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Linear Equation in two variables

1. In a group of goats and hens, the total number of legs is 12 more than twice the total number of heads.

The number of goats is

(a) 8 (b) 6

(c) 2 (d)cannot be determined

2. If 2a – 3b = 1 and 5a + 2b = 50, then what is the value of a – b?

(a) 10 (b) 6 (c) (d) 3

3. If (1, 4) is the point of intersection of the lines 2x + by = 6 and 3y = 8 + ax then find the value of a – b ?

(a) 2 (b) 3 (c) 4 (d) -3

4. Find the minimum value of x 3 11− + .

(a) 8 (b) 11 (c) 0 (d) -8

5. Find the maximum value of 23 2x 3− − is

(a) 20 (b) 26 (c) 17 (d) 23

6. If (a + b, a – b) is the solution of the equations 3x + 2y = 20 and 4x – 5y = 42, then the value of b.

(a) 8 (b) – 2 (c) – 4 (d) 5

7. The solution set of 2 3

x y+ =2 and

3 420

x y− = is

(a) (4, - 2) (b) 1 1

,2 4

−

(c) (2, – 4) (d) 1 1

,4 2

−

8. If we add 1 to the numerator and subtract 1 from the denominator a fraction because 1, It also

becomes 1

2 if we add 1 to the denominator. Then the sum of the numerator and denominator of the

fraction is

(a) 7 (b) 8 (c) 2 (d) 11

9. If 3 x y

x 2y2 4 2

+ = − =1, then x – y =

(a) 1 (b) 3 (c) 2 (d) 11

10. The product of a number and 72 exceeds the product of the number and 27 by 360. Find the number.

(a) 12 (b) 7 (c) 8 (d) 11

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11. In the figure given below, two isosceles right angled triangles, DEF and HGI are on the same base

and DH is parallel to FI . If DE = GH = 9 cm and DH = 20 cm, then the area of the quadrilateral FEGI is

(a) 99cm2 (b) 40.5 cm

12. In the figure given below, PQRS is a rhombus, SQ and PR are the diagonals of the rhombus intersecting

at O. If angle OPQ = 350, then find the value of angle ORS + angle OQP.

(a) 900 (b) 1800

13. The bisectors of two adjacent angles in a parallelogram meet at a point P inside the parallelogram. The

angle by these bisectors at a point is _________________ .

(a) 1800 (b) 900

14. In the given rectangle ABCDD, the sum

in AB such that OE is perpendicular to

(a) 24 cm, 10 cm (b) 12 cm, 10 cm

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m S.C.O.- 320, Sector 40–D, CHD. Phone: 9815527721, 4617721

In the figure given below, two isosceles right angled triangles, DEF and HGI are on the same base

. If DE = GH = 9 cm and DH = 20 cm, then the area of the quadrilateral FEGI is

(b) 40.5 cm2 (c) 81 cm2

ow, PQRS is a rhombus, SQ and PR are the diagonals of the rhombus intersecting

, then find the value of angle ORS + angle OQP.

(c) 1350

The bisectors of two adjacent angles in a parallelogram meet at a point P inside the parallelogram. The

angle by these bisectors at a point is _________________ .

(c) 450

In the given rectangle ABCDD, the sum of the lengths of two diagonals is equal to 52 cm and E is a point

is perpendicular to AB . Find the lengths of the sides of the rectangle, if OE = 5 cm.

(b) 12 cm, 10 cm (c) 24 cm, 5 cm

edical and Non - Medical Classes

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In the figure given below, two isosceles right angled triangles, DEF and HGI are on the same base DH

. If DE = GH = 9 cm and DH = 20 cm, then the area of the quadrilateral FEGI is

(d) 180 cm2

ow, PQRS is a rhombus, SQ and PR are the diagonals of the rhombus intersecting

(d) 450

The bisectors of two adjacent angles in a parallelogram meet at a point P inside the parallelogram. The

(d) none of these

of the lengths of two diagonals is equal to 52 cm and E is a point

Find the lengths of the sides of the rectangle, if OE = 5 cm.

(d) 12 cm, 15 cm



15. In the shown figure (not to scale), AD bisects

then which of the following is the longest ?

(a) AB (b) AD

16. In the given figure, AB DE� and area of the parallelogram ABFD is 24 cm

AGB and ∆ AEB.

