PLACEMENT TEST (Sample 1)
M A T H E M A T I C S
TOPICS : QUADRATIC EQUATIONS, T RATIOS AND IDENTITIES,
SIMPLE CONCETS OF TRIANGLES AND
BASIC APTITUDE – GENERAL CASE STUDIES.
NOTE … This paper is divided into three parts viz. PART– A, PART– B and PART– C. In each part read the instructions carefully.
TIME ALLOWED … 1:55 hrs.
MAX. MARKS … 150.
PART – A ………...
INSTRUCTIONS…
# This part contains 25 questions. Attempt as many as possible .
# Each question has four options out of which only one is correct. Select the correct option and tick the corresponding box
on the
right of options.
# Here each right answer is awarded 4marks whereas wrong one has a penalty of 1mark.
# Use of Calculators, Mathematical Tables is strictly NOT PERMITTED.
Q.01 The quadratic polynomial in x whose zeroes…
are a, 2a is …
(A) (x + a)(x – a)
(B) (x – a)(x + 2a)
(C) (x + a)(x + 2a)
(D) (x – a)(x – 2a)
the equation 12x2 + mx + 5 = 0 are in the…
ratio 3 : 2, is …
5 10
(A) 5 10
(B)
2
5
12
(C)
(D)
12
5
Q.02 Vidya and Vandana solved a quadratic equation. Q.04 The roots of the equation ax2 + bx + c = 0 will
In solving it, vidya made a mistake in the…
be reciprocals if…
constant term and got the roots as 6, 2 while…
(A) a = b
(B) b = c
Vandana made a mistake in the coefficient of x
(C) c = a
(D) none of these
only and obtained the roots as –7, –1. The…
Q.05 A reduction of Rs.1 per kg in the price of sugar
correct roots of the equation are…
Mohan can buy 1 kg sugar more for Rs. 56.
(A) 6 , –1
(B) –7 , 2
The original price of sugar per kg is…
(C) –6 , –2
(D) 7 , 1
(A) 14
(B) 8
Q.03 The positive value of m for which the roots of…
(C) 7
(D) none of these
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S01 I – L1 / Quadratic Equations, T–Ratios, Triangles, General Case Studies
Q.06 If sinx = cosy, x + y is equal to …
(A) 30°
(B) 45°
(C) 60°
(D) 90°
Q.07 In first quadrant, which of followings is true ?
(A) cosθ increases when θ increases
(B) cosθ decreases when θ increases
(C) cosθ remains constant
(D) cosθ does not depend on θ
Q.08 If sin2x + sin2y + sin2z =
(sinx + siny + sinz)2,
then which of the following expression must…
necessarily vanish ...
(A) tanx + tany + tanz
(B) cosx + cosy + cosz
1
1
1
(C)
+
+
sin x sin y sin z
1
1
1
(D)
+
+
cos x cos y cos z
Q.09 If 3sinx + 5cosx = 5, then the value of…
(3cosx – 5sinx)2 is …
(A) 2
(B) 4
(C) 5
(D) 9
Q.10 If x = r sinA cosB, y = r sinA sinB and…
z = r cosA, then …
(A) x2 + y2 + z2 = r2
(B) x2 – y2 + z2 = r2
(C) x2 + y2 – z2 = r2
(D) – x2 + y2 + z2 = r2
Q.11 In an equilateral triangle ABC, If AD⊥BC,
then …
(A) 2AB2 = 3AD2
(B) 4AB2
2
2
(C) 3AB = 4AD
(D) 3AB2 = 2AD2
Q.12 In a right angled triangle, one of the angles …
is 60°. The side opposite to this angle is …
1
(A)   hypotenuse
2
 1 
 hypotenuse
(B) 
 2
[02]
Q.18 If ΔABC and ΔDEF are similar, 2AB = DE and …
BC = 8cm. then, EF is equal to …
(A) 16 cm
(B) 12 cm
(C) 8 cm
(D) 4 cm
Q.19 The ratio of an interior angle to the exterior …
angle of a regular polygon is 7 : 2. The number
of sides of the polygon is …
(A) 6
(B) 9
(C) 7
(D) 8
Q.13 If the medians of a triangle are equal, then the
triangle is …
(A) isosceles
(B) equilateral
(C) scalene
(D) right angled
Q.14 The circumcentre of a triangle is determined by
the …
(A) altitudes
(B) medians
(C) angle bisectors
(D) perpendicular bisectors of the sides
Q.15 The ratio of the length of a side of an …
equilateral triangle and its height is …
(A) 2:1
(B) 1:2
(C) 2: 3
(D) 3 : 2
Q.16 The measure of the sides of the triangles are…
a, a 3 and 2a. The measure of the angle …
opposite to the sides „a‟ in degrees is …
(A) 30°
(B) 45°
(C) 60°
(D) 90°
Q.20 For a triangle ABC, which of the following is …
true ?
(A) BC2 – AB2 = AC2
(B) AB – AC = BC
(C) AB – AC > BC
(D) AB – AC < BC
Read the following instructions for Q.21 – Q.23
2
(C)   hypotenuse
3
 3
 hypotenuse
(D) 
 2 


