Consider the following statements:
1 S(1): The remainder when 19031903 is divided by 21 is 13.
S(2): 192001 - 172001 - 122001 + 102001 is divisible by 14.
Then:
A Only S(1) is true
B Only S(2) is true
C Both S(1) and S(2) are true
D Neither S(1) nor S(2) is true
Consider the following statements:
1 S(1): The remainder when 19031903 is divided by 21 is 13.
S(2): 192001 - 172001 - 122001 + 102001 is divisible by 14.
Then:
A Only S(1) is true
B Only S(2) is true
C Both S(1) and S(2) are true
D Neither S(1) nor S(2) is true
If 𝞪, 𝞫 are the roots of x2 - 5x - 2 = 0 & Pn = 𝞪n + 𝞫n, then
2
S(1):
S(2):
A Only S(1) is true
B Only S(2) is true
C Both S(1) and S(2) are true
D Neither S(1) nor S(2) is true
If 𝞪, 𝞫 are the roots of x2 - 5x - 2 = 0 & Pn = 𝞪n + 𝞫n, then
2
S(1):
S(2):
A Only S(1) is true
B Only S(2) is true
C Both S(1) and S(2) are true
D Neither S(1) nor S(2) is true
The number of ways can a team of six horses be selected
3 out of a stud of 16, so that there shall always be three out
of A, B, C, D, E, F but never AD, BE or CF together, is
A 720
B 840
C 960
D 1260
The number of ways can a team of six horses be selected
3 out of a stud of 16, so that there shall always be three out
of A, B, C, D, E, F but never AD, BE or CF together, is
A 720
B 840
C 960
D 1260
Solution:
A cricketer has to score 4500 runs. Let an denotes the number
4 of runs he scores in the nth match. If a1 = a2 = …… a10 = 150 and
a10, a11, a12 ……. are in A.P. with common difference (-2). If N be
the total number of matches played by him to score 4500 runs.
Then the sum of the digits of N is :
A 7
B 8
C 9
D 10
A cricketer has to score 4500 runs. Let an denotes the number
4 of runs he scores in the nth match. If a1 = a2 = …… a10 = 150 and
a10, a11, a12 ……. are in A.P. with common difference (-2). If N be
the total number of matches played by him to score 4500 runs.
Then the sum of the digits of N is :
A 7
B 8
C 9
D 10
Solution:
Let a, b, c be positive integer such that b/a is an integer.
5 If a, b, c are in geometric progression and the arithmetic
mean of a, b, c is b + 2, then the value of is
A 12
B 14
C 16
D 18
Let a, b, c be positive integer such that b/a is an integer.
5 If a, b, c are in geometric progression and the arithmetic
mean of a, b, c is b + 2, then the value of is
A 12
B 14
C 16
D 18
Solution:
JEE Main 15th April, 2023 - S1
Let an ellipse with centre (1, 0) and latus rectum of length 1/2
6 have its major axis along x-axis. If its minor axis subtends an
angle 60° at the foci, then the square of the sum of the lengths of
its minor and major axes is equal to_________
JEE Main 15th April, 2023 - S1
Let an ellipse with centre (1, 0) and latus rectum of length 1/2
6 have its major axis along x-axis. If its minor axis subtends an
angle 60° at the foci, then the square of the sum of the lengths of
its minor and major axes is equal to_________
Ans: 9
Solution:
If A is a square matrix such that A2 + A + 2I = O, then
7 which of the following is INCORRECT?
(Where I is unit matrix of order 2 and O is null matrix
of order 2 )
A A is non-singular
B A≠O
C A-1 = ½ (A2 + I)
D A-1 = –½ (A + I)
If A is a square matrix such that A2 + A + 2I = O, then
7 which of the following is INCORRECT?
(Where I is unit matrix of order 2 and O is null matrix
of order 2 )
A A is non-singular
B A≠O
C A-1 = ½ (A2 + I)
D A-1 = –½ (A + I)
Solution:
Solution:
If the system of equations 2x - y + z = 0, x - 2y + z = 0,
8 tx - y + 2z = 0 has infinitely many solutions and f(x)
be a continuous function, such that f(5 + x) + f(x) = 2,
Then is equal to
A 0
B -2t
C 5
D t
If the system of equations 2x - y + z = 0, x - 2y + z = 0,
8 tx - y + 2z = 0 has infinitely many solutions and f(x)
be a continuous function, such that f(5 + x) + f(x) = 2,
Then is equal to
A 0
B -2t
C 5
D t
Solution:
Let f(x) be a derivable function satisfying
9 f(x + y) = f(x) + f(y) ∀ x, y ∈ R and f’(0) = 1.
