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PRE FOUNDATION DIVISON IMO Stage-II Exam.-2017
Memory Based Questions CLASS-7 MATHEMATICS Q.1
Find the value of (P + Q) + (S – P) – R.
(A) –2.5 (C) –0.8 Q.2
Q.3
In the given figure (not drawn to scale), PQRS is a rhombus, RST and PSV are isosceles triangles, STUV is a square and QRT is a straight line. Find PSR + SPV.
(B) 2.2 (D) 1.4
Which of the following rational numbers do 4 11 not lie between and ? 33 25 2 14 4 7 (A) (B) (C) (D) 25 33 13 25 How many more triangles in the given figures must be shaded to make the fraction of 5 unshaded part equal to ? 8
(A) 3 Q.4
Q.5
Date : 12-02-2017
(B) 4
(C) 2
(A) 72º (C) 108º Q.6
(D) 5
27x 5 To solve = 6x + 5 following steps are 3 involved. Which of the following step(s) is incorrect? Step 1 : 27x + 5 = 3(6x + 5) Step 2 : 27x + 5 = 3 × 6x + 5 Step 3 : 27x + 5 = 18x + 15 Step 4 : 27x – 18x = 15 – 5 Step 5 : 9x = 10 10 Step 6 : x = 9 (A) 1 and 3 only (B) 2 only (C) 4 only (D) 6 only
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(B) 54º (D) 36º
In the given figure, state whether the triangles are congruent, if yes find the correct order of vertices.
(A) Yes, PQR SRT (B) No, they are not congruent (C) Yes, RST RPQ (D) Yes, STR RPQ Q.7
3 full of soft drink. The drink in 4 the bottle can fill 6 glasses. If the drink in the bottle is poured out to fill 4 glasses, find the fraction of drink left in the bottle. 1 1 (A) (B) 4 3 1 1 (C) (D) 6 2
A bottle is
1
Q.8
Q.9
The average of 5 numbers is 6x. If four of them are x, 7, 6, 4, then find the fifth number. Give your answer in terms of x. 17 x (A) (B) 29x – 17 5 (C) 6x – 17 (D) 5x – 17
Sam sold a guitar at a profit percentage of – 1500, then 25%. If he earns the profit of what was the selling price pf the guitar? – 6000 – 6500 (A) (B) – 7500 – 5500 (C) (D)
Q.14
If the hypotenuse of a right angled triangle is 5th multiple of remainder of (2379 ÷ 4) and one of its sides is the highest common factor of 18 and 27, then what is the length of the other side (in cm)? (A) 12 (B) 15 (C) 18 (D) 10
Q.15
The ages of 9 students are given as 18, 27, 18, 18, 19, 26, 26, 19 and 36. Find the mean, mode and median respectively. (A) 20, 18, 18 (B) 23, 18, 19 (C) 23, 18, 18 (D) 19, 19, 18
Q.16
A cube is rolled, if the numbers –1, –2, 0, 1, –2, 3 are written on the faces of cube, then (i) Find the probability of getting –2. (ii) Find the probability of getting 3. (i) (ii) (A) 1/6 1/3 (B) 1/3 1/6 (C) –2/4 3/6 (D) –4/6 3/6
The given figure shows a circle, centred at O, enclosed in a square. Find the total area of shaded parts.
(A) 121 cm2 (B) 145 cm2 (C) 130 cm2 (D) 119 cm2 37 1 , then (b + c) (11a – 13) =2+ 1 13 a bc is equal to (A) –11 (B) 5 (C) 11 (D) –4
Q.10
If
Q.11
A long metallic wire of length x2y + 5xy + 6xy2 is bent in the form of a triangle. If the two sides are 3xy + 4x2y and 2x2y + 2xy, then find the length of third side. (A) 6x2y + 5xy (B) 4xy2 – 3x2y (C) 6xy2 – 5x2y (D) 4x2y – 3xy2 + 5xy
Q.12
Q.13
In a zoo, the ratio of the deers and elephants was 3 : 4. When two new deers are added to the group, the ratio of the deets to the elephants becomes 4 : 5. How many deers and elephants respectively are there in the zoo new? (A) 32, 40 (B) 30, 40 (C) 30, 42 (D) 32, 42
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Q.17
11 1 and add the result in Subtract from 12 9 5 1 addition of and . 2 8 1 8 9 (C) 113
(A)
Q.18
113 72 263 (D) 72
(B)
When two parallel lines are cut by a transversal, which pair of angles will always be supplementary? (A) Corresponding angles (B) Alternate angles (C) Vertically opposite angles (D) Interior angles on the same side of the transversal
2
Q.19
Q.20
Garima bakes a cake, she uses 250 g brown sugar in 1 kg of flour. Find the ratio of (i) Sugar to flour (ii) Flour to sugar (iii) Sugar to the amount of sugar and flour together (i) (ii) (iii) (A) 4 : 1 1:4 1:5 (B) 3 : 2 3:2 2:5 (C) 2 : 3 3:2 2:5 (D) 1 : 4 4:1 1:5
Q.23
The teacher tells the class that the highest marks obtained by a student in her class is four times the lowest marks plus 5. The highest marks is absolute value of (–6 × 13), find the lowest marks. (A) 18.25 (B) 40 (C) 36.5 (D) 25
Q.24
In a school, 10x2 + 3xy + y2, 2x2 + 9x + 2yx and 7x3 + 8xy + 2y3 students are enrolled for NCO, NSO and IMO respectively. Find the total number of students enrolled for all the three exams when x = 2 and y = 3. (A) 321 (B) 263 (C) 261 (D) 250
Find the value of P, Q and R.
Q.25
(A) (B) (C) (D)
Q.21
Q.22
P 4 5 7 8
Q 5 8 2 2
R 1 1 6 4
1 1 1 1 1 1 Solve : 3 1 2 4 4 2 2 4 6 (A) 78 (B) 100 (C) 128 (D) 26 2x 7 2x 3 = , then find the value of x 3 2 and correct representation on the number line.
If
Q.26
Two towers 18 m and 28 m high stand upright on a ground. If their feet is 24 m apart, then the distance between their tops is _______. (A) 26 m (B) 24 m (C) 8 m (D) 18 m
Q.27
Select the correct option. (A) Orthocentre is the point of intersection of the perpendicular bisectors of the sides of a triangle. (B) Incentre is the point at which the three angle bisectors of a triangle meet (C) Circumcentre is the point at which the median of triangle meet. (D) Centroid is the point at which the altitudes of a triangle meet.
Q.28
The number of diagonals drawn from one vertex of a polygon of 17 sides is _________. (A) 16 (B) 15 (C) 14 (D) 17
(A) (B)
(C)
(D)
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a c and , if ad > bc, b d then ________ and if ad < bc, then _______ . a c a c (A) < and < b d b d a c a c (B) > and < b d b d a c a c (C) > and > b d b d (D) None of these
In two rational numbers
3
4
Q.29
32 16 If × 243 81
x 2
16
4 = , then find the 9
Q.33
What fraction of students like Science to the students like English? 3 2 (A) (B) 1 5 5 5 2 (C) (D) 3 5
Q.34
Ratio of students who like Social Science and Hindi together to the students who like English, Mathematics and Science together is __________ . (A) 25 : 34 (B) 33 : 22 (C) 5 : 3 (D) 3 : 5
Q.35
What percent of students like Hindi? (A) 18.64% (B) 19.35% (C) 10.50% (D) 20.12%
Q.36
35% of the total population of a town are men and 25% are children. If 7,00,000 are men, then what is the total population of the town? (A) 20,00,000 (B) 25,00,000 (C) 11,00,000 (D) 2,00,000
Q.37
In the given figure (not drawn to scale), ABCD is a rhombus, FHI is an equilateral triangle and CEFG is a trapezium with EC parallel to FG. DCFI, BCG and GFH are straight lines. Find CGF and ECF.
2
x2 x 1 . value of 2 x x 1 9 3 (B) (C) 9 (A) 4 2
Q.30
Q.31
Q.32
(D)
1 3
If two third of a number, half of the same number and one seventh of the same number and the number itself are added, the result is 3 less than 4th multiple of 10. The number is __________ . 2 2 (B) 16 (A) 14 97 97 2 2 (C) 18 (D) 17 97 97 In ___________ the incentre of triangle coincides with its circumcentre, orthocenter and centroid. (A) A right angled triangle (B) An isosceles triangle (C) An equilateral triangle (D) A scalene triangle If the average of first 50 natural numbers is 25.5, then sum of numbers is _________ . (A) 1275 (B) 2550 (C) 1500 (D) 1470
(Direction 33-35) : Study the given graph and answer the following questions.
(A) 100º, 46º (C) 48º, 58º Q.38
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(B) 48º, 60º (D) 72º, 120º
The value of x such that 2x + 3 = [(–4) × (–9) × (–25)] × [(–8) ×(–1) × (–2) × (–5) × (0)] is ______ . 3 (A) 0 (B) 2 2 3 (C) (D) 3 2
4
Q.39
– 100 less than 5 The price of an object A is times the price of an object B. A similar set of – one object A and 4 object B is priced at 1400. Find the price of object A. – 750 – 600 (A) (B) – 850 – 800 (C) (D)
Q.40
Find the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder. (A) 1683 (B) 423 (C) 1983 (D) 1263
Q.41
Q.42
In a two digit number, ten's digit is twice the unit digit. The number formed by interchanging the digits is 27 less than the original number. The original number is ______. (A) 36 (B) 63 (C) 84 (D) 42
Q.43
Q.44
The marked price of an article is 12% higher than cost price. A discount of 10% is given on the marked price. In this kind of sales, the seller _________ . (A) Loses (B) Bears no gain, no loss (C) Gains (D) Data inadequate xa xb
1
ab x b xc
1
bc x c xa
(A) 1 (C) Q.45
In a ABC, which of the following conditions holds? (A) AB – BC > CA (B) AB + BC < CA (C) AB – BC < CA (D) AB + CA < BC
1 x ab bc ca
1
ca = ______ . 1 (B) abc x ab (D) ab bc x
Solve : 1 2 3 4 5 6 999 +999 +999 +999 +999 +999 7 7 7 7 7 7 (A) 5997 (B) 5994 (C) 5979 (D) 2997
ACHIEVERS SECTION Q.46
In the given figure (not drawn to scale), PQRS is a square with QT = QU. If SR = (7x – 6) cm and SP = (2x + 9) cm, then find (i) The value of x (ii) Area of TRQ (iii) QTU and UTR
Q.47
Match the following : Expression x
P.
5
Value of x 3
9 3 ( 27) = 27 (3) 2 (81) 4
Q. 25(x + 3) = (5)3x – 5
i.
5 3
ii. 11
2x
6 9 256 2 R. ÷ = 10 4 81 3
iii.
7 2
S. 2x = (32)1/3
iv.
7 2
(A) P (ii); Q (i); R (iv); S (iii) (A) (B) (C) (D)
(i) 3 3 5 5
(ii) 56.25 cm2 56.25 cm2 65.75 cm2 65.75 cm2
(iii) 60º, 30º 67.5º, 22.5º 67.5º, 25.5º 80º, 20º
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(B) P (i); Q (ii); R (iii); S (iv) (C) P (iv); Q (iii); R (ii); S (i) (D) P (iii); Q (ii); R (iv); S (i)
5
Q.48
Q.49
Read the statements carefully and select the correct option. Statement-1 : Mode is most frequently occurring value in a given data. It is always less than the median of the data. Statement-1 : Median of the data (1, 2, 2, 3, 2, 3, 4, 2, 3, 2, 2, 3, 2, 1, 2, 2, 3, 2, 3, 3, 2, 3, 3, 3) is less than the mode. (A) Statement-1 is true and Statement-2 is false (B) Statement-1 is false and Statement-2 is true (C) Both Statement-1 and Statement-2 are false (D) Both Statement-1 and Statement-2 is true
Q.50
Find the value of x + y in the given figures.
(A) (B) (C) (D)
(a) 128º 130º 80º 114º
(b) 114º 90º 66º 128º
Find the values of P, Q, R and S.
(A) (B) (C) (D)
P 5% 5% 4% 4%
Q
R
S
– 1000
– 15,024
– 4250 – 5024 – 5024 – 4250
– 1200 – 1800 – 1100
– 12,560 – 12,560 – 14,231
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