Q1
mcq
1 mark
If n is a natural number, then which of the following numbers ends with zero?
- A. (3 2)n
- B. (2 5)n
- C. (6 2)n
- D. (5 3)n
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Q2
mcq
1 mark
In a lottery, there are 5 prizes and 20 blanks. The probability of getting a prize is :
- A. 1/4
- B. 1/20
- C. 1/25
- D. 1/5
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Q3
mcq
1 mark
If 2x + 3y = 15 and 3x + 2y = 25, then the value of x + y is :
- A. 10
- B. 8
- C. -10
- D. -8
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Q4
mcq
1 mark
In the given figure, A = C, AB = 6 cm, AP = 12 cm, CP = 4 cm. Then length of CD is :
- A. 2 cm
- B. 6 cm
- C. 8 cm
- D. 18 cm
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Q5
mcq
1 mark
The sum of zeroes of the polynomial 2x^2 - 17 are given as :
- A. 17/2
- B. -17/2
- D. 1
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Q6
mcq
1 mark
If the area of the base of a cone is 51 cm^2 and its volume is 85 cm^3, then the vertical height of the cone is given as :
- A. 6/5 cm
- B. 3/5 cm
- C. 2/5 cm
- D. 5 cm
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Q7
mcq
1 mark
What is the length of the arc of the sector of a circle with radius 14 cm and of central angle 90 ?
- A. 22 cm
- B. 44 cm
- C. 88 cm
- D. 11 cm
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Q8
mcq
1 mark
The coordinates of the vertex A of a rectangle ABCD whose three vertices are given as B(0, 0), C(3, 0) and D(0, 4) are :
- A. (4, 0)
- B. (0, 3)
- C. (3, 4)
- D. (4, 3)
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Q9
mcq
The area of the triangle formed by the line x/a + y/b = 1 with the coordinate axes is :
- A. ab
- B. 1/2 ab
- C. 1/4 ab
- D. 2ab
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Q10
mcq
The hour-hand of a clock is 6 cm long. The angle swept by it between 7:20 a.m. and 7:55 a.m. is :
- A. 4/35
- B. 2/35
- C. 35
- D. 70
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Q11
mcq
The zeroes of the polynomial p(x) = x2 + 4x + 3 are given by :
- A. 1, 3
- B. -1, -3
- C. -1, 3
- D. 1, -3
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Q12
mcq
In the given figure, AB PQ. If AB = 6 cm, PQ = 2 cm and OB = 3 cm, then the length of OP is :
- A. 9 cm
- B. 3 cm
- C. 4 cm
- D. 1 cm
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Q13
mcq
In the given figure, the quadrilateral PQRS circumscribes a circle. Here PA + CS is equal to :
- A. QR
- B. PR
- C. PS
- D. PQ
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Q14
mcq
If one zero of the polynomial 6x2 + 37x (k 2) is reciprocal of the other, then what is the value of k ?
- A. 4
- B. 6
- C. -6
- D. -4
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Q15
mcq
If three coins are tossed simultaneously, what is the probability of getting at most one tail ?
- A. 3/8
- B. 4/8
- C. 5/8
- D. 7/8
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Q16
mcq
If the pair of equations 3x y + 8 = 0 and 6x ry + 16 = 0 represent coincident lines, the value of r is :
- A. 1/2
- B. -1/2
- C. 2
- D. -2
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Q17
mcq
If ABC PQR, A = 32 and R = 65 , then the measure of B is :
- A. 32
- B. 65
- C. 83
- D. 97
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Q18
mcq
Which of the following quadratic equations has sum of its roots as 4 ?
- A. 2x2 4x + 8 = 0
- B. x2 + 4x + 4 = 0
- C. 2x2 - 8x + 1 = 0
- D. 4x2 4x + 4 = 0
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Q19
mcq
1 mark
Assertion (A) : A tangent to a circle is perpendicular to the radius through the point of contact. Reason (R) : The lengths of tangents drawn from an external point to a circle are equal.
- A. Both A and R true and R is correct explanation
- B. Both A and R true but R is not correct explanation
- C. A is true but R is false
- D. A is false but R is true
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Q20
mcq
1 mark
Assertion (A) : The polynomial p(x) = x2 + 3x + 3 has two real zeroes. Reason (R): A quadratic polynomial can have at most two real zeroes.
- A. Both A and R true and R is correct explanation
- B. Both A and R true but R is not correct explanation
- C. A is true but R is false
- D. A is false but R is true
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Q21
short answer
2 marks
The length of the shadow of a tower on the plane ground is 3 times the height of the tower. Find the angle of elevation of the sun.
