IIT JEE - CLASS XI & XII MATHEMATICS TOPIC WISE SYLLABUS :
1) QEE Based on formula for roots
2) QEE Based on discriminent
3) QEE one common root
4) QEE both roots common
5) QEE Quadratic expression
6) QEE remainder theorem
7) QEE formation of QE
8) QEE sign of QE
9) QEE interval in which roots lie
10) Log definition
11) Log properties of log
12) Log log inequalities
13) Log Log graph
14) CN definition based problems
15) CN modulus
16) CN argument
17) CN properties of modulus
18) CN properties of argument
19) CN properties of conjugate
20) CN de moivres thm
21) CN nth root of unity
22) CN SL
23) CN C
24) CN E
25) CN H
26) CN Section Formula
27) CN rotation Thm
28) CN Cube roots of unity
29) CN Max. and Min. value of mod. of a complex number
30) CN Roots of complex equations
31) CN Intersection of a straight line and circle on Argand plane
32) BT definition
33) BT greatest co-efficient
34) BT greatest term
35) BT Binomial Co-efficient of a specific type of term
36) BT binomial series with k.Binomial coefficient
37) BT binomial series with Binomial coefficient/k type
38) BT binomial series with Binomial coefficient/Binomial coefficient miscellaneous
39) BT miscellaneous
40) BT Sum of co-efficient and Relationship between the Co-efficient of the expansion like (a + bx + cx2)
41) PS AP
42) PS AM
43) PS GP
44) PS GM
45) PS HP
46) PS HM
47) PS AGP
48) PS Method of differences
49) PS Vn Method
50) PS AM to GM to HM
51) PS weighted AM
52) PS AM of mth power
53) Limits Problems based on LHL and RHL
54) Limits Problems based on existance of limits
55) Limits Problems based on trigonometric limits
56) Limits Problems based on direct substitution
57) Limits Problems based on rationalization or double rationalization
58) Limits Problems based on standard results
59) Limits Problems based on limits of the form x implies infinity
60) Limits Problems based on exponential limits
61) Limits Problems based on log limits
62) Limits Problems based on 1 to power infinity form
63) Limits Problems based on L hospital rule
64) Limits Problems based on Newton Lebnitz rule
65) Limits Problems based on sandwitz thm
66) Limits specially series expansion based problems
67) Limits Limit of composite functions
68) Limits Max. value and MIn. value of a function using limit
69) SL Distance formulae
70) SL section formulae
71) SL Centroid
72) SL Incentre
73) SL circumcentre
74) SL orthocentre
75) SL centroid , incentre , circumcentre orthocentre in a right angle and equilateral D
76) SL area of D
77) SL condition of collinearity of 3 points
78) SL slope of a line
79) SL Equation of st Line in - Slope form
80) SL Equation of st Line in - One point form
81) SL Equation of st Line in - two Point form
82) SL Equation of st Line in - intercept form
83) SL Equation of st Line in - parametric form
84) SL Equation of st Line in - normal form
85) SL general form to different form
86) SL ^distance of a point from a line
87) SL distance b/w two parallel lines
88) SL angle b/w two lines
89) SL Eqn of a line Parallel to a given line
90) SL Eqn of a line perpendicular to a given line
91) SL family of st line
92) SL Locus
93) SL Concurrent Line
94) SL Acute angle bisector
95) SL Obtuse angle bisector
96) SL rotation of axis
97) SL translation of axis
98) SL pair of st lines
99) SL angle between two pair of st lines
100) SL condition for eqn of second degree to represent two lines
101) SL eqn of pair of line joing pts of intersection of a line and a conic
102) Circle Eqn of circle in various forms
103) Circle radius and centre of eqn of circle in various forms
104) Circle condition on eqn of second degree to represent circle
105) Circle position of a point w.r.t. a circle
106) Circle parametric eqn of a circle
107) Circle Tangent
108) Circle normal
109) Circle condition of tangency
110) Circle chord of contact
111) Circle eqn of chord with mid pts
112) Circle pair of tangents
113) Circle length of tangent
114) Circle condition for two circles touching each other
115) Circle condition for two circles touching intersecting other
116) Circle family of circle - passing thrgh pt of intersection of 2 circles
117) Circle family of circle - passing thrgh pt of intersection of line and a circles
118) Circle family of circle - passing thrgh two points
119) Circle family of circle - always touching a st line at given pt
120) Circle radical axis and its property
121) Circle common chord
122) Circle condition for orthogonal intersection
123) Circle common tangent Equation
124) Circle Length of intercept made by a circle on a line
125) Circle Angle between two circles
126) Circle Basing on director circle of a circle
127) Circle Equation of a chord of mid-point is given
128) Parabola eqn of parabola in std form
129) Parabola Problem based on - finding focus, directrix, vertex , latus rectum etc
130) Parabola eqn of tangent
131) Parabola eqn of normal
132) Parabola eqn of chord with mid pts
133) Parabola eqn of chord with mid pts
134) Parabola eqn of pair of tangent
135) Parabola condition of a line to be tangent to parabola
136) Parabola geometrical properties of a parabola
137) Parabola focal chord
138) Parabola condition for focal chord
139) Parabola pt of intersection of tangents
140) Parabola pt of intersection of normals
141) Parabola Condition for z normals
142) Parabola Problems based on normal
143) 12 IITJEE Mathematics Parabola Roots of cubic equations
144) Ellipse Std Form
145) Ellipse Problem based on - finding focus, directrix, vertex , latus rectum etc
146) Ellipse position of a pt w.r.t. ellipse
147) Ellipse parametric co-ordinates
148) Ellipse condition of a line to be tangent to Ellipse
149) Ellipse focal distance
150) Ellipse eqn of tangent
151) Ellipse eqn of normal
152) Ellipse eqn of chord of contact
153) Ellipse eqn of chord with mid pts
154) Ellipse eqn of pair of tangent
155) Ellipse condition of a line to be tangent to parabola
156) Ellipse geometrical properties
157) Ellipse focal chord
158) Ellipse pt of intersection of tangents
159) Ellipse pt of intersection of normals
160) Ellipse chord of contact
161) Ellipse director circle
162) Ellipse auxiliary circle
163) Ellipse Point of intersection of tangents
164) Ellipse Co-normal points
165) Ellipse Angle between the tangents
166) Ellipse Basing on director circle of ellipse
167) Ellipse Intersection of ellipse and a circle
168) Ellipse Equation of chord joining two points having eccentric angle
169) Hyperbola basic definition
170) Hyperbola Std form
171) Hyperbola Problem based on - finding focus directrix, vertex , latus rectum etc
172) Hyperbola position of a pt w.r.t. hyperbola
173) Hyperbola focal distance
174) Hyperbola eqn of tangent
175) Hyperbola eqn of normal
176) Hyperbola eqn of chord of contact
177) Hyperbola eqn of chord with mid pts
178) Hyperbola eqn of pair of tangent
179) Hyperbola condition of a line to be tangent to parabola
180) Hyperbola geometrical properties
181) Hyperbola focal chord
182) Hyperbola pt of intersection of tangents
183) Hyperbola pt of intersection of normals
184) Hyperbola chord of contact
185) Hyperbola director circle
186) Hyperbola Auxiliary circle
187) Hyperbola rectangular hyperbola
188) Hyperbola eqn of tangent to rectangular hyperbola
189) Hyperbola eqn of normal to rectangular hyperbola
190) Hyperbola pt of intersection of rectangular hyperbola and a circle
191) Hyperbola Asymptotes
192) Hyperbola Basic properties of conjugate hyperbola of a hyperbola
193) Hyperbola Co-normal points
194) Hyperbola Intersection of a rectangular hyperbola with a circle
195) Hyperbola Common tangent between hyperbola and circle
196) Hyperbola Equation of Asymptotes
197) PC Fundamental principle of counting (multiplication)
198) PC Fundamental principle of counting (addition)
199) PC Permutation of n things taking r at a time p(n,r)
200) PC Permutation of n things, p are alike, q are alike, r are alike
201) PC Permutation of n things taking r at a time, each may be repeated any number of times ( n^r)
202) PC Permutation under condition
203) PC Arrangement around the circular table
204) PC Arrangement of beads around a circular necklace
205) PC Circular permutation of n different things taken r at a times
206) PC combination of n things taking r at a time(c(n,r)
207) PC Combination of n things taken r at a time when k perticular objects occur (C(n-k, r - k))
208) PC C (n, 1) + C (n, 2) + ……+C(n, n) =2^n - 1.