Q.17 The orthocentre of a triangle will be exterior to
(A) equilateral triangle
(B) acute angled triangle
(C) obtuse angled triangle
(D) right angled triangle
forACE
In the above figure the circle represents…
“house-wives”, the triangle stands for the …
“educated” and the rectangle for the employed.
Which numbered space represents the …
following ( write in the given circle ) …
AXIS – S.C.O. 58, I-II Floor, Sec. 20C,
Chandigarh(U.T.)–160020.
Phs.(O) 0172 500 5555, 501 5555 (R) 500 0055 (F) 467 0083 (M) 9216528383, 9316528383, 9041628383, 9041528383
www.aciax.com(in),[email protected],[email protected]
aps correspondence desk :BEYOND | 83A, Rani KaBagh, Amritsar 143001, Punjab-State (INDIA). Ph. 0183 2220083
S01 I – L1 / Quadratic Equations, T–Ratios, Triangles, General Case Studies
Q.21 Some educated wives are employed.
house-wives.
Q.22 Some educated are neither housewives nor
employed.
Q.23 Some employed are neither educated nor
**********
forACE
[03]
Q.24 Find the next number in the sequence …
1, 1, 3, 7, 17, 41, 99, …
(A) 123
(B) 99
(C) 239
(D) 249
Q.25 complete the pattern ab – aabb – bb–
(A) baba
(B) abbb
(C) baaa
(D) abab
END OF THE PART–A * * * * * * * * * *
AXIS – S.C.O. 58, I-II Floor, Sec. 20C,
Chandigarh(U.T.)–160020.
Phs.(O) 0172 500 5555, 501 5555 (R) 500 0055 (F) 467 0083 (M) 9216528383, 9316528383, 9041628383, 9041528383
www.aciax.com(in),[email protected],[email protected]
aps correspondence desk :BEYOND | 83A, Rani KaBagh, Amritsar 143001, Punjab-State (INDIA). Ph. 0183 2220083
S01 I – L1 / Quadratic Equations, T–Ratios, Triangles, General Case Studies
[04]
PART – B ………...
INSTRUCTIONS…
#
#
#
#
This part contains 3 questions. Attempt as many as possible .
Numbers on the right indicate maximum marks assigned.
Write your answer neatly, with necessary workings / explanations and in the space provided.
Use of Calculators, Mathematical Tables is strictly NOT PERMITTED.
QUESTIONS …
Q.01 Roughly sketch the graph of… f(x) = x2 – 3x + 2
2
12
10
[6]
8
6
Q.02 If sinx + sin x = 1, simplify cos x + 3cos x + 3cos x + cos x – 1.
[6]
Q.03 A field is in the form of an isosceles triangle. If base of this triangle is 24 m and cost of…
growing grass in this triangular field at 25 paise per sq. metre is Rs.15, find the length of
any of the two equal sides.
[6]
SPACE FOR SOLUTIONS …
**********
forACE
END OF THE PART–B * * * * * * * * * *
AXIS – S.C.O. 58, I-II Floor, Sec. 20C,
Chandigarh(U.T.)–160020.
Phs.(O) 0172 500 5555, 501 5555 (R) 500 0055 (F) 467 0083 (M) 9216528383, 9316528383, 9041628383, 9041528383
www.aciax.com(in),[email protected],[email protected]
aps correspondence desk :BEYOND | 83A, Rani KaBagh, Amritsar 143001, Punjab-State (INDIA). Ph. 0183 2220083
S01 I – L1 / Quadratic Equations, T–Ratios, Triangles, General Case Studies
[06]
PART – C ………...
INSTRUCTIONS…
#
#
#
#
This part contains 4 questions. Attempt all possible .
Numbers on the right indicate maximum marks assigned.
Write your answer neatly, with necessary workings / explanations and in the space provided.
Use of Calculators, Mathematical Tables is strictly NOT PERMITTED.
QUESTIONS …
Q.01 (01) Compute… [ 5 –2(4 – 5)–1 ]2
[4]
(02) Suppose that 3% of births rise to twins. What percentage of the population is a …
twin ?
[4]
Q.02 We know that solving two linear equations simultaneously implies knowing the nature of
points of intersection of two lines viz. unique solution arise for one point of intersection
of lines, infinite solution set arise for intersection of two identical lines etc. Now you …
discuss the cases for solving three linear equations simultaneously.
[8]
Q.03 If
1
2

1
2

1
2
 ..................  = k, then …
1
3
5
(evaluate in terms of k only)
1
1
2

1
2
2

1
3
2

1
42
 ................  = … ?
[8]
Q.04 What is the smallest number which when divided by10 leaves a remainder of 9, when…
divided by 9 leaves a remainder of 8, when divided by 8 leaves a remainder of 7 and so
on until when divided by 2 leaves a remainder of 1.
[8]
SPACE FOR SOLUTIONS …
**********
END OF THE TEST
**********
Conceived and Compiled
by…
Mentors @ ACE AXIS
forACE
AXIS – S.C.O. 58, I-II Floor, Sec. 20C,
Chandigarh(U.T.)–160020.
Phs.(O) 0172 500 5555, 501 5555 (R) 500 0055 (F) 467 0083 (M) 9216528383, 9316528383, 9041628383, 9041528383
www.aciax.com(in),[email protected],[email protected]
aps correspondence desk :BEYOND | 83A, Rani KaBagh, Amritsar 143001, Punjab-State (INDIA). Ph. 0183 2220083