COMMON ASSESSMENT EXAM 2025 (MOCK TEST)

1.

2. Find the value of

3. If the point P(2,1) lies on the line segment joining points A(4,2) and B(8,4), then

4. If for an A.P. a5 = a10 = 71, then a15 is

5. The radius of a sphere is 10 cm. If its radius is increased by 1 cm, the volume of the sphere is increased by

6. A bicycle wheel makes 5000 revolutions in moving 11 km. Find the diameter of the wheel.

7. A vertical pole of length 6 m casts a shadow 4 m long on the ground, and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

8. In figure, there are two concentric circles, with centre O and of radii 5 cm and 3 cm. From an external point P, tangent PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP.

9. Find c if the system of equation cx + 3y + (3 – c) = 0; 12x + cy – c = 0 has infinitely many solutions?

10. The ratio of the incomes of two persons, A and B, is 3 : 4 and the ratio of their expenditures is 5 : 7. If their savings are ₹ 15,000 annually, find the annual income of A

11. The roots of the equation 9x² – bx + 81 = 0 will be equal, if the value of b is

12. The average of all 3-digit terms in the arithmetic progression 38, 55, 72, …, is

13. For some real numbers a and b, the system of equations x + y = 4 and (a+b)x + (b² – 15)y = 8b has infinitely many solutions for x and y. Then the maximum possible value of ab is:

14. Let both the series a₁, a₂, a₃… and b₁, b₂, b₃… be in arithmetic progression such that the common differences of both the series are prime numbers. If a5 = b9 , a19 = b19  ​and b2 = 0, then a11 equals…

15. For some constant real numbers a, b and c, consider the following system of linear equations in x and y:
ax + 5y = 3
4x – by = c
A necessary condition for the system to have no solution for (x,y) is :

16. If x and y are real numbers such that 4x² + 4y² – 4xy -6y + 3 = 0, then the value of (4x + 5y) is

17. One-fourth of a herd of cows is in the forest. Twice the square root of the herd has gone to the mountains, and the remaining 15 are on the banks of a river. The total number of cows is

18. From a well suffled pack of playing cards, black jackes, black kings and black aces are removed. A card is then drawn from the pack. Find the probability of not getting a diamond card

19. If area of the sector of a circle bounded by an arc of length 5π cm is equal to 20 π cm², then its radius is :

20. The tops of two towers of heights x and y, standing on a level ground subtend angles of 300 and 600 , respectively at the centre of the line joining their feet. Then, x:y is:

21. Two pipes running together can fill a cistern in 3 and 1/13 minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which each pipe would fill the cistern.

22. ABCD is a cyclic quadrilateral in which BC is parallel to AD. ∠ADC = 110°and ∠BAC = 50°, then find ∠DAC

23. A dealer sells a toy for RS 39 and gains as much percent as the cost price of the toy. The cost price of the radio is:

24. PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T (adjoining figure). Find the length TP.

25. In ΔABC and ΔDEF, < B =

26. If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?

27. The minute hand of a clock is √21 cm long. Find the area described by the minute hand on the face of the clock between 7.00 am and 7.05 am.

28. The ratio of the areas of the incircle and circumcircle of a square is

29. If A(1, 3), B(4, 3) and C(6, 6) are three vertices of parallelogram ABCD, its area will be

30. The nth term of the following series (1×3)+(3×5)+(5×7)+(7×9)+……. will be

31. A fraction becomes 1/3 when 2 is subtracted from the numerator, and it becomes 1/2 when 1 is subtracted from the denominator. Find the fraction.

32. Find the value of k such that the polynomial x² – (k + 6)x + 2(2k – 1) has the sum of its zeros equal to half of their product.

33. If the angle of the depression of an object from a 50 m high tower is 30°, then the distance of the object from the tower is

34. For what value of n, nth terms of the two Arithmetic Progressions (A.P.’s) 63, 65, 67,… and 3, 10, 17,…. will be equal ?

35. To place a pole vertical on the ground a wire of length 26 m is attached to it at a point 10 m away from its foot. Then what will be the length of pole

36. For any two similar triangles the ratio of their sides is equal to the ratio of

37. In the figure, O is the center of the circle then the angle X is

38. Three bulbs red, green and yellow flash at intervals of 80 seconds, 90 seconds and 110 seconds. All three flash together at 8:00 am. At what time will the three bulbs flash altogether again?

39. In the adjoining figure PA= PB and PC:CD = 1:7. If PD = 16 cm, then PB =

40. If A is an acute angle and tan A+ cotA = 2, then the value of sin³A + cos³A is

41. In the given figure, ∠T and ∠B are right angles. If the length of AT, BC and AS (in centimeters) are 15, 16, and 17 respectively, then the length of TC (in centimeters) is:

42. If α and β are the zeros of the polynomial f(x) = x² −p(x+1) -c ; such (α+1) (β+1) =0, then c=

43. x and y are 2 different digits. If the sum of the two digit numbers formed by using both the digits is a perfect square, then value of x+y is

44. Curved surface areas of two hemispheres are in the ratio 9:4. The ratio of their volumes is

45. ABCD is a rectangle whose three vertices are B(4, 0), C(4, 3) and D(0, 3). The length of one of its diagonals is

46. A: Astigmatism usually is caused by an irregularly shaped cornea.
B: Rainbow is the natural phenomenon in which dispersion takes place.

47. Which of the following statements is true?

48. A concave mirror of focal length 20 cm forms an image having twice the size of object.
For the virtual position of object, the position of object will be at

49. A rectangular coil of copper wire is rotated in a magnetic field. The direction of induced current changes once in each:

50. The force experienced by a current-carrying conductor placed in a magnetic field is the largest when the angle between the conductor and the magnetic field is:

51. Safar cannot see through the fog while driving, because

52. A TV set consumes an electric power of 230 watts and runs on a 230 volts mains supply. The correct fuse for this TV set is:

53. Two resistances 10 Ω and 3 Ω are connected in parallel across a battery. If there is a current of 0.2 A in 10 resistors, the voltage supplied by the battery is:

54. The mains power supply of a house is through a 2A fuse. How many 50W bulbs can be used in this house at the normal voltage?

55. If the current I through a resistor is increased by 100% (assume that temperature remains unchanged), the increase in power dissipated will be:

56. The front face of a circular loop of a wire is the North Pole, the direction of current in this face of the loop will be:

57. A________________ consists of a piece of wire made of metal or an alloy (37% lead, 63% tin).

58. The focal length of the eye lens increases when eye muscles

59. A Person got his eye tested. The optician‟s prescription for the
spectacles was: Left eye: −3 D
Right eye: −3.50 D
The person is having a defect of vision called:

60. The refractive index of flint glass is 1.65 and that for alcohol is 1.36 with respect to air. What is the refractive index of the flint glass with respect to alcohol?

61. Which of the following oxide(s) of iron would be obtained on prolonged reaction of iron with steam?

62. Find out the exothermic processes from the following reactions:

(i) Reaction of water with quicklime

(ii) Dilution of an acid

(iii) Evaporation of water

(iv) Sublimation of camphor (crystals)

63. A clean aluminium foil was placed in an aqueous solution of zinc sulphate. When the aluminium foil was taken out of the zinc sulphate solution after 15 minutes, its surface was found to be coated with a silvery grey deposit. From the above observation it can be concluded that:

64. Which of the metals are refined by electrolytic refining?

(i) Au                       (ii) Cu                          (iii) Na                    (iv) K

65. An element X reacts with hydrogen, when heated, to form a covalent hydride H₂X. If H₂X has the smell of rotten eggs, the element X is likely to be

66. Which of the following hydrocarbons undergo addition reaction?

67. A white colour powder’ A’ used in glass and paper industry and removes permanent hardness of water. The compound ‘ A’ is : .

68. Mixing of acid or base with water results in ……… in the concentration of ions per unit volume :

69. Barium chloride on reacting with ammonium sulphate forms barium sulphate and ammonium chloride. Which of the following correctly represents the type of the reaction involved?
(A) Displacement reaction
(B) Precipitation reaction
(C) Combination reaction
(D) Double displacement reaction

70. In the double displacement reaction between aqueous potassium iodide and aqueous lead nitrate, a yellow precipitate of lead iodide is formed. While performing the activity if lead nitrate is not available, which of the given can be used in place of lead nitrate?

71. A substance X, an oxide of a group 2 element, is used intensively in the cement industry. This element is present in bones also. On treatment with water, it forms a solution which turns red litmus blue. Identify X.

72. A student took four metals P, Q, R and S and carried out different experiments to study the properties of
metals. Some of the observations were:
 All metals could not be cut with a knife except metal R
 Metal P combined with oxygen to form an oxide M2O3 which reacted with both acids and bases.
 Reaction with water-
P-Did not react either with cold or hot water but reacted with steam
Q-Reacted with hot water and the metal started floating
R-Reacted violently with cold water
S-Did not react with water at all.
Based on the above observations, answer the following

The increasing order of the reactivity of the four metals is:

73. The atomic numbers of four elements A, B, C and D are 6, 8, 10 and 12 respectively. The two elements which can react to form ionic compounds are

74. Which one of the following salts does not contain water of crystallisation?

75. Which of the following statements is not true:
(i) Alkalies are water soluble bases but all bases are not alkalies.
(ii) Base turns red litmus blue and phenolphthalein solution pink.
(iii) The aqueous solution of bases conduct electricity.
(iv) Bases react with metal oxides to form salt and hydrogen gas.

76. Posture and balance of the body is controlled by

77. The longest fibre on the cell body of a neuron is called

78. How does a mutation in a gene affect protein production?

79. Response of plant roots towards water is called:

80. In artificial kidney, which substance passes from the blood to the dialysis fluid?

81. The main function of abscisic acid in plants is

82. A student sets up an experiment to study the role of enzymes in the digestion of food.

In which test tube, the digestion of protein will occur?

83. Which is not true about haemoglobin?

84. Which of the following endocrine glands does not exist in pairs?

85. Rihaan can use any source of energy for cooking, but he wants to avoid the production of smoke from the source. Which of these sources should he use for cooking?

86. The surprise products formed in the experiment conducted by Miller and Urey were:

87. Which of the following is a pair of analogous organs?

88. How will information travel within a neuron?

89. Choose the function of pancreatic juice from following :

90. The enzyme responsible for the digestion of proteins in the small intestine is: