KTET 2012 Question Paper for Category III Code 717 SET (A) QP

8/13/2019 KTET 2012 Question Paper for Category III Code 717 SET (A) QP

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Code No. : 717 Set - A

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71. If a is 2

1

1 times b, how many times a – b is a + b?(A) 3 (B) 4 (C) 5 (D) 6

72. If a, b, p, q are natural numbers withq

p

b

a< , then which of the following is

true?

(A)q

p

b

a

qb

pa<<

+

+(B)

b

a<

qb

pa

+

+<

q

p

(C)qb

pa

q

p

b

a

++

<< (D)q

p

qb

pa

b

a<

−−

<

73. The recurring decimal 0.3999.... represents

(A)4

1(B)

5

2

(C)9939 (D) an irrational number

74. The product 0.333 ... × 0.666... is equal to

(A) 0.1818... (B) 0.1919... (C) 0.198198... (D) 0.222...

75. For a real number x with –1 < x < 1, which of the following is true?

(A) | x – 1| + | x + 1| < 2 (B) | x – 1| + | x + 1| = 2

(C) | x – 1| + | x + 1| > 2 (D) | x – 1| – | x + 1| = 2

76. If r is a non-zero rational number and x is an irrational number, which of thefollowing is true?

(A) r + x and rx are irrational

(B) r + x irrational and rx is rational

(C) r + x is rational and rx is irrational

(D) r + x and rx are rational




























































77. The sequence of numbers

1, ,3

11− ....,

5

1

3

11 +−

got by alternately adding and subtracting reciprocals of odd numbers get closer

and closer to the number

(A) 2 (B) (C) π

2

1(D) π

4

1

78. Which of the following is true for the arithmetic sequence with first term3

1

and common difference6

1?

(A) contains no natural numbers

(B) contains all natural numbers(C) contains only even natural numbers(D) contains only multiples of 3

79. The sum of n terms of a sequence is 2n2 + n. What is its nth term?(A) 2n + 1 (B) 2n – 1 (C) 4n + 1 (D) 4n – 1

80. What is the last digit of the sum 1 + 6 + 62 + ... + 6100?(A) 1 (B) 3 (C) 6 (D) 7

81. The price of 3 pencils and 4 pens is 26 rupees; the price of 5 pencils and 4pens is 30 rupees. What is the price of a pencil?(A) 1 rupee (B) 2 rupees (C) 1½ rupees (D) 2½ rupees

82. The figure below is made of two squares joined together:

The difference of the sides of the square is 2 centimeters and the difference intheir areas is 20 square centimeters. What is the total area of the figure?

(A) 34sq.cm (B) 52sq.cm (C) 74sq.cm (D) 100sq.cm

83. One side of a rectangle is 4 centimeters longer than the other and its area is221 square centimeters. What is its perimeter?(A) 30 cm (B) 45 cm (C) 60 cm (D) 75 cm



































84. If a, b, c are all positive real numbers and if the equation ax 2 + bx + c = 0 hassolutions, then(A) both solutions are positive(B) one solution is positive and the other negative(C) both solutions are negative(D) one of the solutions is zero

85. In copying a second degree equation, a student mistakenly wrote the constantterm as 6 instead of –6. His answers were –2 and –3. What are the answers tothe original equation?(A) 3 and –2 (B) –3 and 2 (C) 6 and –1 (D) –6 and 1

86. If the degree of the polynomials p( x ) and q( x ) are m and n, then the degree of p( x ) + q( x ) is

(A) equal to m + n (B) equal to the larger of m and n(C) equal to the smaller of m and n (D) cannot be determined

87. The remainder got on dividing 8 x 3 – 4 x 2 + 2 x + 1 by 2 x –1 is(A) –1 (B) 0 (C) 1 (D) 2

88. What number must be added to x 2 + x so that the resulting polynomial isdivisible by x – 1?(A) –2 (B) –1 (C) 1 (D) 2

89. Which of the following cannot be the remainder got when a polynomial isdivided by x 2 – 1?(A) x 2 + 1 (B) x + 1 (C) x – 1 (D) 2 x + 1

90. The constant term in the expansion of4

1⎟ ⎠ ⎞

⎜⎝⎛ +

x x is

(A) 3 (B) 4 (C) 6 (D) 10

91. In the triangles ABC and PQR shown below, ∠P = ∠C and ∠Q = ∠A.

What is the length of PQ?

