Subject

Mathematics

Class

TET Class 12

Pre Boards

Practice to excel and get familiar with the paper pattern and the type of questions. Check you answers with answer keys provided.

Sample Papers

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 Multiple Choice QuestionsMultiple Choice Questions

1.

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

  • 6

  • 8

  • 9

  • 12


B.

8

Consider (x+1)4-(x-1)4

[(x+1)2]2 - [(x-1)2]2

[x2+1+2x]2- [x2+1-2x]2

(x2+1+2x+x2+1-2x) (x2+1+2x-x2-1+2x)

(2x2+2)(4x)

2(x2+1)(4x)

8x(x2+1)

Hence if x is an integer , then (x+1)4-(x-1)will be always divisible by 8 .


2.

What should be subtracted from -57to get -1?

  • -27

  • 47

  • 27

  • -47


C.

27

Let x should be subtracted from -57 to get -1

Then , -57-x = -1

-x = -1+57

-x = -7+57

-x = -27

 x = 27


3.

The hundreds digit of a three-digit number is 7 more than the units digit. The digits of the number are reversed and the resulting number is subtracted from the original three-digit number. The units digit of the final number so obtained is

  • 0

  • 1

  • 2

  • 3


D.

3

Let the three-digit number be 100x +10y+ z

As per question , x = 7 + z .........(i)

On Reversing the number we get : 100z + 10 y + x....(ii)

Now subtracting  (ii) From (i)

100x+10y+z-100z-10y-x

=99x-99z

=99(x-z)

=99 x 7 [ from eqn (i) ]

=693

Hence the unit digit will be 3 


4.

What is the probability that a randomly selected factor from positive factors of 72 is less than 11?

  • 512

  • 711

  • 712

  • 710


C.

712

Factors of 72 are

1 x72

2 x36

3 x 24

4 x18

6 x12

8 x9

 Total number of the possible outcomes =12

Number of favorable outcomes less than 11=7

 Probability = 712

 


5.

The value of 5003×163 is 

  • 16

  • 20

  • 25

  • 18


B.

20

Given 5003×163

 500×163

80003

2×1033

= 2 x 10

=  20


6.

Numbers -1120,7-15,1730and-310are written in descending order as 

  • 17-30>-1120>-310>7-15

  • -310>7-15>-1120>17-30

  • -310>-1120>7-15>17-30

  • -1120>17-30>-310>7-15


B.

-310>7-15>-1120>17-30

We have, -1120,7-15,17-30,-310

LCM of the denominators , 20, 15, 30 and 10 = 60

-1120=-33607-15=-2860,17-30=-3460 and-310=-1860

Therefore the correct descending order on comparing the numerator will be:

-1860>-2860>-3460>-1860

i.e. -310>7-15>-1120>17-30

 


7.

LCM of two prime numbers x and y, ( x > y), is 161. The value of 3y-x is

  • 2

  • -2

  • -5

  • 62


B.

-2

Let the two prime numbers be x and y 

LCM of the two numbers: 161

xy = 161 [ The LCM of the two prime number will be their product since they will not have any common factor ]

Now 161 = 23 x 7 

 3y - x = 3x7 - 23 

= 21-23 

= -2


8.

If a= 20132+2013+2014, then the value of a is 

  • 1002

  • 1007

  • 2013

  • 2014


D.

2014

Given : a = 20132+2013+2014

20132+2013+2013+1

20132+2×2013×1+12

=2013+12

=2013+1

=2014


9.

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

  • a + c < b

  • ab < c

  • a + b > c

  • ac > ab


A.

a + c < b

Given that, a < b < c < 0

Let a=-3, b=-2, C = -1

then -3 < -2 < -1 < 0

From option (1), a + c < b

-3 + (-1) < -2

-4  < -2

which is True


10.

In standard form, the number 829030000 is expressed as k x 10n. The value of k + n is

  • 90.903

  • 16.2903

  • 15.2903

  • 91.903


B.

16.2903

Given  829030000

In standard form k x 10n,  829030000 = 8.2903 x108

On comparing we get k=8.2903, and n=8

 k+n = 8.2903+8 = 16.2903