For some integer q, every odd integer is of the form

1

(a)

q 

(b)

q +1

(c)

2q 

(d)

2q +1

If two positive integers a and b are written as 0 = x ³y ² an d b = xy ³, where x, yare prime numbers, then HCF (a, b) is

1

(a)

xy 

(b)

xy²

(c)

x³y³

(d)

x²y²

If two positive integers p and q can be expressed as p = ab² and q = a³ b;where a, b being prime numbers, then LCM (p, q) is equal to

1

(a)

ab

(b)

a²b²

(c)

a³b²

(d)

a³b³

The product of a non-zero rational and an irrational number is

1

(a)

always irrational

(b)

always rational

(c)

rational or irrational

(d)

one

Which of the following is not the graph of a quadratic polynomial?

1

(a)

(b)

(c)

(d)

The pair of equations x + 2y + 5 = 0 and - 3x - 6y + 1= 0 has

1

(a)

a unique solution

(b)

exactlytwo solutions

(c)

infinitely many solutions

(d)

no solution

If a pair of linear equations is consistent, then the lines will be

1

(a)

parallel

(b)

always coincident

(c)

intersecting or coinciden

(d)

always intersecting

The pair of equations y = 0 and y = - 7 has

1

(a)

one solution

(b)

two solutions

(c)

infinitelymany solutions

(d)

no solution

If the lines given by 3x + 2ky = 2 and 2x + 5y = 1 are parallel, then the value of k is

1

(a)

\(-\frac{5}{4}\)

(b)

\(\frac{2}{5}\)

(c)

\(\frac{15}{4}\)

(d)

\(\frac{3}{2}\)

The sum of the squares of three consecutive integers is 110, then the smallest positive integer is

1

(a)

6

(b)

5

(c)

7

(d)

4

Is -8 is a solution of the equation 3x² + 8x + 2 = 0?

1

(a)

Yes

(b)

No

(c)

Cannot be determined

(d)

None of these

A line segment AB is 8 cm in length. AB is produced to P such that Bp² = AB· AP. Then, the length of BP is

1

(a)

\(5(\sqrt{5}+1)\)

(b)

\((\sqrt{5}+1)\)

(c)

\(4(\sqrt{5}+1)\)

(d)

\((\sqrt{3}+1)\)

If α and β are roots of equation ax² + bx + c = 0, then \(\frac{\alpha}{a \beta+b}+\frac{\beta}{a \alpha+b}\) equals

1

(a)

\(\frac{2}{a}\)

(b)

\(\frac{2}{b}\)

(c)

\(\frac{2}{c}\)

(d)

\(-\frac{2}{a}\)

If x = \(\frac{1}{\sqrt{3}}\) IS root of the equation Px² + ( \(\sqrt3\) - \(\sqrt{2}\)) x - 1 = 0, then the value of p² + 1 is

1

(a)

\(\sqrt{6}\)

(b)

6

(c)

7

(d)

8

Let a be a sequence defined by a₁ = 1, a₂ = 1 and an = a_{n - 1} + a_{n - 2} for all n > 2, then the value of \(\frac{a_{4}}{a_{3}}\) is

1

(a)

\(\frac{2}{3}\)

(b)

\(\frac{5}{4}\)

(c)

\(\frac{4}{5}\)

(d)

\(\frac{3}{2}\)

Which term of the AP 5, 15,25, ... will be 130 more than its 31st term?

1

(a)

42

(b)

44

(c)

46

(d)

48

The 10th term of an AP is 52 and 16 th term is 82, then 32nd term of the AP is

1

(a)

152

(b)

159

(c)

162

(d)

156

Is an sequence defined by a_n = 2n² +1 forms an AP?

1

(a)

Yes

(b)

Not

(c)

Cannot be determined

(d)

None of these

If in two \(\Delta A B C \text { and } \Delta P Q R\) \(\frac{A B}{Q R}=\frac{B C}{P R}=\frac{C A}{P Q}\), then

1

(a)

Δ PQR - Δ CAB

(b)

Δ PQR - Δ ABC

(c)

Δ CBA - Δ PQR

(d)

Δ BCA - Δ PQR

If in \(\Delta A B C \text { and } \Delta D E F, \frac{A B}{D E}=\frac{B C}{F D}\) then they will be similar, when

1

(a)

∠B = ∠E

(b)

∠A = ∠D

(c)

∠B = ∠D

(d)

∠A = ∠F

If Δ ABC - Δ POR with \(\frac{B C}{Q R}=\frac{1}{3}\) then \(\frac{\operatorname{ar}(\Delta P R Q)}{\operatorname{ar}(\Delta B C A)}\) is equal to

1

(a)

9

(b)

3

(c)

\(\frac{1}{3}\)

(d)

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

If sin A \(=\frac{1}{2}\) then the value of cot A is 

1

(a)

\(\sqrt{3}\)

(b)

\(\frac{1}{\sqrt{3}}\)

(c)

\(\frac{\sqrt{3}}{2}\)

(d)

1

If sin \(\theta=\frac{a}{b},\) then cos \(\theta\) is equal to

1

(a)

\(\frac{b}{\sqrt{b^{2}-a^{2}}}\)

(b)

\(\frac{b}{a}\)

(c)

\(\frac{\sqrt{b^{2}-a^{2}}}{b}\)

(d)

\(\frac{a}{\sqrt{b^{2}-a^{2}}}\)

A ladder, leaning against a wall, makes an angle of 60° with the horizontal. If the foot of the ladder is 9.5 m away from the wall. The length of the ladder is

1

(a)

10 m

(b)

16 m

(c)

18 m

(d)

19 m

In figure, if O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50° with PO, then \(\angle\)POQ is equal to

1

(a)

100°

(b)

80^o

(c)

90°

(d)

75°