If x = 1 is a root of equation x² – Kx + 5 = 0 then value of K is

1

(a)

5

(b)

6

(c)

4

(d)

-6

Solve 9x²= 36

1

(a)

±4

(b)

±6

(c)

2

(d)

±2

The roots of quadratic equation x² – 9 = 0 are

1

(a)

± 3

(b)

± 6

(c)

± 4

(d)

± 9

The roots of quadratic equation ax² + bx + c = 0 is given by

1

(a)

\(\frac { b\pm \sqrt { { b }^{ 2 }-4ac } }{ 2c } \)

(b)

\(\frac { -b\pm \sqrt { { b }^{ 2 }-4ac } }{ 2c } \)

(c)

\(\frac { b\pm \sqrt { { b }^{ 2 }-4ac } }{ 2c } \)

(d)

\(\frac { -b\pm \sqrt { { b }^{ 2 }-4ac } }{ 2c } \)

If 4 is a root of the equation x² + 3x + k = 0 , then k is

1

(a)

-12

(b)

12

(c)

28

(d)

-28

For what value(s) of k will the equation kx²-5x+k=0 have a repeated root?

1

(a)

5/2

(b)

3/2

(c)

-5/2

(d)

±5/2

If x = 1 is a common root of the equation x² + ax – 3 = 0 and bx² – 7x + 2 = 0 then ab =

1

(a)

-3

(b)

7

(c)

10

(d)

6

What is the sum of the first 20 whole numbers

1

(a)

190

(b)

200

(c)

100

(d)

140

The 8^th term of 117, 104, 91, 78, …….is.....

1

(a)

26

(b)

27

(c)

4

(d)

17

In an A.P. the two consecutive terms are (2n+3) and (2n+5). Find the common difference of the A.P

1

(a)

2

(b)

2n+2

(c)

2n+3

(d)

2n+1

The sum of 20 odd natural number is

1

(a)

400

(b)

100

(c)

210

(d)

420

Which term of the A.P. 1, 4, 7 … is 88?

1

(a)

35

(b)

26

(c)

27

(d)

30

 PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR=120°, then ∠OPQ is

1

(a)

60^o

(b)

30^o

(c)

90^o

(d)

45^o

If figure 1, O is the centre of a circle, PQ is a chord and PT is the tangent at P. If ∠POQ = 70o, then ∠TPQ is equal to

1

(a)

45^o

(b)

5^o

(c)

35^o

(d)

70^o

A line that intersects a circle in exactly one point is called a

1

(a)

Diameter

(b)

Tangent

(c)

Radius

(d)

Secant

Number of tangents from a point lying inside the circle is

1

(a)

None

(b)

Infinitely many

(c)

Two

(d)

One

A circle may have…….

1

(a)

Infinite tangents

(b)

No tangent

(c)

1 tangent

(d)

2 tangent

To construct a triangle similar to a given \(\triangle\)ABC with its sides 3/7  of the corresponding sides of \(\angle\)ABC, first draw a ray BX such that ∠CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then, locate points  on BX at equal distances and next step is to join

1

(a)

B₁₀ to C

(b)

B₃ to C

(c)

B₇ to C 

(d)

B₄ to C

 A line segment AB can be divided into ratio \(\sqrt { 4+3 } =\frac { 1 }{ \sqrt { 4+3 } } \) by locating a point C which divides AB in the ratio.

1

(a)

7:1

(b)

3:1

(c)

4:1

(d)

4:3

If four sides of a quadrilateral ABCD are tangential to a circle, then

1

(a)

AC + AD = BD + CD

(b)

AB + CD = BC + AD

(c)

AB + CD = AC + BC

(d)

AC + AD = BC + DB

In the triangles PQR and NLM, angle M will be

1

(a)

70°

(b)

40°

(c)

60°

(d)

50°

In the given figure, AC: CB is

1

(a)

4:3

(b)

3:2

(c)

2:3

(d)

3:4

Consider a constellation of 3 stars A, B and C forming a right triangle with angle ABC = 90° and angle BAC = 30° . If the distance between star A and B is 3√3 x 1013 km, then how much time does light take to travel from star C to B with a speed of 3 x 108 m/s?

1

(a)

√3 x 10⁵ sec

(b)

10⁴ sec

(c)

√3 x 10⁴ sec

(d)

10⁵ sec

The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it is 60°. Find the height of the tower.

1

(a)

20

(b)

40√3

(c)

20√3

(d)

40

Consider a ship with a right triangular mast. If the base of the mast is 10 m long, and the angle that the mast makes with the base is 60°, then what area of cloth is used to make the mast?