(a) 8 cm2 (b) 12 cm2

17. In fig. AD and BE are medians of ∆

(a) 1

CF AC2

= (b) 1

CF AC4

=

18. In a ABC∆ , E and F are the mid-points of AC and AB respectively. The altitude of AP to BC intersects

FE at Q then

(a) AQ = QP (b) AQ = 1

2



In the shown figure (not to scale), AD bisects ∠ BAC. If ∠ BAD = 450 and ∆ ABC is inscribed in a circle,

then which of the following is the longest ?

(c) AC

and area of the parallelogram ABFD is 24 cm2. Find the areas of

(c) 10 cm2

ABC∆ and BE�DF. then.

1CF AC

4 (c)

1CF AC

8= (d) CF 4AC

points of AC and AB respectively. The altitude of AP to BC intersects

1

2 QP (c) AQ = 2 QP


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ABC is inscribed in a circle,

(d) BC

. Find the areas of ∆ AFB, ∆

(d) 14 cm2

CF 4AC=

points of AC and AB respectively. The altitude of AP to BC intersects

(d) AQ = 1

4QP



19. In the fig, triangle ABC is right-angled at B. Given that AB = 9 cm, AC = 15 cm and D, E are the mid

points of the sides AB and AC respectively, calculate The length of BC

(a) 11cm (b) 12cm

20. In the shown figure (not to scale), ABC is an isosceles triangle in which AB = AC. AEDC is a

parallelogram. If ∠ CDF = 700 and

(a) 300 (b) 400

21. If a planar region formed by A figure R is made up of two non

figure R1 and R2, then

(a) ar (R) ≥ ar (R1) + ar (R2)

(c) ar (R) < ar (R1) + ar (R2)

22. ABCD is a quadrilateral and BD is one of its diagonals as sh

parallelogram and find its area.

(a) 10 sq. cm2 (b) 11 sq. cm

23. The rhombus ABCD having diagonal AC and BD then the area of rhombus is

(a) 1

2(AC × BD) (b) (AC × BD)



angled at B. Given that AB = 9 cm, AC = 15 cm and D, E are the mid

points of the sides AB and AC respectively, calculate The length of BC

(c) 13 cm

In the shown figure (not to scale), ABC is an isosceles triangle in which AB = AC. AEDC is a

and ∠ BEF = 1000, then find ∠ FBA.

(c) 500

If a planar region formed by A figure R is made up of two non-overlapping planar reason formed by

(b) ar (R) > ar (R1) + ar (R2)

(d) ar (R) = ar (R1) + ar (R2)

ABCD is a quadrilateral and BD is one of its diagonals as shown in fig. Show that ABCD is a

(b) 11 sq. cm2 (c) 12 sq. cm2

The rhombus ABCD having diagonal AC and BD then the area of rhombus is

(b) (AC × BD) (c) 2 × (AC × BD)


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angled at B. Given that AB = 9 cm, AC = 15 cm and D, E are the mid-

(d) 14 cm

In the shown figure (not to scale), ABC is an isosceles triangle in which AB = AC. AEDC is a

(d) 800

overlapping planar reason formed by

own in fig. Show that ABCD is a

(d) 13 sq. cm2

(d) 1

4(AC × BD)



24. In the given figure, the area of trapezium ABCD is

(a) 36 cm2 (b) 20 cm2

25. If ar (parallelogram ABCD) = 25 cm

x cm2, then value of x is

(a) 25 cm2 (b) 12.5 cm

26. In the given figure, find x

(a) 24 cm (b) 26 cm

27. In a parallelogram ABCD, P is a point in the interior of parallelogram ABCD. Also or (parallelogram

ABCD) = 18 cm2. Then ar ( ∆ APD) + ar (

(a) 9 cm2 (b) 12 cm2

28. In the given figure, ar( ∆ ACB) = ar (

(a) CO = OD (b) CO > OD

29. D and E are the points on the sides AB and AC respectively of a

is 15 sq. cm, then ar ( ∆ EBC) is

(a) 30 sq. cm (b) 7.5 sq. cm

30. ABC is triangle. D is a point on AB such that AD =

Then

(a) DE = 1

2 BC. (b) DE =

1

4



In the given figure, the area of trapezium ABCD is

(c) 48 cm2

If ar (parallelogram ABCD) = 25 cm2 and on the same base CD a ∆ BCD is given such that ar (