If then the value
of e4A is ____.
Let f(x) be a derivable function satisfying
9 f(x + y) = f(x) + f(y) ∀ x, y ∈ R and f’(0) = 1.
If then the value
of e4A is ____.
Ans: 4
Solution:
Let f be a differentiable function of R and satisfies
10
then is equal to:
A 1/3
B 1/4
C 7/12
D 5/12
Let f be a differentiable function of R and satisfies
10
then is equal to:
A 1/3
B 1/4
C 7/12
D 5/12
Solution:
Let f : R → R be a differentiable function such
11 that f(x) = x3 + x2f’(1) + xf’’(2) + f’’’(3), x ∈ R.
Then |f(2)| is equal to
Let f : R → R be a differentiable function such
11 that f(x) = x3 + x2f’(1) + xf’’(2) + f’’’(3), x ∈ R.
Then |f(2)| is equal to
Ans: 2
Solution:
Let where and are three unit vectors,
12
then sum of all possible values of is:
A 10
B 12
C 14
D 16
Let where and are three unit vectors,
12
then sum of all possible values of is:
A 10
B 12
C 14
D 16
Solution:
A line l passing through the origin is perpendicular to the lines
13
Then, a coordinate of the point on l2 at a distance of from
the the point of intersection of l and l1 is
B (-1, 1, 0)
C (1, 1, 1)
D
A line l passing through the origin is perpendicular to the lines
13
Then, a coordinate of the point on l2 at a distance of from
the the point of intersection of l and l1 is
B (-1, 1, 0)
C (1, 1, 1)
D
Solution:
Solution:
Solution:
Let A be a 3 × 3 invertible matrix such that
14 |adj 24A| = |adj(3adj(2A)|, then find remainder when
is divided by 10.
Let A be a 3 × 3 invertible matrix such that
14 |adj 24A| = |adj(3adj(2A)|, then find remainder when
is divided by 10.
Ans: 0
Bag A contains 5 white and 5 black balls. Bag B is empty initially,
15 5 balls are drawn from bag A and placed into bag B. Then 4 balls
are drawn from bag B and placed in empty bag C. The probability
that bag C contains exactly 3 white balls is , then k is
A 20
B 80
C 60
D 33
Bag A contains 5 white and 5 black balls. Bag B is empty initially,
15 5 balls are drawn from bag A and placed into bag B. Then 4 balls
are drawn from bag B and placed in empty bag C. The probability
that bag C contains exactly 3 white balls is , then k is
A 20
B 80
C 60
D 33
Solution:
What is the set of values of ‘a’ for which the following
16 function is decreasing on R :
C (-∞, ∞)
D (1, ∞)
What is the set of values of ‘a’ for which the following
16 function is decreasing on R :
C (-∞, ∞)
D (1, ∞)
Solution:
Solution:
then the value
17
A 0
D None of these
then the value
17
A 0
D None of these
Solution:
JEE Main 29th July, 2022
Let be a sequence such that a0 = a1 = 0 and an+2 = 3an+1 - 2an + 1,
18 for all n ≥ 0. Then a25a23 - 2a25a22 - 2a23a24 + 4a22a24 is equal to
A 483
B 528
C 575
D 624
JEE Main 29th July, 2022
Let be a sequence such that a0 = a1 = 0 and an+2 = 3an+1 - 2an + 1,
18 for all n ≥ 0. Then a25a23 - 2a25a22 - 2a23a24 + 4a22a24 is equal to
A 483
B 528
C 575
D 624
Solution:
From a point P(3, 3) on the circle x2 + y2 = 18, two
19 chords PQ and PR each of 2 units length are drawn
on this circle. The value of cos(∠QPR) is equal to
D
From a point P(3, 3) on the circle x2 + y2 = 18, two
19 chords PQ and PR each of 2 units length are drawn
on this circle. The value of cos(∠QPR) is equal to
D
Solution:
The minimum number of elements that must be added to
20 the relation R = {(1, 2), (2, 3)} on the set {1, 2, 3} so that it
becomes symmetric and transitive is :
A 3
B 4
C 5
D 7
The minimum number of elements that must be added to
20 the relation R = {(1, 2), (2, 3)} on the set {1, 2, 3} so that it
becomes symmetric and transitive is :
A 3
B 4
C 5
D 7
