NAME : .....................................................................................................................................................
JEE (Main + Advanced) 2026
JEE (Main + Advanced) 2026
NURTURE COURSE
NURTURE COURSE
ASSIGNMENT # A (SEQUENCE & SERIES) MATHEMATICS
One or more than one correct :
1. Let the positive numbers a, b, c, d be in A.P. Then abc, abd, acd, bcd are
(A) not in A.P./G.P./H.P. (B) in A.P.
(C) in G.P. (D) in H.P.
2. If the sum of the first 2n terms of the A.P. 2, 5, 8 ............. is equal to the sum of the first n terms of the
A.P. 57, 59, 61, .............. then n equals -
(A) 10 (B) 12 (C) 11 (D) 13
3. Consider an infinite geometric series with first term ‘a’ and common ratio r. If the sum is 4 and the
second term is 3/4, then -
7 3 3 3 1 1
(A) a = , r=7 (B) a = 2, r = (C) a = , r= (D) a = 3, r = ]
4 8 2 2 4
4. The first term of an infinite geometric progression is x and its sum is 5. Then -
(A) 0 £ x £ 10 (B) 0 < x < 10 (C) –10 < x < 0 (D) x > 10
5. In the quadratic equation ax2 + bx + c = 0, if D = b2 – 4ac and a + b, a2 + b2, a3 + b3 are in G.P.
where a, b are the roots of ax2 + bx + c = 0, then
(A) D ¹ 0 (B) bD = 0 (C) cD = 0 (D) D = 0
6. Let Tr be the rth term of an A.P. for r = 1, 2, 3, ........... If for some positive integers m, n we
1 1
have Tm = & Tn = , then Tmn equals -
n m
1 1 1
(A) (B) + (C) 1 (D) 0
mn m n
1 1 1
7. If x > 1, y > 1, z >1 are in G.P., then 1 + ln x , 1 + ln y , 1 + ln z are in -
(A) A.P. (B) H.P. (C) G.P. (D) none of above
3
8. Suppose a, b, c are in A.P. and a2, b2, c2 are in G.P. If a < b < c and a + b + c = , then the value of a is -
2
1 1 1 1 1 1
(A) (B) (C) 2 - (D) 2 -
2 2 2 3 3 2
9. Let a , b be the roots of x2 - x + p = 0 and g, d be the roots of x2 - 4x + q = 0. If a, b, g, d are in G.P.,
then the integer values of p and q respectively, are -
(A) –2, –32 (B) –2, 3 (C) –6, 3 (D) –6, –32
10. ( )
The harmonic mean of the roots of the equation 5 + 2 x2 - 4 + 5 x + 8 + 2 5 = 0 is - ( )
(A) 2 (B) 4 (C) 6 (D) 8
11. Let a1, a2, ......., a10 be in A.P. & h1, h2, .......h10 be in H.P. . If a1= h1 = 2 & a10 = h10 = 3 then a4h7 is -
(A) 2 (B) 3 (C) 5 (D) 6
MATHEMATICS /ASSIGNMENT E-1/6
, JEE (Main + Advanced) 2026
NURTURE COURSE
12. Suppose four distinct positive numbers a1, a2, a3, a4 are in G.P. Let b1 = a1, b2 = b1 + a2, b3 = b2 + a3
and b4 = b3 + a4.
Statement-1 : The numbers b1, b2, b3, b4 are neither in A.P. nor in G.P.
and
Statement-2 : The numbers b1, b2, b3, b4 are in H.P.
(A) Statement-1 is True, Statement-2 is True; statement-2 is a correct explanation for statement-1
(B) Statement-1 is True, Statement-2 is True; statement-2 is NOT a correct explanation for statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
1 1 1
13. The sum to infinity of the series + + +...... is equal to -
1 1+ 2 1+2+ 3
(A) 2 (B) 5/2 (C) 3 (D) none of these
¥
æ n ö
14. The value of å (-1) n +1çè 5n ÷ø equals
n =1
5 5 5 5
(A) (B) (C) (D)
12 24 36 16
360 æ 1 ö
15. å çç k k + 1 + ( k + 1) k
÷ is the ratio of two relative prime positive integers m and n. The value of
÷
k =1 è ø
(m + n) is equal to
(A) 43 (B) 41 (C) 39 (D) 37
100
k
16. The sum å k 4 + k 2 + 1 is equal to
k =1
4950 5050 5151
(A) (B) (C) (D) none
10101 10101 10101
¥
æ n ö
17. The sum å çè n 4 + 4 ÷ø is equal to
n =1
(A) 1/4 (B) 1/3 (C) 3/8 (D) 1/2
18. A circle of radius r is inscribed in a square. The mid points of sides of the square have been connected
by line segment and a new square resulted. The sides of the resulting square were also connected by
segments so that a new square was obtained and so on, then the radius of the circle inscribed in the nth
square is
é 1- n ù é 3-3n ù é -n ù é - 5- 3 n ù
(A) ê 2 ú r (B) ê 2 úr (C) ê 2 ú r (D) ê 2 úr
2 2 2 2
êë úû êë úû êë úû êë úû
19. If a, b and c are three consecutive positive terms of a G.P. then the graph of y = ax2 + bx + c is
(A) a curve that intersects the x-axis at two distinct points.
(B) entirely below the x-axis.
(C) entirely above the x-axis.
(D) tangent to the x-axis.