(b) 12.5 cm2 (c) 12.5 cm2

(c) 6 cm

point in the interior of parallelogram ABCD. Also or (parallelogram

APD) + ar ( ∆ CPB) is

(c) 18 cm2

ACB) = ar ( ∆ ADB), then

(b) CO > OD (c) CO < OD

D and E are the points on the sides AB and AC respectively of a ∆ ABC such that DE

(b) 7.5 sq. cm (c) 15 sq. cm

ABC is triangle. D is a point on AB such that AD = 1

4AB and E is a point on AC such that AE =

1

4 BC (c) DE =

1

8 BC.


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(d) 60 cm2

BCD is given such that ar ( ∆ BCD) =

(d) 50 cm2

(d) 8 cm

point in the interior of parallelogram ABCD. Also or (parallelogram

(d) 15 cm2

(d) CO ≤ OD

ABC such that DE �BC. If ar ( ∆ DBC)

(d) 60 sq. cm

AB and E is a point on AC such that AE = 1

4 AC.

(d) DE = 1

16 BC



1. With the increase in the density of a fluid the upthrust experienced by a body immersed in it.

(a) decreases (b) increases

2. A solid piece of lead experiences certain upthrust. The lead piece is then shaped into a hollow cube

and placed in the same liquid. The upthrust acting on it:

(a) increases (b) decreases

3. A glass stopper suspended from the hook of a spring balance and immersed completely in water

reads W gf. If the same stopper is immersed in alcohol (density 0.80 g cm

spring balance will be :

(a) less than Wgf (b) more than Wgf

4. Density of mercury is 13600 kgm-3

(a) 13600 (b)1360

5. Sea water of density 1040 kg m-3

water is

(a) 30 m (b)60 m

6. What change should be effected in the velocity of a body to maintain the same kinetic energy if it’s mass is

increased 4 times?

(a) doubled (b) halved

7. Two bodies A and B of mass 4kg and 16kg respectively. The velocity of B is twice the velocity of A the

ratio of K.E. (A: B) is

(a) 1:4 (b) 4: 1

8. A cricket ball is projected vertically upward such that it returns back to the thrower. The

kinetic energy with time is best represented by :

9. Two bodies A and B of mass 1 kg and 4 kg respectively have equal linear momentum. T

their kinetic energies is

(a) 1 : 4 (b) 4: 1

10. A girl of mass 50 kg runs up a flight of 40 stairs, each measuring 20 cm, in 50 seconds.

power of the girl.

(a) 40W (b) 5OW



Based on floatation

With the increase in the density of a fluid the upthrust experienced by a body immersed in it.

(b) increases (c) remains same

A solid piece of lead experiences certain upthrust. The lead piece is then shaped into a hollow cube

and placed in the same liquid. The upthrust acting on it:

(b) decreases (c) remains same

A glass stopper suspended from the hook of a spring balance and immersed completely in water

If the same stopper is immersed in alcohol (density 0.80 g cm-3), the reading on the

(b) more than Wgf (c) equal to Wgf

3. Its relative density is :

(c)136

exerts a pressure of 3.12 X 105 Pa at sea bed. The depth of the sea

(c) 15 m

What change should be effected in the velocity of a body to maintain the same kinetic energy if it’s mass is

(c) No change

4kg and 16kg respectively. The velocity of B is twice the velocity of A the

(c) 16:1

A cricket ball is projected vertically upward such that it returns back to the thrower. The

energy with time is best represented by :

Two bodies A and B of mass 1 kg and 4 kg respectively have equal linear momentum. T

(c) 1: 16 (d) 1: 2

A girl of mass 50 kg runs up a flight of 40 stairs, each measuring 20 cm, in 50 seconds.

(c) 20W


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With the increase in the density of a fluid the upthrust experienced by a body immersed in it.

