Multiplication trick(1)
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1. This document provides multiplication tricks for multiplying: - 2-digit by 1-digit numbers - 2-digit by 2-digit numbers - 3-digit by 1-digit numbers - 3-digit by 3-digit numbers 2. For 2-digit by 1-digit, you multiply each digit separately and place the results in columns from right to left. 3. For 2-digit by 2-digit, you multiply the digits in pairs and add the results according to the standard multiplication algorithm. 4. For 3-digit by 1-digit, you multiply each digit separately and place the results in columns from right to left. 5. For 3-digit by 3
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(A) (B) 0
(C) 1 (D) log (1 + e)
2a
Q.11
0
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(C) 1/2 (D) – 1/2
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(A) (B) /2
(C) /4 (D) 2
(A) –
3
(1–cos a3) (B) 3 (1– cos a3)
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/2
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1 (1– cos a3)
3
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Q.5
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(C) log (3/4) (D) None of these
etan1 x
1 x2 dx equals-
Q.12 x ex2 dx equals-
0
(A) 1 (B) 2
(C) 1/2 (D) None of these
0
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2
Q.13
1 x
1
x2 1
dx equals-
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0 x
dx , equals-
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2
(A) log3 (3
– 1)
(B) 0
Q.14 The value of
ex3
0
3ex
4j(x2 + ex ) dx
2 2 is-
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z /4 sec2 x
(A) (3e + 2)/6 (B) (3e – 2) /6
(C) (3e – 2)2/36 (D) None of these
Q.7
dx equals-
0 (1 tanx)(2 tan x)
2
3
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0
1 x2
(A) /3 (B) 2/3 (C) 2/3 (D) 4/3
(A) /4 (B) /2 (C) (D) /8
x tan1 x
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(A) /2 (B) /6
bc
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b
(C) /4 (D) /8
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(A) f(x c)dx
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b
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(C)
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a
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2
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2
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+1)
(D) 1 [{f(b)}2 – {f(a)}2]
2
1
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ex 1
1
dx equals-
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2 dx is equal to-
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1
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FGe 1IJ
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(C) (a + b) /3 (D) None of these
(A) k2
b
f(x)dx
a
b
(B) k f(x)dx
a
Q.28
/ 2
ex (log sin x + cot x) dx =
b
(C) k f(kx) dx
a
b
(D) k3 f(k x)dx
a
/ 4
(A) e / 4 log 2 (B) – e / 4 log 2
1 1
(C) 2 e / 4 log 2 (D) – 2 e / 4 log 2
/ 2 sin x cos x
3 1 x
1 x2 1
Q.29 0
1 sin 4 x
dx =
Q.37 tan
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- 3. 1) 2 digit 1 digit A B 2 3 2 3 7 6 7 6 * C * 7 * 7 * 9 * 9 _______ ____ _____ _____ ______ L R 14 1(4+2)1 63 6(3+5)4 =161 =684
- 4. 2) 2 digit 2 digit A B A B A B * C D * C D * C D ______ __________ _________ A * C (A*D)+(B*C) B * D
- 5. Example - 7 5 7 5 7 5 * 6 3 * 6 3 * 6 3 ________ ________ _________ 42|?|? 42+5|1|? 47|1+1|5 =47|1|? =4725
- 6. 3) 3 digit 1 digit A B C * D ___________ A*D|B*D|C*D
- 7. Example - 4 5 6 4 5 6 4 5 6 * 3 * 3 * 3 ________ _________ _________ 12|?|? =12+1|5|? =13|5+1|8 =13|5|? =1368
- 8. 3) 3 digit 3 digit A B C A B C A B C A B C A B C X Y Z X Y Z X Y Z X Y Z X Y Z
- 9. Example - 7 6 5 7 6 5 7 6 5 * 1 2 3 * 1 2 3 * 1 2 3 ________ ___________ __________ 7|?|?|?|? 7+2|0|?|?|? 9|0+3|8|?|? =9|0|?|?|?|? =9|3|8|?|? 7 6 5 7 6 5 * 1 2 3 * 1 2 3 ___________ __________ 9|3|8+2|8|? 9|4|0|8+1|5 =9|4|0|8|? =94095
- 10. THANK YOU E-mail – njp9904@gmail.com Mob - 9714453679