(A) 8cm (B) 12cm (C) 12.5cm (D) 15cm
































































92. There are two triangles, the sides of the larger being double the sides of thesmaller. The area of the larger triangle is 24 square centimeters. What is thearea of the smaller triangle?(A) 12sq.cm (B) 8sq.cm (C) 6sq.cm (D) 3sq.cm

93. If one angle of a triangle is 30º and a side adjacent to this angle is 8 centime-ters long, then the side opposite to this angle must be(A) longer than 4 centimeters (B) shorter than 4 centimeters(C) equal to 4 centimeters (D) longer than 8 centimeters

94. A circle is to be drawn passing through the ends of a line 6 centimeters longand the angle in one of the segments formed by the line should be 60º. Whatshould be the radius of the circle?

(A) 6cm (B) 3cm (C) 32 cm (D) 23 cm

95. When the sun is at an elevation of 45º, the length of the shadow of a tower is(A) more than the height of the tower(B) less than the height of the tower(C) equal to the height of the tower(D) half the height of the tower

96. If x < y < 45, then which of the following is true?

(A) sin x º < sin yº < cos x º < cos yº (B) sin x º < sin yº < cos yº < cos x º(C) cos x º < cos yº < sin x º < sin yº (D) cos x º < cos yº < sinyº < sin x º

97. An arc of a circle is8

1 of the circumference of the circle. What is the radian

measure of its central angle?

(A) π

8

1(B) π

4

1(C) π

2

1(D) π

3

1

98. If x is the radian measure of an angle, which of the following is true?(A) sin x is less than x (B) sin x is greater than x

(C) cos x is less than x (D) cos x is greater than x

99. From a point outside a circle of radius 1 centimeter, two tangents are drawnand the angle between the tangents is 40º. What is the lengths of one tangentfrom this point to the point of contact?

(A) tan 40º (B) tan 20º (C)

º40tan

1(D)

º20tan

1
























































100. In the figure below, O is the center of the circle and OABC is a rhombus withA, B, C on the circle:

The radius of the circle is 10 centimeters. What is the area of the rhombus?

(A) 100 3 sq.cm (B) 50 3 sq.cm

(C) 30 3 sq.cm (D) 25 3 sq.cm

101. In the figure, A, B, C, D are points on the circle:

What fraction of the circumference is the length of arc BDC?

(A)8

1(B)

4

1(C) π

8

1(D) π

4

1

102. If a parallelogram is cyclic, it must be a(A) rhombus (B) trapezium (C) rectangle (D) square

103.A circle is drawn and a point is marked outside it, at a distance from the centerequal to the diameter. What is the angle between the tangents to the circlefrom this point?

(A) 30º (B) 45º (C) 60º (D) 90º

104.What is the radius of the in-circle of an equilateral triangle of side 6 centime-ters?

(A) 2cm (B) 3cm (C) 3 cm (D) 2 3 cm

105.Which of the following cannot be the top angle of a triangular face of a squareprism?

(A) 30º (B) 45º (C) 60º (D) 90º


























106.All the triangular faces of a square pyramid are equilateral. A triangle is formedby joining a pair of opposite vertexes of the base with the top vertex of thepyramid as in the figure:

The top angle of this triangle is

(A) 30º (B) 45º (C) 60º (D) 90º

107.A cylindrical vessel of radius 8 centimeters and height 16 centimeters is half full of water. A cylinder of radius 4 centimeters and height 8 centimeters isimmersed in it. What is the height of the water level now?(A) 9cm (B) 10cm (C) 11cm (D) 12cm

108.A sector of central angle 60º is cut out from a circle of radius 6 centimeters androlled into a cone. What is the base radius of the cone?(A) 1cm (B) 2cm (C) cm (D) 2 cm

109.From a cylinder with height equal to base diameter, a sphere of maximum sizeis cut out. What is the ratio of the surface areas of the cylinder and the sphere?

