Mathematics for CTET & State TET Exams Exams

Question 1

If a³ = 1 + 7, 3³ = 1 + 7 + b and 4³ = 1 + 7 + c where a, b, and c are different positive integers, then the value of a + b + c is

Question 2

n² – (n + 1)² – (n + 2)² + (n + 3)² is equal to

Question 3

Directions: Answer the following questions by selecting the most appropriate option.

If a, b and c are different integers such that a < b < c < 0, then which of the following statements is true?

Question 4

The factorization of 25 - p² - q² - 2pq is:

Question 5

If 8210 = 8.21 × 10^x, then the value of x is

Question 6

If xy = 6 and

then the value of

is

Question 7

Directions: Answer the following questions by selecting the most appropriate option.

If x is an integer, then (x + 1)⁴ – (x – 1)⁴ is always divisible by

Question 8

The number of lines of symmetry of the figure is

Question 9

The average mathematics marks of two Sections A and B of Class IX in the annual examination is 74. The average marks of Section A is 77.5 and that of Section B is 70. The ratio of the number of students of Section A and B is

Question 10

A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30 km upstream and 21 km downstream in 6 hours and 30 minutes. The speed of the boat in still water is

Question 11

The tax imposed on an article is decreased resulting in price to drop by 10% and its consumption increases by 10%. Find the percentage change in revenue from it?

Question 12

The product of the ages of Payal and Rashmi is 240. If twice the age of Rashmi is more than Payal’s age by 4 years what is Rashmi’age?

Question 13

A shopkeeper sold 12 tables at a profit of 20% and 8 tables at a profit of 10%. If he had sold entire 20 table at a profit of 15%, then his profit have been reduced by Rs. 36. What is the cost price of each table?

Question 14

If 50% of (p - q) =30% of (p + q), then p: q is equal to

Question 15

Shekher purchases a track suit for Rs. 2400 cash or Rs. 1000 cash down payments and two monthly installments of Rs. 800 each. Find rate of simple interest.

Question 16

A man travels a distance of 36 km from his house to an exhibition by horse at 15 km/hr and returns back on cycle at 10 km/hr. Find his average speed for the whole journey.

Question 17

24 males can complete a piece of work in 16 hours. The same work can be completed by 8 females in 72 hours, whereas 24 Child take 32 hours to complete it. If 10 males, 15 females and 24 Child work together, in how many hours can the work be completed?

Question 18

The product of the mean and median of the numbers 8, 11, 6, 9, 16 is

Question 19

In standard form, 0.00001278 is expressed as k × 10ⁿ. The value of (k + n) is:

Question 20

The values of y for which the 4-digit number 51y3 is divisible by 9 is:

Question 21

The mean of 10 numbers is 0. If 72 and –12 are included in these numbers, the new mean will be

Question 22

The area of a triangle with base x units is equal to the area of a square with side x units. Then the altitude of the triangle is:

Question 23

In the given figure, PS = SQ = SR and ∠SQP = 54^o. Find the measure of ∠x.
Description: https://www.jagranjosh.com/imported/images/E/Q.46.JPG

Question 24

In ∆PQR, PQ = 4 cm, PR = 6 cm and QR = 3 cm. Which of the following is correct

Question 25

In the figure, ABC is an isosceles triangle with CA = CB and BC is produced to a point D. If CE ⊥ BC, such that

then measure of ∠ACD is

Question 26

Number of degrees in four and two-third right-angles is

Question 27

In the figure, in triangles PQR and TQR, PQ = TR and PR = TQ. Which of the following statements is true ?

Question 28

In a quadrilateral ABCD, ∠D = 60^o and ∠C = 100^o. The bisectors of ∠A and ∠B meet at the point P. The measure of ∠APB is

Question 29

The ratio of the side and height of an equilateral triangle is

Question 30

10 ones + 10 tens + 10 thousands equals

Question 31

Forty-two cubes each of side 1 cm are glued together to form a solid cuboid. If the perimeter of the base of the cuboid is 18 cm then its height is.