209) PC Out of p + q + r + t things p, q, r and t are alike
210) PC total no of divisors of a number
211) PC Division into groups
212) PC Arrangement in groups
213) PC Derangements
214) PC Multinomial theorem
215) PC Exponent of prime p in n!.
216) PC Sum of division of a composite number
217) Trigonometry Identities
218) Trigonometry Compound angles
219) Trigonometry Multiple angles
220) Trigonometry Sub-multiple angles
221) Trigonometry Transformation
222) Trigonometry Graph of trignomety(periodicity) ratio
223) Trigonometry Trignometric equations
224) Trigonometry Trignometric inequations
225) Trigonometry Properties of triangle
226) Trigonometry Trignometric ratios
227) Trigonometry Heights and distances
228) Trigonometry Sum and product formulae
229) Trigonometry Extreme value problems
230) Trigonometry Ratios & Identities Relation between different systems of measurement of Angles
231) Trigonometry Ratios & Identities fundamental identities
232) Trigonometry Ratios & Identities Sign of Trigonometric ratios
233) Trigonometry Ratios & Identities Domain & range of Trigonometric ratios
234) Trigonometry Ratios & Identities Trigonometric ratios of Allied angles ( Sum or difference is multiple of 90)
235) Trigonometry Ratios & Identities Trigonometric ratios of sum & difference of two angles
236) Trigonometry Ratios & Identities Transformation Formula - Product into Sum or Difference
237) Trigonometry Ratios & Identities Transformation Formula - Sum and difference into Poduct
238) Trigonometry Ratios & Identities Trigonometric ratios of multiple angles
239) Trigonometry Ratios & Identities Trigonometric ratios of sub-multiple angles
240) Trigonometry Ratios & Identities greatest & least values of trigonometric expressions
241) Trigonometry Ratios & Identities Trigonometric Identities
242) Trigonometry Ratios & Identities conditional identities
243) Trigonometry Ratios & Identities polygons
244) Trigonometry Ratios & Identities Sum of sine/cos series where angles are in AP
245) Trigonometry Ratios & Identities Product of Cosine where angles are in GP with r = 2 or 1/2
246) Trigonometric Equations Principal & General solution
247) Trigonometric Equations Conversion to lower degree
248) Trigonometric Equations Conversion into quadratic form
249) Trigonometric Equations Change of variable
250) Trigonometric Equations Inequalities
251) Trigonometric Equations Problems based on extreme values
252) Trigonometric Equations Solution of Trigonometric Equations - Priciple values
253) Trigonometric Equations Solution of Trigonometric Equations - in a given Interval
254) Trigonometric Equations Solution of Trigonometric Equations - General Solution
255) Trigonometric Equations Solution of Simultaneous trigonometric equation - in one variable
256) Trigonometric Equations Solution of Simultaneous trigonometric equation - in two variable
257) Trigonometric Equations Trigonometric Inequation
258) Trigonometric Equations Solution of Trigonometric Equations - based on extreme values of Trigonometric ratios
259) Solution of Triangle Sine Rule
260) Solution of Triangle Cosine Rule
261) Solution of Triangle Projection formula
262) Solution of Triangle Napier's Analogy
263) Solution of Triangle Half angle formula
264) Solution of Triangle Area of triangle , Heron's formula
265) Solution of Triangle solution of Triangle - Two sides and included angle are given
266) Solution of Triangle solution of Triangle - Two angles and included side are given
267) Solution of Triangle solution of Triangle - Case of Ambiguity
268) Solution of Triangle Circles Connected with a Triangle - Circumcircle
269) Solution of Triangle Circles Connected with a Triangle - Incircle
270) Solution of Triangle Circles Connected with a Triangle - Escribed Circles
271) Solution of Triangle m-n theorem
272) Solution of Triangle apolloneus theorem
273) Solution of Triangle Distence of Circumcentre from the sides
