in the standard form a+ib (a) (1+i)4(1+i-1)4 (b) (2+3i)2+(3-4i) (c) –3-i33 Q4. Find the additive inverse of (a) (-3-4i)2.(b) (5i64+25i43) Q5. Find Z, if (a) Z = (9+3i47) + (3+8i21)(b) Z = 3+4i1-24i (c) i+24(10+-24 )(2-i)2Q6. Evaluate: (i) 1i35+i152 (ii) 3i313+2i52 Q7.Find the Multiplicative inverse of (a) 1+i1-i(b) 5+3i Q8.Find the real values of x and y, (a) if (x-iy)(3+5i) is the conjugate of -6-24i (b) 13x-14y +34yi= -3+5i (c) (3 x - 2i ) (2+i)2 = 10(1+i) Q9. If Z1= 2-i and Z2 = 1+i , find the value of (a) Z1+Z2+1Z1-Z2+1 (b) Re Z1 Z2Z1 (c) Im Z1 Z2Z1 Q10. If x+iy3 = a+ib , then show that a4x+b4y = (x2-y2) Q11.If x+iy = a+iba-ib , then prove that x2+y2 =1 Q12.Find the conjugate of Z, if Z = 6+i(2-i)1+i(1-2i)Q13. Show that if z-5iz+5i = 1, then z is a real number.Q14. If a+ib = (x+i)22x2 +1 , then prove that a2+b2 = (x2+1)2(2x2+1)2 . Q15. Simplify : 1+i1-i4n+1 CLASS –XI SUB: MATHEMATICS TOPIC: QUADRATIC EQUATIONq1. Find the square root of : (a) 3-4i (b) -7+24iQ2. Solve the following for x: (a) x2+5 = 0 (b) x2-2x +32 = 0 (c) x2-5ix-6 = 0 (d) 2x2-9ix-9 = 0 (e) 5 x2+x+5 = 0 Q3. Solve the following for x: 2x2+3ix+2 = 0 (b) 2x2-(3+7i)x+(9i-3) = 0 (c) x2-(2+i)x - (1-7i) = 0TRIGONOMETRYQ1. Find the values of the following: (i) Sin (-1125o ) (ii) cos(-765 o ) (iii) tan 25π3 (iv) sec(-780 o) (v) Sin 15o (vi) Cos 105o (vii) tan195oQ2.Evaluete : sin-x.cosπ2+x-sin3π2+xcos(2π+x)sec2π+xcosecπ2+x+ tan (2π+x)cot3π2+xQ3.If sinx = 45 and x lies in second quadrant, find the values of cosx ,tanxQ4. Prove that cos 24 o + cos 55 o +cos 125 o +cos 156 o - cos 240 o = 12 Q5. Find the values of (i) sin (x+y) (ii) cos (x+y) (iii) tan (x-y) (a) If cos x = 45 and sin y = -513 x, y lies in IVth quadrant (b) If sin x = 12 and cos y = -35 x, y lies in IInd quadrant Q6.If sinx.secx = -1, x lies in 2nd Quadrant . find the values of sinx, secx.Q7.Prove that: sin2 π18 + sin2 π9 + sin2 7π18 + sin2 4π9 =2 Q8. Prove that : cos3 π8 + cos3 3π8 + cos3 5π8 + cos3 7π8 =0Q9. Prove that : (i) tan3x tan2x tanx = tan3x- tan2x –tan (ii) tan75o +cot 75o = 4 (iii) 1tan 3x-tan x - 1cot 3x-cotx =cot2x.Q10. Prove that : (i) cos 200 cos 400 cos 800 = 18 (ii) sin 200 sin 400 sin 600 sin 800 = 316 (iii) 4 cos A cos(600 – A) cos (600 +A) = cos 3A.Q11. Prove that (i) sinx+sin3x+sin5x+sin7xcosx+cos3x+cos5x+cos7x=tan4x (ii) sinx-sin3x+sin5x-sin7xcosx-cos3x-cos5x+cos7x=cot2x (iii) sin11A.sinA + sin7A. sin 3A cos 11A.sinA + cos 7A. sin 3A=tan 8A.Q12.(i) find sin2A, cos2A if tanA= 12/5 (ii) If x lies in IIIrd quadrant , find the value of Q13. If sin x = 12 x lies in second quadrant , find the value of Q14. Prove that cos 3x cos x – cos 6x cos4x = sin 7x sin 3xQ15. Prove that cos 2x cosQ16. Find the values of : (a) sin 712o (b) cos 2212o (c) sin 6712o (d) tanπ8.Q17. Prove that : (i) 2+2+2+2cos8x = 2cos x (ii) Sec 8A-1Sec 4A-1 = tan 8Atan2A (iii) if sinθ=12x+1x, show that: sin3θ+12 x3+1x3=0Q18. Prove that : (i) cos4x = 1-8sin2x cos2x(ii) cos6x = 32cos6x-48cos4x+18cos2x-1. (iii) cosAcos2Acos4Acos8A= sin16A16sinA (iv) sin26x-sin24x = sin2xsin10x (v) 1+cosπ8 1+cos3π8 1+cos5π8 1+cos7π8= 18.Q19. Prove that: Sin11x4 Sinx4 + Sin7x4 Sin3x4 = Sin2x SinxQ20. Find the principal solutions for the following : Sin θ = -1 (b) cos θ = ? (c) tan θ = √3 (d) cosec θ = √3/2LINEAR INEQUALITIESQ1 .