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IPMAT Indore 2019 (SA) PYQs

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IPMAT Indore 2019 Past Year Papers with Solutions filter tool

Q1:

The sum of the interior angles of a convex nn-sided polygon is less than 2019∘2019^\circ. The maximum possible value of nn is
13
Correct Answer
Explanation →

Q2:

Suppose that a, b, and c are real numbers greater than 1. Then the value of 11+log⁡a2bca+11+log⁡b2cab+11+log⁡c2abc\dfrac{1}{1+\log_{a^2 b} \frac{c}{a}} + \dfrac{1}{1+\log_{b^2 c} \frac{a}{b}} + \dfrac{1}{1+\log_{c^2 a} \frac{b}{c}} is
3
Correct Answer
Explanation →

Q3:

A real-valued function ff satisfies the relation f(x)f(y)=f(2xy+3)+3f(x+y)−3f(y)+6yf(x)f(y) = f(2xy + 3) + 3f(x + y) - 3f(y) + 6y, for all real numbers xx and yy, then the value of f(8)f(8) is
19
Correct Answer
Explanation →

Q4:

Let A,B,CA, B, C be three 4×44 \times 4 matrices such that det A=5,det B=−3det \ A = 5, det \ B = -3, and det C=12det \ C = \frac{1}{2}. Then the detdet 2AB−1C3BT2AB^{-1}C^3B^T is
10
Correct Answer
Explanation →

Q5:

If AA is a 3×33 \times 3 non-zero matrix such that A2=0A^2 = 0 then the determinant of (I+A)50−50A(I + A)^{50} - 50A is equal to
1
Correct Answer
Explanation →

Q6:

Three friends divided some apples in the ratio 3:5:73 : 5 : 7. After consuming 16 apples they found that the remaining number of apples with them was equal to the largest number of apples received by one of them at the beginning. The total number of apples these friends initially had was
30
Correct Answer
Explanation →

Q7:

A shopkeeper reduces the price of a pen by 25% as a result of which the sales quantity increased by 20%. If the revenue made by the shopkeeper decreases by x% then x is
10
Correct Answer
Explanation →

Q8:

For all real values of xx, 3x2−6x+12x2+2x+4\dfrac{3x^2 - 6x + 12}{x^2 + 2x + 4} lies between 11 and kk, and does not take any value above kk. Then kk equals:
9
Correct Answer
Explanation →

Q9:

The maximum distance between the point (−5,0)(-5, 0) and a point on the circle x2+y2=4x^2 + y^2 = 4 is
7
Correct Answer
Explanation →

Q10:

If x,y,zx, y, z are positive real numbers such that x12=y16=z24x^{12} = y^{16} = z^{24} and the three quantities 3log⁡yx,4log⁡zy,nlog⁡xz3 \log_y x, 4 \log_z y, n \log_x z are in arithmetic progression, then the value of nn is
16
Correct Answer
Explanation →

Q11:

The number of pairs (x,y)(x, y) satisfying the equation sin⁡x+sin⁡y=sin⁡(x+y)\sin x + \sin y = \sin(x + y) and ∣x∣+∣y∣=1|x| + |y| = 1 is
6
Correct Answer
Explanation →

Q12:

The circle x2+y2−6x−10y+k=0x^2 + y^2 - 6x - 10y + k = 0 does not touch or intersect the coordinate axes. If the point (1,4)(1, 4) does not lie outside the circle, and the range of kk is (a,b](a, b], then a+ba + b is
54
Correct Answer
Explanation →

Q13:

If a 3×33 \times 3 matrix is filled with +1's and -1's such that the sum of each row and column of the matrix is 1, then the absolute value of its determinant is
4
Correct Answer
Explanation →

Q14:

Let the set P={2,3,4,...,25}P= \{2,3,4,..., 25\}. For each k∈Pk ∈ P, define Q(k)={x∈PQ(k)= \{x ∈ P such that x>kx > k and kk divides x}x\}. Then the number of elements in the set P−Uk=225Q(k)P - U_{k=2}^{25} Q(k) is
9
Correct Answer
Explanation →

Q15:

The number of whole metallic tiles that can be produced by melting and recasting a circular metallic plate, if each of the tiles has a shape of a right-angled isosceles triangle and the circular plate has a radius equal in length to the longest side of the tile (Assume that the tiles and plate are of uniform thickness, and there is no loss of material in the melting and recasting process) is
12
Correct Answer
Explanation →

Q16:

If ∣x∣<100|x| <100 and ∣y∣<100|y| <100, then the number of integer solutions of (x,y)(x, y) satisfying the equation 4x+7y=34x + 7y = 3 is
29
Correct Answer
Explanation →

Q17:

The average of five distinct integers is 110 and the smallest number among them is 100. The maximum possible value of the largest integer is
144
Correct Answer
Explanation →

Q18:

Assume that all positive integers are written down consecutively from left to right as in 1234567891011...... The 6389th digit in this sequence is
4
Correct Answer
Explanation →

Q19:

The number of pairs of integers whose sums are equal to their products is
2
Correct Answer
Explanation →

Q20:

You have been asked to select a positive integer N which is less than 1000, such that it is either a multiple of 4, or a multiple of 6, or an odd multiple of 9. The number of such numbers is
388
Correct Answer
Explanation →

IPMAT Indore 2019 SA Past Year Questions (Free PDF Download)

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