274) Solution of Triangle Distence of incentre from the vertices
275) Solution of Triangle Distence of orthocentre from the vertices
276) Solution of Triangle Distence of orthiocentre from the sides
277) Solution of Triangle Distance between various centres
278) Solution of Triangle Circles circumscribing or inscribing a regular Polygon
279) Solution of Triangle cyclic quadrilaterals
280) Addition of matrices
281) Multiplication of matrices
282) properties of matrix multiplication
283) Transpose
284) Adjoint
285) inverse of matrix
286) types of matrices
287) system of linear equation and solution
288) Conjugate of a matrix
289) Equality of two matrices
290) Using of determinant to explain some properties of adjoint of matrix
291) DET evaluation of 2X2 det
292) DET evaluation of 3X3 det
293) DET minors and cofactors of a set
294) DET reflection property
295) DET all zero property
296) DET proportionality property
297) DET Switching property
298) DET Scalar multiple property
299) DET sum property
300) DET property of invarience
301) DET factor property
302) DET triangle property
303) DET product of 2 det
304) DET conjugate of a det
305) DET differentiation of a det
306) DET solution of linear eqn
307) DET cramers rule
308) DET Solution of linear equations using Crammer’s Rule
309) FN sets and types of sets
310) FN number of elements in sets
311) FN operation on sets
312) FN venn diagram based problems
313) FN cartesian products of two sets
314) FN relation and types of relations
315) FN function and types of functions
316) FN one to one functions
317) FN onto functions
318) FN bijective functions
319) FN inverse of a function
320) FN composite function
321) FN binary operation
322) FN modulus function
323) FN GIF
324) FN domain of a function
325) FN Range of a function
326) FN Algebra of a function
327) FN composite function
328) FN even fn
329) FN odd fn
330) FN period of a function
331) FN functional relationship (investigate fn)
332) FN no of solution type problems
333) FN Graphical solution of function
334) Continuity & Differentiabilty To check continuity of a fn
335) Continuity & Differentiabilty type of discontinuity
336) Continuity & Differentiabilty continuity of composite fn
337) Continuity & Differentiabilty finding unknown parameters from continuity
338) Continuity & Differentiabilty to find points of discontinuity
339) Continuity & Differentiabilty no of points of discontinuity
340) Continuity & Differentiabilty to check differentiability of a fn
341) Continuity & Differentiabilty LHD & RHD of a fn
342) Continuity & Differentiabilty existance of derivative
343) Continuity & Differentiabilty Problems based on continuity and differentiability using graph
344) Continuity & Differentiabilty Problems based on finding unknown parameters
345) Continuity & Differentiabilty Problems based on piece wise defined function
346) Continuity & Differentiabilty Problems based on investigating fns using functional relationship
347) Continuity & Differentiabilty Problems based on first principle
348) Continuity & Differentiabilty Using continuity & differentiability to determine number of real roots of a function
349) Differentiation derivative of algebric fn
350) Differentiation derivative of log fn
351) Differentiation derivative of exponential fn
352) Differentiation derivative of trigonometric fn
353) Differentiation derivative of inverse trigonometric
354) Differentiation derivative of sum and difference of two or more fn
355) Differentiation derivative of product of two fn
356) Differentiation derivative of quotient of two fns
357) Differentiation derivative of implicit fn
358) Differentiation derivative of parametric fn
359) Differentiation derivative of one function w.r.t another fn
360) Differentiation derivative of fn to power fn form
361) Differentiation derivative of infinite series type problems
362) Differentiation chain rule