1

(a)

50 (√3 + 1) m²

(b)

50 √3 m²

(c)

50 m²

(d)

100 m²

The angle of depression from the top of a tower 12 m high, at a point on the ground is 30°. The distance of the point from the top of the tower is:

1

(a)

12√3 m

(b)

24 m

(c)

6 m

(d)

12 m

In the given figure, the respective values of y and x are

1

(a)

60° and 30°

(b)

45° and 60°

(c)

60° and 45°

(d)

30° and 45°

A bag has 9 red, 7 green and 4 blue balls. A student randomly selects a ball from the bag. The probability of not getting a blue ball is

1

(a)

9/20

(b)

1/5

(c)

7/20

(d)

4/5

In a throw of a die, the probability of getting a prime number is

1

(a)

6

(b)

1/2

(c)

3/2

(d)

3/4

The probability that a leap year has 53 Sundays is

1

(a)

3/7

(b)

2/7

(c)

1/7

(d)

4/7

If a digit is chosen at random from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 then the probability that it is odd is

1

(a)

1/9

(b)

2/3

(c)

4/9

(d)

5/9

Cards each marked with one of the numbers 4, 5, 6 …20 are placed in a box and mixed thoroughly. One card is drawn at random from the box. The probability of getting an even prime number is

1

(a)

1

(b)

Zero

(c)

2

(d)

4

An urn contains lottery tickets numbered from 1 to 100. If a ticket is selected at random, then the probability that it is a perfect square is

1

(a)

0.01

(b)

0.08

(c)

0.09

(d)

0.1

If the probability of an occurrence of an event A is denoted by P(A), then the range of P(A) is

1

(a)

0

(b)

0≤P(A)<1

(c)

1

(d)

0≤P(A) ≤1

What are the total outcomes when we throw three coins?

1

(a)

4

(b)

5

(c)

8

(d)

7

Find the value of p for which the points (–5, 1), (1, p) and (4, –2) are collinear.

1

(a)

-3

(b)

-2

(c)

0

(d)

-1

The coordinates of the centre of a circle passing through (1, 2), (3, – 4) and (5, – 6) is:

1

(a)

(11, – 2)

(b)

(-2, 11)

(c)

(11, 2)

(d)

(2, 11)

The perimeter of the triangle formed by the points A(0,0), B(1,0) and C(0,1) is

1

(a)

√2 + 1

(b)

1 ± √2

(c)

2 + √2

(d)

3

The point on x-axis which is equidistant from (5,9) and (-4,6) is

1

(a)

(3,0)

(b)

(1,0)

(c)

(2,0)

(d)

(4,1)

The distance of the point P(6,-6) from the origin is equal to

1

(a)

3 √4 units

(b)

8 units

(c)

6 √2 units

(d)

3 units

The ratio of radii of two circles is in the ratio of 1:5. Calculate the ratio of their perimeters

1

(a)

1:8

(b)

1:2

(c)

1:6

(d)

1:5

In the given figure, ABCPA is a quadrant of a circle of radius 14cm. With AC as diameter, a semi-circle is drawn. Then the area of the shaded region will be

1

(a)

72 cm²

(b)

98 cm²

(c)

102 cm²

(d)

35 cm²

A garden roller has a circumference of 4 m. The number of revolutions it makes in moving 40 metres are:

1

(a)

10

(b)

12

(c)

8

(d)

16

The length of a minute hand of a wall clock is 7 cm. What is the area swept by it is 30 minutes?

1

(a)

2.308

(b)

3.608

(c)

-3.208

(d)

3.208

The shaded part of the circle in the given figure represents a

1

(a)

Segment

(b)

semi-circle

(c)

Sector

(d)

Chord

Total surface area of a cylinder is equal to

1

(a)

πr + 2πrh

(b)

2πrh

(c)

πr²h

(d)

2πr(h + r)

If two identical solid cubes each of volume 64 cm3 are joined end to end, then the total surface area of the resulting cuboid is:

1

(a)

210 cm²

(b)

200 cm²

(c)

160 cm²

(d)

180 cm²

If H and h be the heights of two cylinders, then the ratio of curved surface areas of two cylinders with equal radii is

1

(a)

√H : 2√h

(b)

H : h

(c)

H² : h²

(d)

2H : h

There are two cones. The curved surface area of one is twice that of the other. The slant height of the latter is twice that of the former. The ratio of their radii is

1

(a)

4:1

(b)

1:3

(c)

2:5

(d)

2:1

The total surface area of an open pipe of length 50 cm, external diameter 20 cm and internal diameter 6 cm will be

1

(a)

4657.71 cm²

(b)

4757.71 cm²

(c)

4677.75 cm²

(d)

4557.81 cm²

A petrol tank is a cylinder of base diameter 21cm and length 18cm fitted with conical ends each of axis length 9cm. Determine the capacity of the tank

1

(a)

8316cm³

(b)

9456 cm³

(c)

10160 cm³

(d)

None of the above

The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?

