MATHEMATICS MHT-CET TRIUMPH. Salient Features MULTIPLE CHOICE

Transcription

1 Written in aordane with the latest MHT-CET Paper Pattern whih inludes topis based on Std. XII S. and relevant hapters of Std. XI S. (Maharashtra State Board) MHT-CET TRIUMPH MATHEMATICS MULTIPLE CHOICE Salient Features Inludes all hapters of Std. XII and relevant hapters of Std. XI as per latest MHT-CET Syllabus. Exhaustive subtopi wise overage of MCQs. Important formulae provided in eah hapter. Various ompetitive exam questions updated till the latest year. Inludes MCQs from JEE (Main) 0, 07 and 08. Inludes MCQs upto MHT-CET 08. Evaluation test provided at the end of eah hapter. Two Model Question Papers with answer key at the end of the book. San the adjaent QR ode or visit to download Hints for relevant questions and Evaluation Test in PDF format. Printed at: India Printing Works, Mumbai Target Publiations Pvt. Ltd. No part of this book may be reprodued or transmitted in any form or by any means, C.D. ROM/Audio Video Cassettes or eletroni, mehanial inluding photoopying; reording or by any information storage and retrieval system without permission in writing from the Publisher. TEID: 750_JUP P.O. No.

2 Sr. No. Textbook Chapter No. CONTENT Chapter Name Std. XI Page No. Trigonometri Funtions Trigonometri Funtions of Compound Angles Fatorization Formulae 9 Straight Line Cirle and Conis 57 Sets, Relations and Funtions 8 7 Sequene and Series 8 Probability Std. XII 9 Mathematial Logi 7 0 Matries 8 Trigonometri Funtions 0 Pair of Straight Lines 5 Vetors 8 Three Dimensional Geometry 5 7 Line 75 8 Plane Linear Programming 8 Continuity 8 9 Differentiation 7 0 Appliations of Derivatives 8 Integration 0 5 Definite Integrals 55 Appliations of Definite Integral 8 7 Differential Equations Probability Distribution 5 9 Binomial Distribution 5 Model Question Paper - I 59 Model Question Paper - II 5 Note: Questions of standard XI are indiated by * in eah Model Question Paper.

3 Textbook Chapter No. 0 Trigonometri Funtions Chapter 0: Trigonometri Funtions Subtopis. Trigonometri Funtions. Fundamental Identities Trigonometry in Graphial Motion In omputer graphis, Trigonometry is used in graphial motion and rotation, D rotation matries are used to rotate objets and these matries are made up of several trigonometri funtions. Chapter at a glane. Trigonometri Funtions with the help of standard unit irle: Let mxop = be the angle in standard position and P(x, y) be the point on the terminal ray suh that l(op) = r > 0. Then, Y y x i. sin = ii. os = r r iii. tan = y x, (if x 0) iv. ose = r P(x, y), (if y 0) y v. se = r x, (if x 0) vi. ot = x X X, (if y 0) M O y. Interrelation between trigonometri funtions: i. ose = sin, (if sin 0) ii. se =, (if os 0) os iii. tan = sin os, (if os 0) iv. ot =, (if sin 0) os sin Note: i. Trigonometri funtions do not depend upon the position of point P on terminal ray but depends upon the measure of angle (). ii. Co-terminal angles have same trigonometri funtions. iii. P (x, y) (os, sin ). Signs of trigonometri funtions in different quadrants: Quadrant I II III IV Signs of the T-funtions All T-funtions are positive sin and ose are positive. All others are negative. tan and ot are positive. All others are negative. os and se are positive. All others are negative. X sin is (II) tan is (III) Y O Y Y All are (I) os is (IV) X

4 MHT-CET Triumph Maths (MCQs) Mnemonis: The above table an be memorized with the help of All sin tan os (I) (II) (III) (IV) Add Sugar To Coffee. Trigonometri funtions of partiular angles: Angles Trigonometri funtions 0 (0 ) sin 0 os tan 0 0 π 5 π 0 π 90 π 80 ( ) 70 π 0 ( ) ot 0 0 se ose 5. Fundamental Identities: For any angle of measure, i. sin + os = sin = os os = sin ii. + tan = se se tan = se = tan iii. + ot = ose ose = ot ose ot =. Domain and range of trigonometri funtions: i. The domain, range and period of the six trigonometri funtions are given below: T-funtions Domain Range Period sin x R [, ] os x R [, ] tan x xr: x (n),ni R ot x {x R : x n, n I} R se x xr: x (n),ni R (, ) ose x {x R : x n, n I} R (, )

5 Chapter 0: Trigonometri Funtions ii. iii. Standard inequalities of trigonometri funtions: a. sin b. os. se or se d. ose or ose Periodiity of trigonometri (irular) funtions: A funtion is periodi if its value repeats after every fixed interval. The fixed interval is alled period. f(x) = f(x + n), for all x and x + n in domain of f, and n 0 a. sin ( + n) = sin, os ( + n) = os, where n I Hene sin and os are periodi funtions and the period is. b. tan ( + n) = tan, ot ( + n) = ot, where n I Hene tan and ot are periodi funtions and the period is. 7. Trigonometri funtions of negative angle: i. sin () = sin ii. os () = os iii. tan() = tan iv. ot () = ot v. se () = se vi. ose () = ose Shortuts. If x = se + tan, then x = se tan. If x = ose + ot, then = ose ot x. sin + sin sin n = n sin = sin =.. = sin n =. os + os os n = n os = os =.. = os n = 5. i. sin + ose = sin = ii. sin + ose = sin =. i. os + se = os = ii. os + se = os = 7. sin + os = sin os 8. sin + os = sin os 9. sin + os = os + sin = sin os 0. sin + ose, os + se and se + ose. If se + tan = m, m >, then lies in the first quadrant. If se + tan = m, 0 < m <, then lies in the fourth quadrant. If se + tan = m, m <, then lies in the seond quadrant. If se + tan = m, < m < 0, then lies in the third quadrant.

6 MHT-CET Triumph Maths (MCQs) Classial Thinking. Trigonometri Funtions. If sin = and tan = 9, then os is 8 7 (B) (D) 7 8 setan. If 5 sin =, then is equal to setan (B) (D) sin os. ot tan 0 (B) os sin (D) os + sin. If sin = and tan =, then lies in first quadrant (B) seond quadrant third quadrant (D) fourth quadrant 5. If sin = and os =, then lies in I st quadrant (B) II nd quadrant III rd quadrant (D) IV th quadrant. When x =, then tan x is (B) 0 (D) not defined 7. sin + os tan = (B) (D) 8. If x sin 5 os tan 0ose0 0=, then x = se 5ot 0 (B) 8 (D) 9. If sin = os, then is equal to 5 (B) 0 75 (D) 0 0. If sin ( ) = and os ( + ) =, where 5 and are positive aute angles, then = 5, = 5 (B) = 5, = 5 = 0, = 5 (D) = 5, = 0. Fundamental Identities. If tan = 0, then os is equal to 0 (B) 0 (D) 9. If tan = and lies in the fourth 0 quadrant, then se = (B) 0 (D) 0. If tan = 5 and lies in the Ist quadrant, then os is (B) 5 5 (D). If sin = and lies in the seond 9 quadrant, then the value of se + tan is 5 5 (B) (D) For any real number x (n+), se xse x is equal to tan x tan x (B) tan x + tan x tan x tan x (D) tan x. Whih of the following is true? tan sin = tan sin (B) se ose = se ose ose + ot = ose ot (D) none of these 7. If x = se + tan, then x x = (B) se (D) tan 8. ot x + tan x = ot x (B) ot x se x ose x (D) ot x

7 Chapter 0: Trigonometri Funtions sin 0os 0 9. The value of sin 0os 0 0 (B) (D) 0. If x = a os + b sin and y = a sin b os, then a + b is equal to x y (B) x + y (x + y) (D) (x y). If x = a os, y = b sin, then a b b a (B) x y x y x y x y (D) a b b a. If os x + os x =, then the value of sin x + sin x is (B) 0 (D). If sin x+sin x=, then os 8 x+ os x+os x = 0 (B) (D). Whih one of the following is inorret? sin = 5 (B) os = se = (D) tan = 0 5. Whih of the following is possible? os = 7 5 (B) sin = 8 5 se = 5 (D) tan = 5. The smallest value of 5 os + is 5 (B) 7 (D) 7 Critial Thinking. Trigonometri Funtions. If tan = p psin qos, then the value of q psin qos is p q p q (B) p q p q pq 0 (D) pq. The value of os + se is always less than (B) equal to greater than, but less than (D) greater than or equal to. If sin x + ose x =, then sin n x + ose n x is equal to (B) n n (D) n. Whih of the following relations is orret? sin < sin (B) sin > sin sin = sin (D) sin = sin Whih of the following is orret? tan > tan (B) tan = tan tan < tan (D) tan =. If os A =, then tan A = 0 (B) (D) not defined 7. If tan (A B) =, se (A + B) =, then the smallest positive value of B is 5 9 (B) (D) 8. If sin (A + B + C) =, tan (A B) = se (A + C) =, then A = 0, B = 0, C = 0 (B) A = 0, B = 0, C = 0 A = 90, B = 0, C = 0 (D) A = 0, B = 0, C = 0. Fundamental Identities and 9. If os A = 5, os B = 5 and < A < 0, < B < 0, then the value of sin A + sin B = (B) (D) 0 0. If tan + se = and 0 < <, then is equal to 5 (B) (D). sin If, then is equal to sin se tan (B) se + tan tan se (D) se + tan 5