363) Differentiation first principle
364) Differentiation higher order derivative
365) AD Problems based on Tangents to a curve
366) AD Problems based on Normals to a curve
367) AD Problems based on angle of intersection of two curves
368) AD monotonocity based problems - interval of increase and decrease
369) AD monotonocity based problems - inequality based
370) AD monotonocity based problems - inequality based - using first derivative
371) AD monotonocity based problems - inequality based - using second derivative
372) AD maxima/minima based problems - first derivative test based
373) AD maxima/minima based problems - second derivative test based
374) AD maxima/minima based problems - higher order derivative test based
375) AD maxima/minima based problems - local maxima or minima based
376) AD maxima/minima based problems - global maxima or minima based
377) II Problems based on substitution - Algebric substitution
378) II Problems based on substitution - trigonometric substitution
379) II Problems based on by parts
380) II Problems based on integration of rational function
381) II Problems based on integration of irrational function
382) II integration using complex number
383) II integration using standard substitution
384) II conversion of unknown form to known form
385) II based on ò ex (f(x) + f`(x)) dx type
386) DI Limit as a sum
387) DI Problems based on a-x property
388) DI Problems based on integral seperator property
389) DI Problems based on a+b-x property
390) DI Problems based on even and odd fn
391) DI Problems based on f(2a-x) = f(x) property
392) DI Problems based on periodic fns
393) DI Problems based on partial derivatives
394) DI lebnitz rule
395) DI inequalities
396) DI piece wise continious fns
397) DI Solving definite integration using graphs
398) DE order and degree of DE
399) DE formation of DE
400) DE solution of DE by variable seperable method
401) DE solution of DE by eqn reducible to variable seperable method
402) DE solution of DE of the homogeneous form
403) DE solution of DE reducible to the homogeneous form
404) DE solution of LDE
405) DE solution of bernoulis eqn
406) DE solution of general form of LDE
407) DE solution of general form of variable seperation
408) DE orthogonal trajectories
409) DE application of DE
410) DE rate of change problem
411) DE geometrical apllication
412) DE Solution of DE reducible to Bernoulii form
413) Area area bounded by f(x) , x axis, x=a and x=b.
414) Area area bounded by g(y) , y axis, y=a and y=b.
415) Area area bounded by f(x) , g(x) x=a and x=b
416) Area curve and its asymptotes
417) Area Area bounded by a single curve y = f(x)
418) Vector Modulus or magnitude
419) Vector Types of vectors
420) Vector Addition and subtraction of vectors
421) Vector Position vectors
422) Vector Section formula internal
423) Vector Section formula external
424) Vector Component of a vector
425) Vector Linear combination
426) Vector Linear dependent or independent
427) Vector Collinearity of three points
428) Vector Collinearity of two vectors
429) Vector Collinearity of four points
430) Vector Collinearity of three vectors
431) Vector Product of two vectors
432) Vector Scalar product
433) Vector Work done
434) Vector Vector product
435) Vector Geometrical interpretation of cross product
436) Vector Moment of a force
437) Vector Triple product
438) Vector Scalar triple product
439) Vector Vector triple product
440) Vector Geometrical interpretation
441) 3D Distance formula
442) 3D Section formula
443) 3D Centriod of a triangle
444) 3D Centriod of a tetrahedron
445) 3D Direction cosines
446) 3D Direction ratios
447) 3D Angle between two vectors
448) 3D Angle in terms of direction ratios
449) 3D Projection of the join of two points
450) 3D Line through a point and parallel to a vector (vector form)
451) 3D Line through a point and parallel to a vector (cartesiabn form)
452) 3D Line passing through two points (v.f.)
