IPMAT (I) 2023 QA MCQ | Previous Year IPMAT - Indore Paper
In a triangle ABC, let D be the mid-point of BC, and AM be the altitude on BC. If the lengths of AB, BC and CA arc in the ratio of 2:4:3, then the ratio of the lengths of BM and AD would be
- A.
12 : 11
- B.
12 : 11
- C.
11 : 4√10
- D.
11 : 12
Solution
Discuss
ReportLet a, b, c be real numbers greater than 1. and n be a positive real number not equal to I. If logn(log2 a) = 1, logn(log2b) = 2 and logn(log2c) = 3. then which of the following is true?
- A.
(an + b)n = ac
- B.
an + bn = cn
- C.
a + b = c
- D.
(b - a)n = (c - b)
Let a1,a2,a3 be three distinct real numbers in geometric progression. If the equation a1x2 + 2a2x + a3 = 0 and b1x2 + 2b2x + b3 = 0 have a common root, then which of the following is necessarily true?
- A.
are in geometric progression
- B.
are in arithmetic progression
- C.
b1, b2, b3 are in geometric progression
- D.
b1, b2, b3 are in arithmetic progression
In a chess tournament there are 5 contestants. Each player plays against all the other exactly once. No game results in a draw. The winner in a game gets one point and the loser gets zero point. Which of the following sequences cannot represent the scores of the five players?
- A.
2, 2, 2, 2, 2
- B.
3, 3, 2, 1, 1
- C.
3, 2, 2, 2, 1
- D.
4, 4, 1, 1, 0
If cosα + cosβ = 1, then the maximum value of sinα – sinβ is
- A.
2
- B.
√2
- C.
1
- D.
√3
In a group of 120 students, 80 students are from the Science stream and the rest are from the Commerce stream. It is known that 70 students support Mumbai Indians in the Indian Premier League; all the other students support Chennai Super Kings. The number of Science students who are supporters of Mumbai Indians is
- A.
30 or more
- B.
Between 20 and 25
- C.
Exactly 20
- D.
Between 15 and 25
The Probability that a randomly chosen positive divisor of 102023 is an integer multiple of 102001 is
- A.
23 / 2024
- B.
232 / 20242
- C.
223 / 20232
- D.
22 / 2023
Consider an 8 × 8 chessboard. The number of ways 8 rooks can be placed on the board such that no two rooks are in the same row and no two are in the same column
- A.
7
- B.
7!
- C.
8
- D.
8!
A polynomial p(x) leaves a remainder 2 when divided by (x – 1) and a remainder 1 when divided by (x – 2). The remainder when P(x) is divided by (x -1)(x – 2) is
- A.
2
- B.
3 - x
- C.
x - 3
- D.
3
A rabbit is sitting at the base of a staircase which has 10 steps. It proceeds to the top of the staircase by climbing either one step at a time or two steps at a time. The number of ways it can reach the top is
- A.
34
- B.
89
- C.
144
- D.
55
If A = where a is a real number and det (A3 - 3A2 - 5A) = 0, then one of the values of a can be
- A.
4
- B.
5
- C.
6
- D.
1
If , which of the following is always true?
- A.
a = c
- B.
a = c, and b = d
- C.
a = c, or a + b + c + d = 0
- D.
a + b + c + d = 0
If the difference between compound interest and simple interest for a certain amount of money invested for 3 years at an annual interest rate of 10% is INR 527, then the amount invested in INR is
- A.
170000
- B.
17000
- C.
15000
- D.
150000
A person standing at the center of an open ground first walks 32 meters towards the east, takes a right turn and walks 16 meters, takes another right turn and walks 8 meters, and so on. How far will the person be from the original starting point after an infinite number of such walks in this pattem?
- A.
64 meters
- B.
32/√5 meters
- C.
32 meters
- D.
64/√5 meters
Let p be a positive integer such that the unit digit of p3 is 4. What are the possible unit digits of (p+3)3?
- A.
1, 3
- B.
1, 3, 7
- C.
4, 7
- D.
1, 7, 9
If a three-digit number is chosen at random, what is the probability that it is divisible neither by 3 nor by 4?
- A.
1/2
- B.
1/4
- C.
2/3
- D.
1/3
The set of all real values of x satisfying the inequality .
- A.
(-1, -1/2) ∪ (0, ∞)
- B.
(-1, -1/2) ∪ (1, ∞)
- C.
(-1, 0) ∪ (1, ∞)
- D.
(-∞, -1) ∪ (-1/2, 0) ∪ (1, ∞)
A goldsmith bought a large solid golden hall at INR 1 000000 and melted it to make a certain number of solid spherical beads such that the radius of each bead was one-filth of the radius of the original hall Assume that the cost of making golden beads is negligible. If the goldsmith sold all the heads at 20% discount on the listed price and made a total profit of 20% then the listed price of each golden bead. in INR, was
- A.
12000
- B.
48000
- C.
9600
- D.
24000
What of the following straight lines are both tangent to the circle x2 + y2 – 6x + 4y – 12 = 0?
- A.
4x + 3y + 19 = 0, 4x + 3y + 31 = 0
- B.
4x + 3y – 19 = 0, 4x + 3y + 31 = 0
- C.
4x + 3y – 19 = 0, 4x + 3y – 31 = 0
- D.
4x + 3y + 19 = 0, 4x + 3y – 31 = 0
The equation x2 + y2 – 2x – 4y + 5 = 0 represents
- A.
a circle
- B.
an ellipse
- C.
a point
- D.
a pair of straight lines
Let [x] denote the greatest integer not exceeding x and {x} = x – [x]. If is a natural number, then the sum of all values of x satisfying the equation 2[x] = x + n{x} is
- A.
n(n + 2)/2
- B.
3/2
- C.
n
- D.
n(n + 1)/2
If logcosxsinx + logsinxcosx = 2, then the value of x is
- A.
nπ/4 + π/4, n is an integer
- B.
2nπ + π/4, n is an integer
- C.
nπ + π/4, n is an integer
- D.
nπ/4, n is an integer
The minimum number of times a fair coin must be tossed so that probability of getting at least one head exceed 0.8 is
- A.
3
- B.
7
- C.
5
- D.
6
If the harmonic mean of the roots of the quadratic (5 + √2)x2 - bx + 8 + 2√5 = 0 is 4, then the value of b is
- A.
2
- B.
4 + √5
- C.
4 - √5
- D.
3
A helicopter flies along the sides of a square field of side length 100 kms. The first side is covered at a speed of 100 kms, and for each subsequent side the speed is increased by 100 kmph till it covers all the sides. The average speed of the helicopter is
- A.
184 kmph
- B.
200 kmph
- C.
250 kmph
- D.
192 kmph
Answer the next 5 questions based on the information given below.
A pharmaceutical company has tested five drugs on three different organisms The following incomplete table reports if a drug works on the given organism For example. drug A works on organism R while 13 and C work on Q.
- Each drug works on at least one organism but not more than two organisms.
- Each organism can he treated with at least two and at most three of these five drugs,
- On whichever organism A works. B also works. Similarly, on whichever organism C works. D also works,
- D and E do not work on the same organism.
Drug E works on
- A.
Q and R
- B.
Only P
- C.
P and R
- D.
Only R
Organism P can be treated with
- A.
Only B and D
- B.
A, B, and D
- C.
Only C and D
- D.
B, C and D
Organism R can be treated with
- A.
A, B and E
- B.
A,B and C
- C.
Only A and B
- D.
Only A and E
The organism(s) that can be treated with three of these five drugs is (are)
- A.
Only P
- B.
Only Q
- C.
Q and R
- D.
P and Q