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athematics 11‘ ( ) Most Important MCQs (It is challenge you can pet 20/20 marks in Annual 2026) Chapter 1: Complex Numbers.» 1 The number »/—1 is called: Real number Naturakge: , “Coniplex Rational number “snumber 4 number 2 | (-i)"* is equal to: -i aes “1 -l zm . . poe 3 | (-1) equals: t iv | ] The multiplicative inverse of the “s ‘ complex number (0,—1) is equal to: (1,0) (@.1) ¥ (-10) (0.0) 8 | Multiplicative inverse of (1,0) is: (0,1): (0,-1) (1,0) ¥ None 6 | Multiplicative inverse of -i is: iv® -i 1 -1 . . 3 a a 1 3 1 Real part of ——— is: we = v3 jo 7 ve-V=12 ral A x % 8 | Any real number ‘a’ is equal to: 4° “*) ia (a,b) (a,0) ¥ (b, a) 9 | The real part of is: ay = 1 2 Fa Pe. = 3 40 " modus of the complex el +5 45 VE sv a | ifZ =-2 +4 3ithn" hay -2-3iV¥ 2-31 —243i 243i 12 | Ifz,=1+i% -i: ZS zy Zy > Zo $ zl 13 ie equigitag a = 0 has a solution R Cy Q Pp 4a a” + b® has factors: (a+b)(a | (a+ib\(a-| (a+ib)(a (a+ b)(a —5) ib)v —4) — tb) 15 | For acomplex number (0,1)i =: (1,0) (-1,0) ¥ (0,1) (0,—1) 16 IfZ = —7 — 24% then the real part of YZ 2 av 4 I is: If @ is a complex cube root of unity then 17 | the value of (3 + w)(3 + w#) =? 6 iw ° 13 48 ‘Complex cube roots of -1 are: wa? 1w,w? -1,-w, -—w? ~o,-w* v Four fourth roots of 16 are: 2,-2,21, -20 ag | |Our four roatsoune are a 1,-1,1,-i | 3,-3,34,-3¢ | 4,-4,41,-41 20 | Three cube roots of 27 are: 3,3w,3w7 v Law, a* -3,-3w,3w?| —3,-3,3i 24 | Cube roots of unity are: -1,-2,1 1,-l.a@ 1a, a? So =1-a,w 22 | Sum ofall three cube roots of unity is: 1 -1 3 ov 23 | Sum of complex roots of unity i 0 2 24 | Product of all cube roots of unity is: lv 2 25 If w is the imaginary/complex cube root wo wo of unity, then w~* = + 28 ue al s complex cube root of unity then w 3 Py) If w is a complex cube root of unity then ai 1 ow? +78 41 =. 28 is teow root of unity then: (1+ 256 ¥ 2560 a@-w*)i = If w is the cube root of unity then w + 1 29 2 " 0 1 — w* equals: w 30 iowa the cube root of unity, then a = ll 1 34 ont is a complex cube root of unity, ws? a ose we - If w is complex cube root of unity theg 1 143i w= z If w is a complex cube root oF then 2 2 _ = the conjugate of w is: ll aiid « ® ‘ 34 1+ wt = w -w w?
) equals: = +3i vf -l i 1 11 ee ee oeamation xtat Radical ¥ Reciprocal Rational None of these 12 | The solution of ,/y + 3 = /3y — 5 is: 2 4v 1 4 . . Chapter 4: Matrices and Determinants Ifa matrix A is of order m > nm then A i mxnd m+n m=-n m has a number of elements: [8] is a: Square F P a ae Rectangular 2 mantic Unit matrix Scalag Matrix matrix A matrix which has only one row is Row matrix Column “Square. : a called a: v matrix hy. mattix None of these 4 | The matrix [) 9) is: Null Identify’ [5 “Scalar | Diagonal v If ord(A) = m X n, ord(B) = n X p, then > a 5 ord((AB)') is: mxm 7 pdms pxn 6 Transpase of a diagonal matrix is a: Scalar matrix })Row thatrix | Null matrix Diagonal [oo matrix ¥ 20 0 oy ¥ 7 | The matrix [0 2 Ojisa: Rectangulary Diagonal Scalar 4 Hermitian oO. 0 2 . ‘h If A is a matrix of order m xn and Bis ay” & | matrix of order n x / then what is the « ixm mxlv nxl order of A x