Question 32

When recast, the radius of an iron rod is made one-fourth. If its volume remains constant, then the new length will become:

Question 33

Examine the following match stick patterns:

If the pattern continues, how many match sticks are needed in the 15th stage?

Question 34

The number of vertices in a polyhedron which has 30 edges and 12 faces is

Question 35

A square and a circle have equal perimeters.The ratio of the area of the square to the area of the circle is

Question 36

Perimeter of a square and a rectangle are equal. If the perimeter of a square is 40 cm and length of rectangle is 2 cm more than the side of the square, then the area, in square cm, of the rectangle is

Question 37

Number of minutes in 10 days is equal to the number of seconds in:

Question 38

If the time now is 2.17 P.M., what will be the time 11 hours and 59 minutes from now?

Question 39

The perimeter of a square is 20 cm. A rectangle has the same width as the square. The length of the rectangle is double its width. The area, in square cm, of the rectangle is

Question 40

The diagonals of a rhombus are 6 cm and 8 cm. What is the perimeter of the rhombus?

Question 41

Internal length, breadth and depth of a (rectangular) box are 4 cm, 3 cm and 2 cm respectively. How many such boxes are needed to pack 8664 centimetre cubes?

Question 42

The number n is doubled and then y is added to it. The result is then divided by 2 and the original number n is subtracted from it. The final result is

Question 43

Given n numbers, n > 1, of which, one is

and all others are 1’s. The mean of the n numbers is

Question 44

The difference of the place value and the face value of 5 in 35362 is

Question 45

The product of remainders of 19009 ÷ 11 and 9090 ÷ 11 is

Question 46

The difference between the smallest common multiple and biggest common factor of 5, 10 and 35 is

Question 47

When 3488 is divided by 12 and 2478 is divided by 11, the difference between the remainders in both cases is

Question 48

HCF of two numbers is 28 and their LCM is 336. If one number is 112, then the other number is

Question 49

Which of the following numbers is a perfect square?

Question 50

For a unit 'Perimeter and Area' of two dimensional shapes, one of the instructional objective identified by the teacher is as follows: "Learner will be able to calculate the area of triangle as

and area of circle as

and hence will be able to calculate the area of composite shapes."
The above objective refers to

Question 51

Mr. Sharma was assessing the students' work on exponents. One of the response sheet was as follows:

(a) 2³ × 2⁵ = 2⁸
(b) 3² × 4² = (12)⁴
(c) 3³ ÷ 3⁵ = 3^–2
(d) 7²⁰ ÷ 7¹⁴ = 7⁶
(e) 9³ ÷ 18⁶ =

On the basis of this response sheet Mr. Sharma can make the following observations:

Question 52

Class VI students were given the following layout of a house:

The students were asked to find out the –

(A) Perimeter and area of each room.
(B) Total perimeter and total area of the house.

The above activity can be used by the teacher as a formative assessment task because:

Question 53

In Class VII, a teacher taught the 'properties of all types of quadrilaterals'. In the class test that followed after the unit, the teacher asked about the problems with the construction of quadrilateral. No one in the class was able to perform in the test. The reason maybe:

Question 54

Hamida always allows her students to observe the number pattern and to form conjectures on their own in order to enhance their mathematical abilities. She wrote the following problems on board and asked the students to write the answers:

21 ÷ 7 =
2.1 ÷ 0.7 =
0.21 ÷ 0.07 =
0.021 ÷ 0.007 =

Through the set of questions, she wants the students to observe that:

Question 55

Rubrics of assessment for the geometry lesson on points and lines in Class IV shall be:

Question 56

Higher Order Thinking Skills (HOTS) based questions demand the:

Question 57

Anil is able to answer all questions orally but commits mistakes while writing the solutions of problems. The best remedial strategy to remove errors in his writing is:

Question 58

A teacher asked the students to collect leaves and to identify symmetry patterns. This task reflects the teacher’s efforts to:

Question 59

NCF, 2005 states that Mathematics teaching should be ambitious, coherent and important. Here, ‘ambitious’ refers to achievement of:

Question 60

A child of primary class is not able to differentiate between number, operation symbols, coins and clock hands. This indicates that the child has problem regarding: