If n(A x B) = 6 and A = {1,3} then n(B) is

(a)

1

(b)

2

(c)

3

(d)

6

A = {a,b,p}, B = {2,3}, C = {p,q,r,s} then n[(A U C) x B] is

(a)

8

(b)

20

(c)

12

(d)

16

If f : R⟶R is defined by (x) = x² + 2, then the preimage 27 are _________

(a)

0.5

(b)

5, -5

(c)

5, 0

(d)

\(\sqrt { 5 } ,-\sqrt { 5 } \)

Euclid’s division lemma states that for positive integers a and b, there exist unique integers q and r such that a = bq + r , where r must satisfy

(a)

1 < r < b

(b)

0 < r < b

(c)

0 \(\le\) r < b

(d)

0 < r \(\le\) b

Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are

(a)

0, 1, 8

(b)

1, 4, 8

(c)

0, 1, 3

(d)

0, 1, 3

What is the HCF of the least prime and the least composite number?

(a)

1

(b)

2

(c)

3

(d)

4

A system of three linear equations in three variables is inconsistent if their planes

(a)

intersect only at a point

(b)

intersect in a line

(c)

coincides with each other

(d)

do not intersect

The solution of the system x + y − 3z = −6, −7y + 7z = 7, 3z = 9 is

(a)

x = 1, y = 2, z = 3

(b)

x = −1, y = 2, z = 3

(c)

x = −1, y = −2, z = 3

(d)

x = 1, y = -2, z = 3

Which of the following are linear equation in three variables ___________

(a)

2x = z

(b)

2sin x + y cos y + z tan z = 2

(c)

x + 2y² + z = 3

(d)

x - y - z = 7

If in triangles ABC and EDF,\(\cfrac { AB }{ DE } =\cfrac { BC }{ FD } \) then they will be similar, when

(a)

\(\angle B=\angle E\)

(b)

\(\angle A=\angle D\)

(c)

\(\angle B=\angle D\)

(d)

\(\angle A=\angle F\)

In ∆LMN, \(\angle\)L = 60^o, \(\angle\)M = 50^o. If ∆LMN ~ ∆PQR then the value of \(\angle\)R is

(a)

40^o

(b)

70°

(c)

30°

(d)

110°

If triangle PQR is similar to triangle LMN such that 4PQ = LM and QR = 6 cm then MN is equal to ____________

(a)

12 cm

(b)

24 cm

(c)

10 cm

(d)

36 cm

The area of triangle formed by the points (−5, 0), (0, −5) and (5, 0) is

(a)

0 sq.units

(b)

25 sq.units

(c)

5 sq.units

(d)

none of these

A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y axis. The path travelled by the man is

(a)

x = 10

(b)

y = 10

(c)

x = 0

(d)

y = 0

Find the ratio in which the line segment joining the points (-3, 10) and (6,-8) is internally divided by (-1, 6) ____________

(a)

7:2

(b)

3:4

(c)

2:7

(d)

5:3

The value of \(si{ n }^{ 2 }\theta +\frac { 1 }{ 1+ta{ n }^{ 2 }\theta } \) is equal to

(a)

 \(ta{ n }^{ 2 }\theta \)

(b)

1

(c)

\(cot^{ 2 }\theta \)

(d)

0

tan \(\theta \) cosec²\(\theta \) - tan\(\theta \) is equal to 

(a)

sec\(\theta \)

(b)

\(cot^{ 2 }\theta \)

(c)

sin\( \theta \)

(d)

\(cot\theta \)

If cos A = \(\frac{4}{5}\), then the value of tan A is ___________

(a)

\(\frac{3}{5}\)

(b)

\(\frac{3}{4}\)

(c)

\(\frac{4}{3}\)

(d)

\(\frac{5}{3}\)

The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is

(a)

60\(\pi\) cm²

(b)

68\(\pi\) cm²

(c)

120\(\pi\) cm²

(d)

136\(\pi\) cm²

If two solid hemispheres of same base radius r units are joined together along their bases, then curved surface area of this new solid is

(a)

4\(\pi\)r² sq.units

(b)

6\(\pi\)r² sq.units

(c)

3\(\pi\)r² sq.units

(d)

8\(\pi\)r² sq.units

The radio of base of a one 5 cm and to height 12 cm. The slant height of the cone ___________

(a)

12 cm

(b)

17 cm

(c)

7 cm

(d)

60 cm

Which of the following is not a measure of dispersion?

(a)

Range

(b)

Standard deviation

(c)

Arithmetic mean

(d)

Variance

The range of the data 8, 8, 8, 8, 8. . . 8 is

(a)

0

(b)

1

(c)

8

(d)

3

If are event occurs surely, then its probability is ___________

(a)

0

(b)

1

(c)

\(\frac{1}{2}\)

(d)

\(\frac{3}{4}\)

Two dice are through simultaneously the probability if getting a double is ___________

(a)

\(\frac{5}{36}\)

(b)

\(\frac{1}{12}\)

(c)

\(\frac{1}{9}\)

(d)

\(\frac{1}{6}\)