B? - 3.0 "4 ™” |* Given that 5 = [ ], then S$? isgiven: 9 0 0 9 6 0 0 6 9 by: 0 3 ee ad | | olY lg gl lo 6 le 10 If each element of a matrix is zéro, then Null matrix Identity Scalar matri Diagonal it is called a: r ae v matrix PSSUAC LOSER. matrix ‘The matrix obtained ‘by.intere hanging its — . . Suman merie sat 11 rows and colffiins is called a: Inverse Transpose # Symmetric Adjoint 13 Transpose,of a.row matrix is a: Square Column Symmetric Skew- ~~ 2 matrix matrix v matrix symmetric If the order of'a matrix A is m x n, then 13 tic. mxn nxn nxmv¥ mxm the order of A is: 14 | If A=[abc] then the order of At is: 1x3 3x1iv 3x3 1x1 15 HEA in a maicix fonder: 22 then the 3x2 2x3 2x2v 3x3 order of A‘A is: Wa=[} 2,8=Cg Zitmenat+ | 0 5 1s 10 22 16 _ + = 3 the form: \ a A sequence, n whose domain 2n + Lis: 1 is a subschARTRBMbt of: Real numbers ciguibersaf Integers None of these 2 | A sequence is denoted by: {Sn} None of these 3 For a sequence, a, represents the: General term Tenth term Lester 2 7 Dist (3— 4 If the nth term of an A.F is3(3 n), Lal iiov then the first three terms are: a 5 The Sth term of the sequence a,, = 8 7 (—1)"(2n — 3) is: 6 The fifth term of the sequence a,, = liv B 7 | Ifa, = (—1)"*" then the 26th term is: 1 “lv 26 24 8 | Fa, =a,_, +n, a, = 2 then a; =--- 6 WW ul 17 9 The next term of the sequence I, 3, 7, av @ 80 81 15, 31,.... 1s 10 te fro seins Gfthe sequence? 9.) 94. 99 21,26¥ 20, 27 20, 26 1 {ied tom af tes. eequenceds Sy, 24 6 0 4iv The nth term of the sequence +,2,5, ... n n La TB | ae wer in-1 ina 3n+1 13] 16a, =? inen ay =? 1/8 1/16 -1/64¥ A sequence {a, } is an arithmetic he 14 | sequence if a, — @,_, is same Vn € N is same ¥ is different” | “is negative | None of these and n> 1. 15 Coinage difference a the arithmetic - av V3 sequence 3,5, 7, ... is: 16 Ifa, b, c are in A.P, then b=... 2ac 2ac atc a—c 7 If=,z,+are in A.P then the common at+ec aby difference is: Zac oe 18 2, 4, 6, 8, 10, ... is: WLP Geometric % * “ series 49 The nth term of an A.P with usual ooo [ay (n — a, +(n a +(n a+ (n notation is: a Ppdav -1)d —2)d +1d 20 | The A.P whose nth term is 2n-] is: 4) 1,3,6,.. 2,5, So 1,3, 5,...4 5,3, 1,... 21 | If a,—y = 3n— 11 then nth term iss 3n4+5 3n-3 3n-5¥ 3n+2 22 | If ay_3 = 2n — 5, then the 7th term is: 9 sv ul 13 23 The Sth term of the sega ay -3) 55~ 15 15 Wv 47 Ifa; = 20+and othef-consecutive terms 5 24 | re 23, 26, 29, then the Sth term is: ae ial as a8 25 | Which term of 64, 60, 56, 52. ... is zero? 16th 17th ¥ 14th 15th . od 26 The nth term of an A.P is; (3n), the 3.21 12,3 aady 29 first three terms are: at 2°°2 27 The A.M between two numbers a and b ath 2ab ashy 2 is: 2ab a+b z a+h 28 Ifa, A, b are in A.P, then 2A =: ut Te, a+b) a=k 29 | A.M between 3V5 and 5V5 is: aS 5v5 10 2v5, Position Winning MCQs >» | BR Mathematics 11" (NEW SNC) 53 2b are in G.P then the common +f + fy b None ratio is equal to: a a a If a, and r are the first term and 54 | common ratio respectively, then the ar" ar" ay"? ar’ vw (n+ 1)th term of G_P is: 55 | The next term of G.P 1, 2, 4, 8, 16, ... is: 15 19 21 327 56 | InG.P 3, 6, 12, .... ag will be: 4g 64 128 224 Ifa, b, c