(a) Solve 5x-3 < 7 when (i) x is an integer (ii) x is a real number (b) Solve for x : 5x + 4 > 9 (a) x Z (b) x R.Q2. Solve: (i) 3(x-2)5≤ 5(2-x)3 . (ii) (3x-4)2 ≥ 1+x)4-1 . Q3. Solve the inequalities also represent the solution on a number line: 5(2x-7)-3(2x+3) ≤ 0 , 2x+ 19 6x+47Q4. Solve the in equation for x QUOTE R . (i) QUOTE (ii) QUOTE Q5. Solve the in equation for x QUOTE R. (i) QUOTE (ii) QUOTE (iii) QUOTE Q6. Find graphically the solution set of the linear in equations (i) 3x+y 6 , x+y QUOTE 4 , x QUOTE , y QUOTE , x,y 0 (ii) 3x+4y QUOTE , x+3y QUOTE , x,y QUOTE (iii) 2x +3y -12 QUOTE 3x – 4y +12 QUOTE , 2x-y +2 QUOTE , y QUOTE .(iv) x+y QUOTE 3x +y QUOTE x+5y QUOTE , x QUOTE , QUOTE .PRINCIPAL OF MATHEMATICAL INDUCTIONQ1. Using PMI, prove that for all n QUOTE : (a ) QUOTE + QUOTE + …………………… QUOTE = 1 - QUOTE (b) (1+ QUOTE ) (1+ QUOTE ) …………( 1 QUOTE ) = QUOTE (c ) 1.2.3 +2.3.4 +3.4.5 +………………………n(n+1)(n+2) = QUOTE 1.3+2. 32 + 3. 33+…………………+ n. 3n = QUOTE . (e) 1 3+2 3+3 3+………………………….+n3 = QUOTE Q2. Using PMI , prove that (i) 6n +2 +7 2n+1 is divisible by 43, for all n QUOTE (ii) 32n +2 – 8n - 9 is multiple of 64, for all n QUOTE (iii) 2.7n + 3.5n – 5 is divisible by 24, for all n QUOTE SETS ,RELATIONS AND FUNCTIONSQ1.If A= {1,3,5,7,9} , B= { 0,2,5,7} . find A QUOTE B, A QUOTE B. Q2. Describe the following set into Property method : {2,9,28,65,126} , { QUOTE , QUOTE , QUOTE } Q3.Find a , b. if QUOTE Q4.find the domain and range of the following functions : (a) f(x) = QUOTE (b) f(x) = QUOTE (c) f(x) = QUOTE (d) f(x) = QUOTE Q5. If A={1,2,3,4…….20) write a relation (a,b) QUOTE R on A X A s.t a is one-fourth of b.Q6. (i) If U = { 1,2,3,4,5,6,7,8,9} , A= {2,4,6,8} and B= {1,3,4,5,6}, find the following:(A QUOTE B) (ii) A QUOTE B (iii) A – B (iv) (A QUOTE B)c (v) Ac QUOTE Bc(ii) If A = {1,2,3,4}, B= {2,3,6,7,8,9} and C = {2,3,7}, then verify that: A X (B - C) = (A X B ) – (A X C)Q7.In a survey of 600 students in a school, 150 students were found to be drinking Tea and 225 drinking coffee, 100 were drinking both tea and coffee. Find how many students were drinking neither Tea nor Coffee.Q8. In a group of 30 players , 10 play table tennis, 8 play cricket and 11 play volleyball, 4 play both cricket and table Tannis, 6 play cricket and volleyball , 5 play table Tannis and volleyball . 2 play all the three games. Find the no. of players who play (i)Only cricket (ii) only table tannis (ii) volleyball and cricket but not table tannis (iv) any one of the game (v) atleast one of the games Q9. A class of 175 students, the following is the description showing the no. of students studying one or more subjects as : 100- maths, 70- physics, 46- chemistry, 28- maths+ chemistry , 30- maths+physics, 23- physics+ chemistry, 18- study all three subjects.Find: (i) how many students are enrolled in at least one of the subjects? (ii) how many students are are not studying any of the subjects?PERMUTAIONS AND COMBINATIONS Q1.(a) Find the number of arrangements of standing four students in row .Find the number of ways to arrange five boys in a circle. Find the number of ways to select a team of 4 students out of 20 students. Q2. Find the number of words end with “E” that can be formed from the letters of word “SMILE”. Q3 (a)Evaluate : QUOTE (b) find n, from the equation: QUOTE . if n QUOTE N (c) Prove the following: QUOTE QUOTE , QUOTE QUOTE QUOTE Q4 (a) .find ‘n’ if C(n,n-2) = C(n,6) . (b) If 11 P r = 12 P r-1 find r Q5. How many straight lines can be formed from 10 non collinear points. Q6. How many ways are there to select a cricket team of 11 –players from 15 players, if the captain is already selected for the team.Q7. Find the total number of 3- digit even numbers that can be formed by using the digits 1,2,3,5,6,7,8. Q8. Find the total number of the words that can be formed from the letters of the word (a) “ MATHEMATICS” (b) EXAMINATION (c) INDEPENDENCE (d) COMBINE (e) NATIONAL In how many of them vowels do not occur together ? Q9. Find the numbers of committees of 5 members that can be formed out of 5 boys and 4 girls, if in each committee at least 2 girls must be taken. Q10. Find n and r if C(n,r): C(n,r-1):C(n,r-2) :: 1:7 :42. Q11. In how many distinct permutations of the letters in “MISSISSIPPI” (i) do the four I’s not come together . (ii) all S come togetherQ12. There are 5 consonents and 3 vowels. How many words of 6 letter words can be formed if they are to contain 4 consonants and 2 vowels.Q13. On the occasion of friendship day 65 cadets purchased F’bands for each other. They tied the bands to each other and shake hands. Find the total number of hand shakes that occurred.Q14. What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of these:4 cards are of the same suit? (ii) 4 cards belong to four different suits ? (iii) two are red and two are black ? BINOMIAL THEOREMQ1. Find the number of terms : (i) QUOTE (ii) [ (2x+y)9+ (2x-y)9 ]Q2. Evaluate : [ ( QUOTE +1)6 -( QUOTE 1)6 ] (ii) [ ( QUOTE +3)5 - ( QUOTE )5 ] Q3. Find the 11th term from end in the following expansion : QUOTE Q4. Find the middle term in the expansions of the following : (i) QUOTE (ii) QUOTE (iii) QUOTE (iv) QUOTE Q5. Find the coefficient of x32 and x-17 in the expansion of QUOTE Q6. Find the term independent of x in the expansion of : QUOTE Q7. For what ‘m’ , the coefficients of (2m+1)th and (4m+5)th terms, In the expansion of (1+x)10 are equal.Q8. The coefficients of (r-1)th , rth and (r+1)th terms in the expansion of (1+a)n are in the ratio 1:7:42 find n Q9. If coefficient of (n+4)th and nth terms of (1+x)r are equal, prove that : r-2n = 2.Q10. Using Binomial theorem QUOTE – 8n – 9 is divisible by 64.Q11. If the 4th term in the expansion of QUOTE is 5/2, find the values of n and a.Q12. The coefficients of consecutive three terms in the expansion of (1+x)n be 45, 120 and 210, find n.Q13. Show that there is no term involving x6 in the expansion of QUOTE .Q14. Find the value of k so that the absolute term in QUOTE (Geometry)Q1. Find the slope of the line whose inclination is (a) 150o with +ve X axis. (b) 45o with y-axisQ2 A line is perpendicular to the line passing through the points (2,7) and (5,1). Find the slope of theLine. Q 3.(a) Find the equation of the line passes through origin and perpendicular to the line 3x-2y=0 (b) Find the equation of the line passes through (4,5) and perpendicular to the line x-3y +3=0Q4.(a) Find the value of K such that the line joining the points (2, K) and (-1, 3) is parallel to the line joining (0, 1) and (-3, 5)(b)Find the value of ‘k’ such that the points A(2,k) , B(3,2)and C(5,1) are collinear. Q5. Find the angle between the pair of the lines y-√3x-5=0 and x-√3y-6=0 Q6.(a) Find the co-ordinates of the image of the point (2,3) to the line as a plane mirror 3x-4y + 7=0.Find the coordinates of the foot of perpendicular drawn from the point (2,3) to the line 3x-4y + 7=0.Q7. (a) Find the equation of the line passing through the point (3,4) and the sum of whose intercepts On the coordinate axes is 14.(b) Find the equation of the line passing through the point (3,4) and whose x- intercept exceeds the y- intercept by 4 .Q8. A line is passing through the mid pt. of join of (0,0) & (2,6) and parallel to X axis.Q9. (a) Find the equations of two lines passing through (4,2) and making 45o with the line 2x+y=0 (b) Find the equations of two lines passing through (-1,2) and making 30 with the line 2 x-y+3=0. Q10. Find the Eq of the straight line whose perpendicular distance from origin is 2√3 units amd the perpendicular line makes an angle of 135o with +ve x-axis.Also convert the eq. into intercept form.Q11. Find the centre of the circle and radius : 4x2+4y2-4x-10y-5=0 Q12.Find the eq. of the circle passes through (2,5) and with centre (0,2).Q13. Find the equation of parabola whose focus is (0,4) and directrix is y=-4 Q14. Find the equation of parabola whose focus is (3,4) and vertex (2,1)Q15. Find the eq of ellipse whose focus is (5,0) , e=2/3Q16. Find the equation of an ellipse whose axis along x-axis and passing through (1,-1) and vertices are (±2,0)Q17. Find the equation of the line passing through the point (3,4) and whose x- intercepts exceeds the y- intercept by 4 .Q18. Find the coordinates of point on z –axis which are at a distance of √5 from the point P(1,1,0)Q19. Find the equation of the circle passing through (2,3) ,( 1,-1) and whose centre lies on the line 2x+3y-10=0Q20. Find the eq. of the circle concentric with x2+y2-4x-10y-5=0 and whose area is 16 QUOTE .SEQUENCE AND SERIESQ1. If the pth term of an A.P is q and qth term is p , prove that rth term is p+q-rQ2. If in an A.P , the sum of m terms is equal to ‘n’ and the sum of n terms is equal to ‘m’ , prove that the sum of (m+n) terms is -(m+n).Q3. If first , second and last term of an A.P. be a,b,c respectively , show that the sum is QUOTE Q4. The pth term of an A.P. is ‘a’ and qth term is ‘b’ . prove that the sum of its (p+q) terms is QUOTE Q5. If p,q,r are in A.P. , and x,y,z are in G.P . , then prove that xp-r . yr-p . zp-q = 1 Q6. Evaluate the sum : (i) 4+44+444+4444+……………………… (ii) 7+ 7.7+7.77+7.777+……………………. Q7. How many terms of the G.P . , 3, QUOTE , QUOTE ,………….. are nedded to give the sum QUOTE Q8. Find the sum of the following series up to n terms : (i) if nth term is 4n3+6n2+2n+1 (ii) 12 + (12+22) + (12+22+32)+ …………….. (iii) 5+11+19+29+41+……………………… (iv) 3+7+13+21+31+………………..CLASS XI SUBJECT : MATHEMATICS TOPIC : LIMITS Q1.Evaluate the following limits:Q2. If f(x) = QUOTE , Find QUOTE & QUOTE Q3. Find the value of m if the limit of given function exist at x=1 : f(x)= QUOTE Q4. Suppose QUOTE and QUOTE d b.CLASS XI SUBJECT : MATHEMATICS TOPIC : DIFFERENTIATIONFind the derivative of the following/ find QUOTE .Q1. Y= x + cos xQ2. Y= sec x +cosec xQ3. Y = QUOTE Q4. Y = QUOTE Q5. Y= QUOTE Q6. Y = QUOTE , QUOTE Q7. Y= QUOTE . QUOTE Q8. Y = QUOTE . QUOTE Q9. Y = QUOTE Q10. Y= QUOTE Q11. Y = QUOTE Q12. Y= QUOTE Q13. Y = QUOTE Q14. Y = QUOTE Q15. Y = QUOTE Q16. Y= QUOTE Q17. Y= QUOTE prove that QUOTE Q18 . Y= QUOTE Q19. Y= QUOTE Q20 . Y= QUOTE Q21. Y= QUOTE Q22. Y= QUOTE Q23. Y = x + QUOTE , QUOTE Q24. Y = QUOTE ................
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