1

(a)

 2 ,21,11

(b)

1,10,19

(c)

-1 ,8,17

(d)

2 ,11,20

From among a minimum of how many integers can you say that one is divisible by 3?

1

(a)

1

(b)

4

(c)

3

(d)

5

 A number of the form 4ⁿ cannot be divisible by

1

(a)

10

(b)

4

(c)

2

(d)

All the above

The H.C.F.of 145 and 220 is

1

(a)

11

(b)

15

(c)

10

(d)

5

The reciprocal of an irrational number is

1

(a)

An integer

(b)

Rational

(c)

Irrational

(d)

None of these

Given that the H.C.F. of 35 and 49 is 7, what is their LCM?

1

(a)

265

(b)

245

(c)

195

(d)

225

There is a circular path around a sport field. Sonia takes 18min to drive one around of the field, while Ravi takes 12min for the same. Suppose they both start at the same point at the same time, and go in the same direction, after how minutes will they meet again at the starting point?

1

(a)

3

(b)

36

(c)

6

(d)

18

The decimal expansion of 21/24 will terminate after how many places of decimal?

1

(a)

2

(b)

3

(c)

1

(d)

4

The largest number which divides 70 and 125 leaving remainders 5 and 8, respectively is

1

(a)

1750

(b)

15

(c)

63

(d)

13

If 1 is a zero of the polynomial p(a)=x²a²-2xa+3x-2 . Then x=

1

(a)

-1, -2

(b)

2, 1

(c)

2,-1

(d)

-2, 1

If the degree of the dividend is 5 and the degree of the divisor is 3, then the degree of the quotient will be

1

(a)

0

(b)

2

(c)

1

(d)

-2

The graph of y = p(x) is given below. The number of zeroes of p(x) are

1

(a)

3

(b)

0

(c)

4

(d)

2

 α and β are the zeroes of the polynomial 5x² – 7x + 2, then sum of their reciprocals is::

1

(a)

7/2

(b)

14/25

(c)

7/5

(d)

2/5

The zero of the polynomial represented by the given graph

1

(a)

Does not exist

(b)

Is 3

(c)

Is y = 3

(d)

Is 0

A quadratic polynomial____

1

(a)

Is always a binomial

(b)

Is always a Trinomial

(c)

May be a monomial, binomial or a trinomial

(d)

Is always a Monomial

The number of zeroes for the polynomial y = p (x) from the given graph is :

1

(a)

2

(b)

3

(c)

0

(d)

1

If two of the zeroes of the polynomial f (x) = x⁴ – 3x³ – x² + 9x – 6 are -√3 and √3 then all the zeroes are

1

(a)

√3, -√3, 1 ,3

(b)

-1, 4, √3, -√3

(c)

√3, -√3, 2, 3

(d)

√3, -√3, 1, 2

A fraction becomes when subtracted from the numerator and it becomes . when 8 is added to its denominator. Find the fraction

1

(a)

4/12

(b)

  3/13

(c)

5/12

(d)

11/7

The number of solutions of the pair of linear equations x + 2y – 8 = 0 and 2x + 4y = 16 are

1

(a)

Infinitely many

(b)

1

(c)

0

(d)

None

A system of simultaneous linear equations has infinitely many solutions if two lines:

1

(a)

intersect at one point

(b)

are parallel

(c)

intersect at two points

(d)

are coincident

Five liters of 31.2% acid solution has to be made out of a 40% and a 18% acid solution. How many litres of each of the 40% and 18% solution need to be mixed?

1

(a)

2 and 3

(b)

5 and 4

(c)

4 and 5

(d)

3 and 2

The graph below represents equations that have

1

(a)

unique solution

(b)

solution as 0

(c)

infinite solution

(d)

no solution

In \(\triangle ABC\), if \(AB=6\sqrt { 3 } \) cm, AC = 12 cm and BC = 6 cm. Then, \(\angle B\) is

1

(a)

120°

(b)

60°

(c)

90°

(d)

45°

Given two triangles ABC and DEF ,AG and DH are perpendiculars on BC and EF respectively ∠B = ∠E , AB=5,DE=8 .What is \(\frac { AG }{ DH } =?\)

1

(a)

5/8

(b)

2/5

(c)

3/5

(d)

3/8

Which of the following cannot be the sides a right triangle?

1

(a)

400mm, 300 mm, 500mm

(b)

9 cm, 15 cm, 12 cm

(c)

2 cm, 1 cm, √5 cm

(d)

9 cm, 5 cm, 7cm

In a triangle ABC, AC= √180 ,AB=6 ,BC=12 .What is ∠B = ?

1

(a)

90°

(b)

30°

(c)

45°

(d)

60°

Which of the following is a Pythagorean triplet?