are in G.P and a > 0,b > 57 | 0,c > 0 then the reciprocals of a, b, c AP None of these form: 58 | geometric mean between a and b is: ath 2ab 2 ath Ifa, G, b are in G,P where a, b are bi numbers then G.M is equal to: Vab ah A number G is said to be the GM. 5 , 60 between a and b ifa, G, b are in: AI None 61 | GM between : and ; is: te vf None 62 fhe geometric mean between -2i and 8i +4 +3 +2 +1 63 | The G.M between 1 and 16 is: 4 +4V7 1/4 Chapter 6: Sequences and Series (II) Que 1s A B € D 1 | G.M between two numbers =2 and +V8 +2V2 +212 ¥ 42 2 The geometric mean gbetye and 4 48 44 4oviv 43y2 3 | Ifa=2i,b=4i, then'G=, +2V2i¥ 6i +2i 4i For what value ofn, — is the 4 | positive geometric mean between a and ne=-l n=l n=12¥ n=0 b? Suit of n terms ofa GP with first term "(2a +(n aur) 2ab ath 5 | ‘a’ and common ratio 'r' is: 2 —1)d} inf a+b 2 é For the series 1 + 5 + 25+... Sun ist 1/4 1/4 0 Not onan By fF the infiniu tric series ? ie ein inite geometric series 442 4-2 442iv None 2,V2, 1... is: The sum of the infinite geometric series & with a, = 2,r = 1/3 is: av * ; 6 Sum to infinity of the series ~ + + 9 4 _ a ME 1/10 1/ov 1/8 1/7 Toon te IS The sum of the series 1 — 1/2 + 1/4 — 10 1/8+.. is: 1/72 3/2 2/34 1 Ee 1 14 Sum to infinity of the series 1+ x + l-x a 1+x x°+... IS: i-x 1+x ‘The sum of the infinite series == + 12), 5 fav 5/4 4/5 a/4 125 Which one of the following infinite 1¢s4tH., 346 13 | geometric series is convergent? ¥ ‘/ 1424 4+... +124... 14 —— is convergent if: $ r $ a eee 15 y= 5x +5 +3* +... then the ose 0G>H 26 | and Harmonic means between a and b, AH>G G>A>H then: 27 eee Gh=ANny A? =GH H2 =AG A=G=H If A, G, H are means between a and b, 4 “e then A, G, H are in: sand GP¥ HF Nake 29 | For two unequal positive real numbers: A>Gd = AG =G A | 9 Factorial form of n(n-1)(n-2) = ? nl! n! ay nt (n—1)! (n—2)! (n=3)! (n—4)! Factorial form of 22 2GUGeD j.. (a+1)! (n=1)! n! 10 3.21 Suna Tima Bima! None of these 41 The expression = ae + a] reduces my 1 7 to: n je — he nm Factorial notation was i ced by: os P 12 actorial notation was introduced by Leibniz Fuler Saivlanwn 13 ——e taken all ata time can (n-1)! ways | (n+1)! ways n! ways (2n)! ways 14 | The value of §P, is 5 10 204 15 | "Py =--: n 0 n! 16 | Ifr=l, then "PR. =: n! nv wT None of these 17 | The value of 3P, is: 18 6v 0 18 | If =n, then "PF, equals: 1 (n+1! (n-1)! 19 | The value of n when "P; = 11,10.9 is: liv 9 10 20 | If"P, = 30 thenn-...: 6v 5 8 21| =. "Pre vimbe’ "Cv "Py "C4 The number of ways that 5 persons can 7 a2 be seated on a bench is: 3 . a aah 240 23 Nernber of Permutations of the wr : % “220 v 360 120 60 The number of permutations of the» sal letters of the word ‘APPLE! ist ual salad aa 20 How many arrangements of the betters 25 | of the word 'AT) TACKED Man be 5040 10080 20160 4 40320 made? 5 persons can be: seat ata round table j 4 26 | Show many Waa 23 24 25 120 The number of permutations of the word 27 | PANAMA where? is the first letter: a sid nial 30 2B Number of ways in which a necklace of 5! ay 6! 6! 