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Q22
short answer
2 marks
The angle of elevation of the top of a tower from a point on the ground which is 30 m away from the foot of the tower, is 30. Find the height of the tower.
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Q22
short answer
2 marks
Show that the points (-2, 3), (8, 3) and (6, 7) are the vertices of a right-angled triangle.
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Q23
short answer
2 marks
In the given figure, O is the centre of the circle. AB and AC are tangents drawn to the circle from point A. If BAC = 65, then find the measure of BOC.
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Q25
short answer
2 marks
If 4 cot2 45 sec2 60 + sin2 60 + p = 4/3, then find the value of p.
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Q25
short answer
2 marks
Prove that 6 7 is irrational number, given that 7 is an irrational number.
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Q26
short answer
2 marks
If cos A + cos2 A = 1, then find the value of sin2 A + sin4 A.
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Q26
short answer
3 marks
Prove that : (1+tan) / cos2 + (sin+cos) / sin3 = 1 + sin cos
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Q27
short answer
3 marks
A chord of a circle of radius 14 cm subtends an angle of 60 at the centre. Find the area of the corresponding minor segment of the circle. (Use = 3.14 and 3 = 1.73)
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Q29
short answer
3 marks
In the given figure, O is the centre of the circle and QPR is a tangent to it at P. Prove that QAP + APR = 90 .
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Q30
short answer
3 marks
Find by prime factorisation the LCM of the numbers 18180 and 7575. Also, find the HCF of the two numbers.
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Q30
short answer
3 marks
If Q(0, 1) is equidistant from P(5, 3) and R(x, 6), find the values of x.
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Q31
short answer
3 marks
Three bells ring at intervals of 6, 12 and 18 minutes. If all the three bells rang at 6 a.m., when will they ring together again ?
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Q32
long answer
5 marks
The mode of the following frequency distribution is 55. Find the missing Class Interval 0-15, 15-30, 30-45, 45-60, 60-75, 75-90. Total Frequency 6, 7, a, 15, 10, b, 51.
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Q33
long answer
5 marks
Prerna saves < 32 during the first month, < 36 in the second month and < 40 in the third month. If she continues to save in this manner, in how many months will she save < 2,000 ?
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Q34
short answer
3 marks
If the system of linear equations 2x + 3y = 7 and 2ax + (a + b)y = 28 has infinitely many solutions, find the values of a and b.
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Q35
short answer
3 marks
If 217x + 131y = 913 and 131x + 217y = 827, then solve the equations for the values of x and y.
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Q36
short answer
If the system of linear equations 2x + 3y = 7 and 2ax + (a + b)y = 28
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Q39
long answer
5 marks
Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of triangle PQR. Prove that triangle ABC ~ triangle PQR.
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Q40
long answer
5 marks
Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD (produced) in E. Prove that EL = 2BL.
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Q41
long answer
5 marks
As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30 and 60. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (Use 3 = 1.73)
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Q42
long answer
5 marks
From a point on the ground, the angle of elevation of the bottom and top of a transmission tower fixed at the top of 30 m high building are 30 and 60, respectively. Find the height of the transmission tower. (Use 3 = 1.73)
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In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with diameter 7 cm and height 14 cm and the other is hemispherical with diameter 21 cm.
Q43
short answer
1 mark
Find the area of the base of the cylindrical cup.
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Q44
short answer
2 marks
What is the capacity of the hemispherical cup ?
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Q45
short answer
2 marks
Find the capacity of the cylindrical cup.
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Q46
short answer
1 mark
What is the curved surface area of the cylindrical cup ?
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Computer-based learning (CBL) refers to any teaching methodology that makes use of computers for information transmission. At an elementary school level, computer applications can be used to display multimedia lesson plans. A survey was done on 1000 elementary and secondary schools of Assam and they were classified by the number of computers they had. Number of Computers: 1-10, 11-20, 21-50, 51-100, 101 and more Number of Schools: 250, 200, 290, 180, 80 One school is chosen at random. Then :
Q47
short answer
1 mark
Find the probability that the school chosen at random has more than 100 computers.
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In an annual day function of a school, the organizers wanted to give a cash prize along with a memento to their best students. Each memento is made as shown in the figure and its base ABCD is shown from the front side. The rate of silver plating is 20 per cm2.
Q48
short answer
1 mark
What is the area of the quadrant ODCO ?
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Q50
short answer
2 marks
What is the total cost of silver plating the shaded part ABCD ?
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