453) 3D Line passing through two points (c.f.)
454) 3D Angle between two lines (v.f.)
455) 3D Angle between two lines (c.f.)
456) 3D Perpendicular from a point to a line
457) 3D Shortest distance between two skew lines
458) 3D General equation of a plane
459) 3D Plane in normal form ( v. F. )
460) 3D Plane in normal form ( C. F. )
461) 3D Transformation of general form of normal form
462) 3D Plane passing through a point and perpendicular to a vector ( v. F. )
463) 3D Plane passing through a point and perpendicular to a vector ( C. F. )
464) 3D Equation of a plane in intercept form
465) 3D Plane passing through three points ( V.F.)
466) 3D Plane passing through three points ( C.F.)
467) 3D Plane passing through two points and parallel to a vector ( v. F.)
468) 3D Plane passing through two points and parallel to a vector ( C. F.)
469) 3D Plane passing through two points and parallel to two vectors ( V. F.)
470) 3D Plane passing through two points and parallel to two vectors ( C. F.)
471) 3D Plane parallel to a given plane ( v.F.)
472) 3D Plane parallel to a given plane ( c.F.)
473) 3D Angle between two planes ( v. F. )
474) 3D Angle between two planes ( C. F. )
475) 3D Angle between a line and a plane ( V.F)
476) 3D Angle between a line and a plane (C.F)
477) 3D Planes bisecting the angles between two planes ( v. F. )
478) 3D Planes bisecting the angles between two planes ( C. F. )
479) 3D Bisector of acute / obtuse angle
480) 3D Distance of a point from a plane (V.F
481) 3D Distance of a point from a plane (C.F)
482) 3D Distance between two parallel planes ( v. F. )
483) 3D Distance between two parallel planes ( C. F. )
484) 3D Planes passing through the intersection of two planes ( v. F. )
485) 3D Planes passing through the intersection of two planes(V.F)
486) 3D Two sides of a plane
487) 3D Condition for a line to lie in a plane ( v. F. )
488) 3D Condition for a line to lie in a plane ( C. F. )
489) 3D Condition for two lines to be intersecting coplaner and the plane containing them ( v. F. )
490) 3D Condition for two lines to be intersecting coplaner and the plane containing them (C.F.)
491) 3D Equation of a sphere ( v. F. )
492) 3D Equation of a sphere (C. F. )
493) 3D Equation of a sphere through four points ( v. F. )
494) 3D Equation of a sphere the extremities of diameter being
495) 3D Equation of a sphere the extremities of diameter being given ( c. F. )
496) 3D Condition of tangency ( v. F. )
497) 3D Condition of tangency ( C. F. )
498) Probability Sample space
499) Probability Mixed events
500) Probability Equally likely events
501) Probability Independent events
502) Probability Complementary events
503) Probability Mutually exclusive events
504) Probability Exhaustive events
505) Probability Classical definition of probability
506) Probability Addition theorem of probability
507) Probability Compound probablity
508) Probability Conditional probablity
509) Probability Bay`s theorem
510) Probability Binomial theorem on probability
511) Probability Multinomial theorem on probablity
512) Probability Binomial distribution
513) Probability Random variable
514) Inverse Trigonometry Definition of inverse functions
515) Inverse Trigonometry Domain and Range
516) Inverse Trigonometry Graphs of inverse functions
517) Inverse Trigonometry Properties of inverse functions
518) Inverse Trigonometry Inequalities
519) Inverse Trigonometry Sum of series
520) Inverse Trigonometry Max and Min. values
521) Inverse Trigonometry Solution of Inverse trigonometric Equations
522) Inverse Circular Function Inverse circular Function - domain & range
523) Inverse Circular Function problems based on inverse trigonometric function of trigonometric functions
524) Inverse Circular Function problems based on trigonometric functions of inverse trigonometric function
525) Inverse Circular Function Conversion of one ICF to other
526) Inverse Circular Function sum & Difference of Two or more ICFs