6 beads of different colors can be made? 2 2 29 | "C, is valid only if: ner renv r>n r=0 30 | "C, xr! =o "py "py Loan np, 31 | "C, is equal to: "P. "Chor v "Fir "Ch 32 | "Cc, =" C,_, is useful when: n=r nnj/iv 33 | Ifr=n, "C,. is equal to: i] lv n n! 34 "p+ "Cry =? mic yf mits . None 35 | "Cy is equal to: lv 0 n 2 36 awois equal to: "Cv np. 7c, "Cy 37 | I1f"C, =" C, then nis equal to: 4 8 3 ov 38 | The value of !7C, is: 667 132 IL 12 In how many ways can a cricket team of 39 | 11 players out of 15 be selected if the 15! Be, Moov It captain must be included? Chapter 8: Mathematical Induction and Binomial Theorem 1 we method of induction was devised Laplace Euclid soe py REHEH Irrational For n=2," ey 2 number Even number | Integer ¥ n m4 9n-1ig 3 poral Ny > 3" +2""" is true n>iv ne<2 for: ee Ls! 4 If S(n): n? — n+ 41 isa prime number, Prime .*...| * Composite Even numb Irrational S(S) isa: number ¥ number sh aemameieing number 5 145+ S...+dn— a) = n(Za — 1) n=2 AlneNnv None is true for: For all positive integral values Of Tyetey 2 7 6 n(n + 1) is divisible by: ; at 3 4 2 o ! 2 is not<° 7 For which value of n, n! a. is not, n=4 n=5 n=3¥ n=6 true? i 8 n® — 1 is divisible by 8ikn i — Natural iyin integer Odd integer i a” ° number v 9 | 3" < al is true for all iitegers: n>6V¥ n<6 n=6 n<0 Ifn is any positive.integer, then 2" > < 10 2(n + 1) 4s true-for all: ne<3 n23Vv n>3 ns3 5 at mes n® i > for integre 14 Show that rfp n* is true for integral n=3 ne4 nea n<4 values of n: 12 Which one is divisible by2 for all nonv sn gn on wan positive integral values of n? For positive integral values of n, 5" — aa 2" is divisible by: . iv * 4 If n is a positive integer then n?+nis > oii divisible by: av A * 5 If n is any positive integer then 1+ 3 + _ | ForallneN 1B lca. +(2n — 1) =n? is true for: nm'l only n= 2only v Mong HR Mathematics 41" (NEW SNC) i6 Position Winning MCQs > | expansion of (x — y)° is: The sum of the exponents of ‘a’ and 'b’ 38 | in every term of the expansion of (a + I nv n+l n-l by" is: The sum of odd coefficients in the expansion of (1+ x)° is: 5 ov 25 32 The sum of even coefficients in the expansion of (1+ x)° is: nv 64 16 8 The sum of binomial coefficients in the a expansion of (a + x)? is: av +e - ba 42 The number of terms in the binomial ¥ we Infinite ¥ series is: & di ‘a Binomial series is used to find the value aniunniee Irrational /"Zranseendent | All of these of: ¥ ‘ numbers}. @hauinber v rr Qexytae: Textx? | 1l+x+a2+ | OL-2x 1+2x — x34... oe £ + 3x74... ro ‘The expansion (1 —x)7? is: 1-—3x 1-3x + 6x7—... of ~ 6x2... 46 | In (1 — x)~*, the coefficient of x” is: n#2 4 . 1 13 135 47 The series 1 +7 +75 +5555 +. sums 1/2 to: The number of terms in (x + a)!0° + 5 48 | Oe a)" ig 202 Slv¥ 50 ‘The coefficient of the term indepen ee * 49 | ofxin (VF -2)" is: A}? 1804 120 90 720 50 Tr xx? — x34... is the Q4x7v] G-27 (14+x)7 (1-2)? ‘The 2nd term in thee anor pot (1 + 51 2x)? is: @ ( xv 2x xf2 Ax ‘The 2nd term’ Sg emttaion of (1 — 3 2 52 2x)1/3 ig 3% ¥ zt 6x x/3 53 | The 2nd ore on, el. I xv 2x x In the expansion of (1 + x)~ = the 4th aad 2 4 i 54 Sais li 3x -10x7 ¥ 6x 10x: The second term in the expansion of 55 a thay is: =x/3 2x —xfl¥ x/2 The second term in the expansion of 1 1 56 Biya sa: =xV¥ -=x 3x 2x a- 3%) is: 3 3 57 | The second term in (1 — x)? is: x/3 3x —x/3v —3x 58 The second term in the expansion of ow) o 3x es (1 — 2x)" is: The second term in the expansion of 2x 2x 59 | 1 — 2x) is: 7 7 xf2 2/8 The second term in the expansion of 2 9 4 ‘ pial Jy? ay? 80 a+ is: ai 7 a” 9° Chapter 8: Mathematical Induction and Binomial Theorem (II) 1 lacealae of (1.03)*/° up to 3 decimal Lowy 1.020 1,030.8] 1.040 2 | The value of ¥30 is approximately: 5.477 ¥ 4.477 % 647m, © 3.477 3 | The value of V65 is approximately: 4,021 ¥ 3.021 ePeay 1.021 Ifx is so small that its square and higher ew J P ers ¢ e ei e x 4 ewe then 1- zy 1 += (eexy= The term independent of x in the \ 5 expansion of (x -3" is: —252 ys 210 “210 The term independent of x in the a | spansion of (r+ is: 79/16 V4) 16/70 8/16 16/8 7 | lf x is very small, then = =; 1+3x/2 | 1-3x/2v 1+x/2 Chapter 9: D of Polynomials 1 | x3-— 3x? + 2x — 6 hasaafactor: x-4 x3 v7 x3 xt2 When 3x? + 4x? +'x — 6 is divided by 2 ¥ +1 the remainder 7 5 $v =e cosd ¥ sin@ seco cescé gg | etter ... tan11° cot11* tan56" ¥ cot56" pg | Ser tan8* cots” tan37° vv cots?" cos8*+sinB" 27 | If rcos@ = 3,rsin@ = 4 thenr=?: 5a 4 3 2 28 | 1—cos2a =--: 2sin2a ¥ 2cos*@ 2sing 2cose 29 sin2@ =o am 2tan@ 1=tan*@ | None 14+tanz@ Towne —tan®6 ious Fe cos == cos*(@/2)— | 2sin*(@/2) 1 » None 30 sin?(9/2)¥ | —1 + 2605766 Gs ga | 510388 =~ 3sin@ — 4sin*@ “a3costd 4cos*@ dsin39 — 3sin)}) —4eosé — 3cos@ 32 | SMa tan(A/2) ¥ cot(A/2), | \-sin(A/2) cos(A/2) 1+cosA i. teste” 33 tan(a/2) =~: 1 — cosa 1-sina 1+sina + | £ 5 —_ | & ; 1+ tant@ 1 cosa 1—sine gq | tanze = -: tané 2tan?@ 1 —tan?6 “1+tan?d 1—tan76 1+ tan?6 cos3a = +: 2cos(3a 4cos?a@ — None of these 35 /2)sin(3a | 3cosaV¥ f2) ag | COs28 =: SM Po “2tane 2tan@ 1-tan?@ None of these “S| 1 — tan’ 1+tantg | t*tan*@ 37 | (cos@ + sind)* + (cos? ing)” S92" | 0 lv 4 1 ge | 222 isequalto: ome We” tan2@ cot26 sin2@ ¥ cos20 i+tant@ stat 39 | + sin(6/2) ¥ cos(@/2) sin@ cosé 40 | On simplifying the result is: sine cod tand ¥ secO 41 — » * sind cot(@/2) ¥ esc2@ None sin : 42 | 2cos®(@/2) equals: 14+cosd ¥ 1-cosé 1-—siné 1+siné 4g | ifsina = 2/3, cosa = V¥5/3,sinta= | 4/5/9V 1/3 | 2 ts 44 sin3@ — sin5@ equals: 2sin48cos2@ | 2cos4@sind | —2cos4@sin@ | 2sin4@cos0 v 45 sinSé@ + sin3@ is equal to: 2cos2@sin@ | —2cos4@sin@ | —2cos4Acosé | 2sin40cos0 v 46 | cos48° + cos12° =?: 2cos18° V3cos18° ¥ 3cos 19° None of these BR Mathematics 11™ (NEW SNC) 20 Position Winning MCQs >» | 47 | cos(@ +B) + cos(a — B) ==: 2sinecasf 2sinasinf | 2cosacosf ¥ | —2sinesinf 2sin(2)cos(@=2) =?; sinP+sin@ | sinP—sinQ | cosP +cosQ | cosP — cosQ 48 2 2 v Chapter 11: Trigonometric Functions and their Graphs 1 Trigonometric functions are also called: | Discontinuou | Non- jadic Not pericdi s functions functions ¥ ot pesos € ain of y = is: x= 2 The domain of y = cotx is [-1,1] (-1/2,n/2) R % ae Q 3 | Domain of y = sinx is: {-1,1] [—2/2, 7/21, Rv Q Range of y = secx is: L Digs —1 or y<-lLy 4 [0.77] fo yziv | 21 5 | Range of y = tanx is: Rv All real Any of them numbers . 6 | Range of y = sinx is: (-1,1] ¥ (-1,1] Range of y = is: 7 ange of y = cosx 1s: yoaken -l
