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# TET Class 12 Mathematics Solved Question Paper 2017

#### Multiple Choice Questions

1.

If x=2, y=1, z=-3, then x3+ y= z3- 3xyz equals

• 6

• 2

• 8

• 0

D.

0

Here x+y+z = 2+1-3=0

$\therefore$ x3+y3+z3-3xyz

=(x+y+z)(x2+y2+z2-xy-yz-zx)

=0

2.

Find the biggest 4- digit number which is a perfect square.

• 9999

• 1899

• 9000

• 9801

D.

9801

9801 is the square of 99

3.

When x13+1 is divided by x-l, then what is the remainder?

• 0

• 1

• 2

• -1

C.

2

Let p(x) = x+1 then, x-1 = O

then by remainder theorem

p(1) =(1)13 + 1

$⇒$1+1 =2

4.

If A and B are non- empty subsets of a set C, then  A$\cup$(A$\cap$B) is equal to

• A$\cap$B

• A$\cup$B

• A

• B

C.

A

Given, A and B are non-empty subsets of C

$⇒$A$\subseteq$C and B$\subseteq$C

Now, A$\cup$(A$\cap$B)= A

5.

The population of a village increases by 5% yearly. If at present the population of the village is 4410, then what was the population before two years?

• 4420

• 4430

• 4440

• 4000

D.

4000

The population before two years = $4410×\frac{100}{105}×\frac{100}{105}=4000$

6.

From a pack of 52 playing cards, a card is drawn at random. What is the probability that the card is a spade or an ace?

• $\frac{4}{13}$

• $\frac{6}{13}$

• $\frac{8}{13}$

• $\frac{2}{5}$

A.

$\frac{4}{13}$

Let A be the event of getting a spade and B be the event of getting an ace then,
P(A)=$\frac{13}{52}$, P(B)=$\frac{4}{52}$

and P(A$\cap$B)=$\frac{1}{52}$ ($\because$one spade is an ace)

$\therefore$Required probability

P(A$\cup$B)=P(A)+P(B)-P(A$\cap$B)

=$\frac{13}{52}+\frac{4}{52}-\frac{1}{52}$

=$\frac{16}{52}$

=$\frac{4}{13}$

7.

A company makes an advertisement of shares to collect a capital of 25 lakh. If the printed price of one share is $₹$100, then find the number of shares circulated by the company.

• 20000

• 25000

• 30000

• 15000

B.

25000

Number of shares =$\frac{2500000}{100}$= 25000

8.

In the given figure, ABCD is a cyclic quadrilateral. Then, the ordered pair (x,y) is

• (15o, 25o)

• (10o, 15o)

• (15o, 35o)

• (40°, 35°)

A.

(15o, 25o)

Given, ABCD is a cyclic quadrilateral.

We know that sum of opposite angles of a cyclic quadrilateral is 180.

$⇒$4x+ 4y+ 20 = 180

$⇒$4x + 4y=160

$\therefore$x+ y= 40 ... (1)

Also, (7x+5) +(3y-5)= 180°

$⇒$7x+3y=180 ...(2)

On solving Eqs. (1) and (2), we get,

x = 15° and y= 25°

9.

If a, a + 2, a + 4 are prime numbers, then the number of values of a is

• One

• two

• three

• more than three

C.

three

Given, a, a+2, a+4 are prime numbers.

1) If a= 2 (prime)

then 2, 4, 6 all are not prime numbers.

2) If a= 3 (prime)

then, 3, 5, 7 all are prime numbers.

3) If a =5

then, 5,7, 9 all are not primer numbers.

4) If a =7

then, 7, 9, 11 all are not prime numbers.

10.

For what value of x, the mode of the following data is 27?

25,26,27,23,27,26,24,x,27,26,25,25

• 27

• 24

• 25

• 26

A.

27

Mode is the most frequent value in a data, here 25,26 and 27 have occurred three times in the data, so in order to be 27 as Mode of the data then x must be 27.