(A) 2:1 (B) 3:2 (C) 4:3 (D) 5:3

110.A cone, sphere and cylinder all have the same radius and the heights of thecone and cylinder are equal to the diameter. Then the volumes of the cone,sphere and cylinder are in the ratio(A) 1:2:3 (B) 2:3:4 (C) 3:4:5 (D) 4:5:6

111.The ends of a string 6 centimeters long are attached to two pins fixed 2 centi-meters apart on a board. By stretching the string with the tip of a pencil, an

ellipse is drawn:

What are the lengths of the axes of the ellipse?(A) 2cm, 4cm (B) 4cm, 6cm

(C) 6cm, 8cm (D) 6cm, 4 2 cm




















112. In the figure, P and Q are points on a circle centered at the origin

What are the coordinates of Q?(A) (–1, 2) (B) (–2, 1) (C) (–1, 5 ) (D) )5,3(−

113.Which of the points below is on the line joining (1, 2) and (2, 6)(A) (3, 6) (B) (3, 8) (C) (3, 9) (D) (3, 10)

114.What is the third vertex of the triangle in the figure below?

(A) (5, 0) (B) (4, 0) (C) (3, 0) (D) )0,52(

115.The lowest point on the graph of y = x 2 – 2 x is

(A) (–1, 0) (B) (0, –1) (C) (–1, 1) (D) (1, –1)

116.The graph of the equation y = x n, where n is an even natural number is

(A) symmetric about the x -axis

(B) symmetric about the y-axis

(C) symmetric about neither axis

(D) symmetric about the line y = x

























117.The figure shows the graph of an equation:

What is the equation?

(A) y = | x + 1| (B) y = | x – 1| (C) y = | x | + 1 (D) y = | x | – 1

118. In the histogram of a frequency distribution, a line is drawn parallel to the y-axis, dividing the area of the histogram into two equal parts. The pointwhere the line cuts the x -axis corresponds to which of the following?

(A) arithmetic mean (B) geometric mean

(C) median (D) mode

119.Two dice are rolled and the sum of the numbers found. What is the sum withthe highest probability?

(A) 6 (B) 7 (C) 10 (D) 12

120.Cards numbered 1 to 100 are put in a box. One card is selected and it isannounced to be an even number. What is the probability that it is multiple of 3?

(A)

6

1(B)

6

5(C)

25

8(D)

25

4

121.Which of the following is suitable for a constructivist Mathematics class?

(A) Problem centres round the subject matter is presented by the teacher

(B) Problem occurs in a situation in which a felt difficulty to act is realised bythe students themselves

(C) Problem is defined by the teacher clearly in the beginning itself

(D) Problem is analysed by the teacher and give clear cut directions





























122.Most important role of a Mathematics teacher is to:

(A) organise teaching (B) deliver lecture(C) evaluate students (D) take care of children

123.Mathematics is mostly correlated to:

(A) Medicine (B) Philosophy

(C) Psychology (D) Engineering

124.The mental changes involved in acquiring new ways of perceiving ideas arereferred to as:

(A) cognitive (B) conative

(C) affective (D) effective

125.Summative assessment of the unit ‘Analytic Geometry’ can be done through a(A) Mathematics lab activity (B) Project work

(C) Written test (D) Home assignment

126.A teacher starts the class with a puzzling situation. He intends to take the classusing a ‘Model of Teaching’. Which among the following Model is his choice?

(A) Concept Attainment Model (B) Inquiry Training Model

(C) Inductive Thinking Model (D) Advance Organiser Model

127. “Find the remainder obtained on dividing ( x 3 – 2 x 2 + 3 x + 1) by ( x – 1)” Forsolving the above problem a teacher asks the following analytic questions.(1) How will you find the remainder?

(2) What is to be found out?

(3) Do you know Remainder theorem? Then state the theorem.(4) What is the remainder?

Which among the following is in the sequential order?

(A) 3, 1, 2, 4 (B) 1, 2, 3, 4(C) 1, 2, 4, 3 (D) 2, 1, 3, 4

128. “ 2 is irrational”. This fact is discovered by:

(A) Babylonians (B) Egyptians

(C) Indians (D) Pythagoreans

129.For finding the surface area of a cylinder having radius ‘r ’ and height ‘h’ themost suitable method of teaching is:

(A) Lecture method (B) Analytic method

(C) Synthetic method (D) Heuristic method




























130.The purpose of conducting a visit to a historical place before starting the unit‘Solids’.(A) Field trips are recommended in the curriculum.(B) Students get opportunity to see different shapes in the architecture and to

correlate with the subject.(C) It would be a change for the students and teacher from the routine Math-

ematics class.(D) Providing leisure to the students.

131.Which of the following is a sign of motivation in a Mathematics class?(A) Pindrop silence(B) Full attendance(C) High interaction among the students and teacher

(D) Use of learning aids by the teacher.

132.To introduce the concept ‘Arithmetic Progression’, a teacher can start with(A) Numbers (B) Number patterns(C) Letters (D) Arithmetic progressions

133.The most important purpose of lesson planning is to:(A) prepare the learning activities (B) refresh the knowledge(C) make the class interesting (D) manage the class ef fectively

134.Choose the odd one : co-curricular activities in a Mathematics class areintended for(A) maintaining interest in learning Mathematics.(B) cultivating a sense of co-operation among the students.(C) developing self discipline.(D) distracting the students from curricular activities.

135.While explaining the method of finding the slope of a straight line, a studentsuggests an alternative method. Which of the following objective is attainedin this context?(A) Knowledge (B) Comprehension(C) Application (D) Skill

136.Problem solving method is to:(A) stimulate reflective and creative thinking to arrive at the correct solution.(B) direct the students to use a particular method and find the answer.(C) help the students to find the correct solution.(D) ask the students to solve the problem.




















137.For active involvement of the learners in the teaching-learning process, a teacher must:

(A) organise discussions in the class.

(B) encourage students to take part in class room activities.

(C) organise educational games/programmes relevant to the context.

(D) assign grades to the students.

138.Previous knowledge for learning the topic ‘Quadratic Equations’.

(A) Algebraic expressions

(B) Factorization of algebraic expressions

(C) Simple equations

(D) All the above

139.A teacher is trying to differentiate between ‘Congruence’ and ‘Similarity’.Which one of the following is more effective?

(A) Drawing congruent and similar figures on the Black board and explainsthe attributes.

(B) Listing all the attributes of both the concepts on the black board.

(C) Showing models of congruent and similar figures and discussing all theattributes.

(D) Presenting a chart in which congruent and similar figures are drawn

140.Which among the following is suited for a child centred Mathematics class?

(A) Teacher gives instructions and children are obeying in a disciplined way.

(B) Children work individually.

(C) Teacher assess the students every day.

(D) Children interacts freely and work independently under the guidance of the teacher.

141.The most difficult stage in diagnosis

(A) Finding the areas of difficulty (B) Preparing diagnostic tests

(C) Finding the causes of difficulty (D) Providing remediation

142.Who wrote ‘Bija Ganita’?

(A) Aryabhata (B) Bhaskara

(C) Brahmagupta (D) Gauss



















143.You have prepared an achievement test for evaluating all the curricularobjectives stated in standard IX Mathematics curriculum. Then the test is saidto have the following validity.(A) Concurrent (B) Content(C) Construct (D) Predictive

144. In which stage of development suggested by Jean Piaget, a child developslogical thinking ability?(A) Sensory motor (B) Pre operational(C) Concrete operational (D) Formal operational

145.A project in Mathematics is intended to:(A) develop competition among the learners.(B) develop a high level of ambition.(C) develop collaboration, critical thinking and problem solving ability.(D) develop good memory in the learners.

146.An effective class for a topic in Mathematics begins with:(A) a discussion on the learning objectives.(B) a discussion on the previous knowledge and motivation through some

funny activities.(C) a presentation of the learning points in an orderly way.(D) a list of all the important points in the topic on the black board.

147.The advantage of a multiple choice test item is:(A) easy to prepare (B) chance for guessing(C) reduces subjectivity (D) increases fluency of expression

148.The topic best suited for Laboratory method of teaching Mathematics is(A) Volume of a cone(B) Sum to n terms of a progression

(C) Proving2

is an irrational number

(D) Division of polynomials

149.Which is against individualisation of instruction?(A) Learner centredness (B) Teacher Centredness(C) Frequent feed back (D) Self-pacing

150.Disciplinary value can be developed in the learners through(A) Constructing diagrams (B) Writing definitions(C) Solving Problems (D) Doing Computations













































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KTET 2012 Question Paper for Category III Code 717 SET (A) QP