MATHEMATICS PAPER
1. CONSIDER AN AP –
A1, A2, A3, A4…………………………….An
WITH COMMON DIFFERENCE D.
NOW THE FIRST TERM OF THE AP IS THE DISTANCE BETWEEN THE ORIGIN AND THE
INTERSECTION OF THE LINES –
x + 2y = 10 ---------------(1)
2x + 3y = 20 -------------(2)
NOW THE COMMON DIFFERENCE OF THE AP IS SUM OF FIRST 5 NATURAL NUMBERS.
EVALUATE THE TERM WHICH IS GREATER THAN 205 AND LESS THAN 235 AND ALSO
CALCULATE THE SUM OF LAST 20 TERMS IF THE AP CONTAINS 100 TERMS.
OPTIONS –
1. 15TH TERM AND 27050
2. 15TH TERM AND 25070
3. 16TH TERM AND 20750
4. 16TH TERM AND 27500
2. CONSIDER AN AP –
A1, A2, A3, A4,…………………………………An ---------------(1)
A1 = NUMBER WHICH IS DIVISIBLE BY 3 AND 19 IN THE AP –
42, 45, 48,……………………………..B 9 --------------(2)
C.D(D) = SUM OF FIRST 7 TERMS OF THE AP –
11, 13, 15,…………………………………. ------------------(3)
Sn = SUM OF FIRST ‘n’ TERMS OF THE FIRST AP.
EVALUATE THE VALUE OF THE EXPRESSION –
S 19 – S 15
S 21 – S 14
OPTIONS –
1. 0.553
2. 0.556
3. 0.550
4. 0.559
3. CONSIDER AN AP –
A1, A2, A3,………………………….An
LET Sn = 2 n2 +19 n
A1 = S18 – S20
C.D(D) = sin(S12) – tan (S14) (CONSIDER BOTH THE SUM TO BE IN DEGREE AND TAKE UPTO 2
DECIMAL PLACES)
EVALUATE THE EXPRESSION FOR FIRST ‘n’ TERMS OF THE AP.
OPTIONS –
1. 1.14n2 – 191.13n
2. 1.13n2 – 191.14n
3. 1.14n2 – 191.14n
4. 1.13n2 – 191.13n
4. CONSIDER THE WORD ‘ADVANCED’ AND ‘GATE’ –
LET THERE BE AN AP WITH TERMS AS –
A1, A2, A3,…………………………………..An
LET THE FIRST TERM OF THE AP BE THE NUMBER OF WORDS WITH OR WITHOUT MEANING
FORMED FROM THE WORD ‘GATE’ SUCH THAT G ALWAYS COMES BEFORE T.
LET THE 85TH TERM OF THE AP BE THE NUMBER OF WORDS FORMED FROM THE WORD
‘ADVANCED’ SUCH THAT ALL THE VOWELS NEVER COMES WITH EACH OTHER.
LET Sn = SUM FIRST ‘n’ TERMS OF THE AP.
LET THE VALUE OF THE EQUATION –
S 24−S19
= tan(a)
S 20
FIND THE VALUE OF tan(4a).
(EVALUATE THE ANSWER UPTO 2 DECIMAL PLACES)
ANSWER –
5. CONSIDER AN ARITHEMATIC PROGRESSION –
A 1, A2, A3 ……………………………..An
n=k
A1 = MODULUS OF ∑ ω WHERE ω IS CUBE ROOT OF UNITY.
n
n =1
K = SUM OF FIRST 100 NATURAL NUMBERS WHICH ARE NEITHER DIVISIBLE BY 4 NOR BY 2.
C.D (D) = ¿) * 240 (ROUND OFF TO NEAREST INTEGER)
LET Sn = SUM OF ‘n’ TERMS OF THE AP.
sin S 9 +cos S 9
LET a =
tan S10 +sec S10
FIND THE VALUE OF ‘a’.
(ROUND OFF TO 2 DECIMAL PLACES)
ANSWER –