1

(a)

(36,18,43)

(b)

(15,20,25)

(c)

(3,12,13)

(d)

(24,25,26)

Two friends A and B start from the same point in the Eastern and Northern directions at the same time. How far are they from each other when A has travelled 5 km and B has travelled 12 km. distance?

1

(a)

8 km

(b)

17 km

(c)

10 km

(d)

13 km

In figure, ΔABC ~ ΔPQR

1

(a)

2 + √3

(b)

4 + √3

(c)

3 + 4√3

(d)

4 + 3√3

In an equilateral triangle ABC, if AD ⊥ BC. Then

1

(a)

3AB² = 4AD²

(b)

2AB² = 3AD²

(c)

3AB² = 2AD²

(d)

4AB² = 3AD²

In two triangles ABC and PQR,Given that ∠A = ∠R and ∠B = ∠Q, which of the following is true?

1

(a)

ΔABC ~ ΔQRP

(b)

ΔABC ~ ΔPQR

(c)

ΔABC ~ ΔPRQ

(d)

ΔABC ~ ΔRQP

In the adjoining figure, PQ||BC , the what could be the values of AQ & QC respectively

1

(a)

3 cm and 6 cm

(b)

2 cm and 6 cm

(c)

3 cm and 4 cm

(d)

1 cm and 6 cm

Choose the correct option. Justify your choice.
\((\sec { A } +\tan { A } )(1-\sin { A } )\) is equal to

1

(a)

\(\sec { A } \)

(b)

sin A

(c)

cosec A

(d)

cos A

The square root  \(\frac { 1+sin\quad A }{ 1-sin\quad A } \)=

1

(a)

cot A – cosec A

(b)

sec A – tan A

(c)

sec A + tan A

(d)

cot A + cosec A

If cos (∝+β)=0 , then sin (∝-β) can be reduced to

1

(a)

cos β

(b)

sin α

(c)

sin 2α

(d)

cos 2β

In given figure, if RP = 13 cm, QR = 5 cm and PS = 14 cm, then, tan S =In given figure, if RP = 13 cm, QR = 5 cm and PS = 14 cm, then, tan S =

1

(a)

4/3

(b)

9/4

(c)

8/4

(d)

5/4

If cos (40° + A) = sin 30°, the value of A is   

1

(a)

40°

(b)

30°

(c)

60°

(d)

20°

If \(\frac { x }{ a } cos\theta +\frac { y }{ b } sin\theta =1\quad and\quad \frac { x }{ a } sin\theta -\frac { y }{ b } cos\theta \quad then\quad \left( \frac { x }{ a } \right) ^{ 2 }+\left( \frac { y }{ b } \right) ^{ 2 }=\)

1

(a)

12

(b)

3

(c)

2

(d)

1

The value of \(\frac { cos30^{ o }+sin60^{ o } }{ 1+cos60^{ o }+sin{ 30 }^{ o } } \)is

1

(a)

3/2

(b)

√3/2

(c)

1

(d)

2/√3

The mean of the following data is: 45, 35, 20, 15, 25, 40

1

(a)

15

(b)

25

(c)

35

(d)

30

Which measure of central tendency is obtained graphically by the point of intersection of less than and more than o gives

1

(a)

Arithmetic mean

(b)

Geometric mean

(c)

Mode

(d)

Median

A batsman in his 12th innings makes a score of 63 runs and thereby increases his average score by 2. His average score after 12th

1

(a)

41

(b)

60

(c)

51

(d)

45

The median of the following data is:

Rent (in Rs)	15-25	25-35	35-45	45-55	55-65	65-75	75-85	85-95
No. of houses	8	10	15	25	40	20	15	7

1

(a)

65

(b)

45

(c)

50

(d)

58

For the following distribution the differences in the upper limit of median and modal class is

C1	0-10	10-20	20-30	30-40	40-50
F	2	5	7	5	2

1

(a)

40

(b)

10

(c)

0

(d)

20

Median of the data given below will lie in the class

Height(in cm)	frequency
Below 140	4
140-145	7
145-150	18
150-155	11
155-160	6
160-165	5

1

(a)

150-155

(b)

140-145

(c)

160-165

(d)

145-150

Mode is not affected by

1

(a)

Maximum value

(b)

Minimum value

(c)

Extreme values

(d)

All of the above

If the mean and the median are 25.41 and 26.5 respectively. then the mode is

1

(a)

29

(b)

28.68

(c)

25.6

(d)

28

The mean of a data set with 12 observations is calculated as 19.25. If one more value is included in the data, then for the new data with 13 observations, mean becomes 20. Value of this 13th observation is

1

(a)

30

(b)

28

(c)

31

(d)

29

If the mean of the following distribution is 6, find the value of ‘p’.

x	2	4	6	10	p+6
f	3	2	3	1	2

1

(a)

7

(b)

12

(c)

8

(d)

6