20. If a, b, c, d are positive real numbers such that a + b + c + d = 2, then M = (a + b) (c + d) satisfies the
relation -
(A) 0 £ M £ 1 (B) 1 £ M £ 2 (C) 2 £ M £ 3 (D) 3 £ M £ 4
E-2/6 MATHEMATICS /ASSIGNMENT
JEE (Main + Advanced) 2026
JEE (Main + Advanced) 2026
NURTURE COURSE
NURTURE COURSE
ASSIGNMENT # A (SEQUENCE & SERIES) MATHEMATICS
One or more than one correct :
1. Let the positive numbers a, b, c, d be in A.P. Then abc, abd, acd, bcd are
(A) not in A.P./G.P./H.P. (B) in A.P.
(C) in G.P. (D) in H.P.
2. If the sum of the first 2n terms of the A.P. 2, 5, 8 ............. is equal to the sum of the first n terms of the
A.P. 57, 59, 61, .............. then n equals -
(A) 10 (B) 12 (C) 11 (D) 13
3. Consider an infinite geometric series with first term ‘a’ and common ratio r. If the sum is 4 and the
second term is 3/4, then -
7 3 3 3 1 1
(A) a = , r=7 (B) a = 2, r = (C) a = , r= (D) a = 3, r = ]
4 8 2 2 4
4. The first term of an infinite geometric progression is x and its sum is 5. Then -
(A) 0 £ x £ 10 (B) 0 < x < 10 (C) –10 < x < 0 (D) x > 10
5. In the quadratic equation ax2 + bx + c = 0, if D = b2 – 4ac and a + b, a2 + b2, a3 + b3 are in G.P.
where a, b are the roots of ax2 + bx + c = 0, then
(A) D ¹ 0 (B) bD = 0 (C) cD = 0 (D) D = 0
6. Let Tr be the rth term of an A.P. for r = 1, 2, 3, ........... If for some positive integers m, n we
1 1
have Tm = & Tn = , then Tmn equals -
n m
1 1 1
(A) (B) + (C) 1 (D) 0
mn m n
1 1 1
7. If x > 1, y > 1, z >1 are in G.P., then 1 + ln x , 1 + ln y , 1 + ln z are in -
(A) A.P. (B) H.P. (C) G.P. (D) none of above
3
8. Suppose a, b, c are in A.P. and a2, b2, c2 are in G.P. If a < b < c and a + b + c = , then the value of a is -
2
1 1 1 1 1 1
(A) (B) (C) 2 - (D) 2 -
2 2 2 3 3 2
9. Let a , b be the roots of x2 - x + p = 0 and g, d be the roots of x2 - 4x + q = 0. If a, b, g, d are in G.P.,
then the integer values of p and q respectively, are -
(A) –2, –32 (B) –2, 3 (C) –6, 3 (D) –6, –32
10. ( )
The harmonic mean of the roots of the equation 5 + 2 x2 - 4 + 5 x + 8 + 2 5 = 0 is - ( )
(A) 2 (B) 4 (C) 6 (D) 8
11. Let a1, a2, ......., a10 be in A.P. & h1, h2, .......h10 be in H.P. . If a1= h1 = 2 & a10 = h10 = 3 then a4h7 is -
(A) 2 (B) 3 (C) 5 (D) 6
MATHEMATICS /ASSIGNMENT E-1/6
, JEE (Main + Advanced) 2026
NURTURE COURSE
12. Suppose four distinct positive numbers a1, a2, a3, a4 are in G.P. Let b1 = a1, b2 = b1 + a2, b3 = b2 + a3
and b4 = b3 + a4.
Statement-1 : The numbers b1, b2, b3, b4 are neither in A.P. nor in G.P.
and
Statement-2 : The numbers b1, b2, b3, b4 are in H.P.
(A) Statement-1 is True, Statement-2 is True; statement-2 is a correct explanation for statement-1
(B) Statement-1 is True, Statement-2 is True; statement-2 is NOT a correct explanation for statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
1 1 1
13. The sum to infinity of the series + + +...... is equal to -
1 1+ 2 1+2+ 3
(A) 2 (B) 5/2 (C) 3 (D) none of these
¥
æ n ö
14. The value of å (-1) n +1çè 5n ÷ø equals
n =1
5 5 5 5
(A) (B) (C) (D)
12 24 36 16
360 æ 1 ö
15. å çç k k + 1 + ( k + 1) k
÷ is the ratio of two relative prime positive integers m and n. The value of
÷
k =1 è ø
(m + n) is equal to
(A) 43 (B) 41 (C) 39 (D) 37
100
k
16. The sum å k 4 + k 2 + 1 is equal to
k =1
4950 5050 5151
(A) (B) (C) (D) none
10101 10101 10101
¥
æ n ö
17. The sum å çè n 4 + 4 ÷ø is equal to
n =1
(A) 1/4 (B) 1/3 (C) 3/8 (D) 1/2
18. A circle of radius r is inscribed in a square. The mid points of sides of the square have been connected
by line segment and a new square resulted. The sides of the resulting square were also connected by
segments so that a new square was obtained and so on, then the radius of the circle inscribed in the nth
square is
é 1- n ù é 3-3n ù é -n ù é - 5- 3 n ù
(A) ê 2 ú r (B) ê 2 úr (C) ê 2 ú r (D) ê 2 úr
2 2 2 2
êë úû êë úû êë úû êë úû
19. If a, b and c are three consecutive positive terms of a G.P. then the graph of y = ax2 + bx + c is
(A) a curve that intersects the x-axis at two distinct points.
(B) entirely below the x-axis.
(C) entirely above the x-axis.
(D) tangent to the x-axis.
20. If a, b, c, d are positive real numbers such that a + b + c + d = 2, then M = (a + b) (c + d) satisfies the
relation -
(A) 0 £ M £ 1 (B) 1 £ M £ 2 (C) 2 £ M £ 3 (D) 3 £ M £ 4
E-2/6 MATHEMATICS /ASSIGNMENT