(d) none of these

A solid piece of lead experiences certain upthrust. The lead piece is then shaped into a hollow cube

(d)none of these

A glass stopper suspended from the hook of a spring balance and immersed completely in water

), the reading on the

(d) none of these

(d)13.6

Pa at sea bed. The depth of the sea

(d) none of these

What change should be effected in the velocity of a body to maintain the same kinetic energy if it’s mass is

(d) quadrupled

4kg and 16kg respectively. The velocity of B is twice the velocity of A the

(d)l: 16

A cricket ball is projected vertically upward such that it returns back to the thrower. The variation in

Two bodies A and B of mass 1 kg and 4 kg respectively have equal linear momentum. The ratio of

(d) 1: 2

A girl of mass 50 kg runs up a flight of 40 stairs, each measuring 20 cm, in 50 seconds. Calculate the

(d) 80 W



Chemistry

1. In a compound such as water, the ratio of the mass of hydrogen to the mass of oxygen is always:

(a) 1:8 (b) 2 : 8 (c) 1 : 16 (d) 3: 16

2. Which of the following postulates of Dalton's atomic theory is/challenged by the next generation

scientists ?

(a) All matter is made of very tiny particles called atoms.

(b) Atoms are indivisible particles, which cannot be created or destroyed in a chemical reaction.

(c) Atoms combine in the ratio of small whole numbers to form compounds.

(d) Atoms of a given element are identical in mass and chemical properties.

3. One mole of H2O means :

(a) 18 g of H2O (b) 6.022 x 1023 molecules of H2O

(c) 180 g of H20 (d) 1.8 g of H2O

(i) Both (a) and (b) are correct (ii) Both (b) and (c) are correct

(iii) Only (a) is correct (iv) Both (c) and (d) are correct

4. A molecule can be defined as the :

(a) A group of two or more atoms that are chemically bonded together.

(b) A smallest particle of an element or a compound that is capable of an independent existence and

shows all the properties of that substance

(c) Substance which is formed by the combination of atoms of the same element or of different

elements. (d) All of these are correct

5. Which of the following will have maximum mass?

(a) 1022 molecules of H2O (b) 2 moles of NH3 (c) 1022 molecules of NH3 (d) 2 moles of H2O

6. The molecule having an atomicity of 4 is :

(a) Sulphur molecule (b) Ozone molecule (c) Phosphorus molecule (d) Methane molecule

7. The molecular formula of aluminium sulphate is :

(a) Al2(SO4)3 (b) AlSO4 (c) AI3(S04)2 (d) Al2(SO4)4

8. Which of the following represents 14 u?

(a) Mass of 1 hydrogen atom (b) Mass of C-14 atom

(c) Mass of O -16 atom (d) 1/12th of mass of C-14 atom

9. The chemical formula of the aluminium nitride is:

(a) AlN (b) Al3N2 (c) Al2N3 (d) AlN3

10. What weight of Sodium contains the same number of atoms as are present in 16 g of sulphur?

(a)llg (b)11.5g (c)12g (d)12.5g



Biology

1. Hair-like cilia or whip-like flagella for locomotion are present in kingdom :

(a) Monera (b) Protista (c) Fungi (d) Plantae

2. The branch of biology which deals with the principles and practice of classification of plants and

animals is :

(a) Taxonomy (b) Morphology (c) Ecology (d) Geology

3. The organisms having 'pores' all over the body and a canal system for bringing in food and oxygen

belongs to phylum:

(a) Coelenterata (b) Porifera (c) Annelida (d) Echinodermata

4. All organisms that are similar enough to breed and perpetuate are called :

(a) Genera (b) Phylum (c) Family (d) Species

5. The animals having blood-filled coelomic cavity belongs to phylum:

(a) Arthropoda (b) Mollusca (c) Annelida (d) Echinodermata

6. The animals having two chambered heart belongs to the class:

(a) Amphibia (b) Reptiiia (c) Pisces (d) Aves

7. The system of scientific naming was introduced by:

(a) Ernst Haeckel (b) Robert Whittaker (c) Carl Woese (d) Carolus Linnaeus

8. Plants that do not have well-differentiated body design fall into the group called :

(a) Pteridophyta (b) Thallophyta (c) Bryophyta (d) Gymnosperms

9. The common name for Fasciola hepatica and Taenia solium are :

(a) Liver fluke and Tape worm (b) Liver fluke and Round worm

(c) Liver fluke and Pin worm (d) Round worm and Tape worm

10. The phylum in which organisms contain pseudocoelom is:

(a) Platyheiminthes (b) Anneliada (c) Arthropoda (d) Nematoda

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