Mathematics

TET Class 12

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1.

If x=2, y=1, z=-3, then x^{3}+ y^{3 }= z^{3}- 3xyz equals

6

2

8

0

D.

0

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

$\therefore $ x^{3}+y^{3}+z^{3}-3xyz

=(x+y+z)(x^{2}+y^{2}+z^{2}-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 x^{13}+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

$\Rightarrow $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

$\Rightarrow $A$\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 = $4410\times \frac{100}{105}\times \frac{100}{105}=4000$

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 $\u20b9$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

(15

^{o}, 25^{o})(10

^{o}, 15^{o})(15

^{o}, 35^{o})(40°, 35°)

A.

(15^{o}, 25^{o})

Given, ABCD is a cyclic quadrilateral.

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

$\Rightarrow $4x+ 4y+ 20 = 180

$\Rightarrow $4x + 4y=160

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

Also, (7x+5) +(3y-5)= 180°

$\Rightarrow $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.

Textbook Solutions | Additional Questions

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