Q1
mcq
1 mark
If for any event E, P(E) + P( ) = q, then the value of q is :
- B. 2
- C. 2
- D. 1
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Q2
mcq
1 mark
If sin = cos (0 < < 90 ), then the value of sec . sin is :
- A. (A) (B) (C) 0 (D) 1
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Q3
mcq
1 mark
If an arc of a circle of diameter 10 cm subtends an angle of 144 at the centre of the circle, then the length of the arc is :
- A. 2 cm
- B. 4 cm
- C. 5 cm
- D. 6 cm
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Q5
mcq
1 mark
If one zero of the polynomial q(x) = (p2 + 4) x2 + 65x + 4p is reciprocal of :
- A. 1
- B. 1
- C. 2
- D. 2
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Q6
mcq
1 mark
The equation of a line parallel to y-axis and at a distance of 5 units to the right of y-axis is :
- A. x = 5
- B. x = 5
- C. y = 5
- D. y = 5
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Q7
mcq
1 mark
The sum of the exponents of prime factors in the prime factorisation of 4004 is :
- A. 5
- B. 4
- C. 3
- D. 2
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Q8
mcq
1 mark
The probability of drawing an even prime number out of numbers from 1 to 30 is :
- A. A
- B. B
- C. C
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Q9
mcq
1 mark
In the given figure, PQ||BC. If = and AC = 20·4 cm, then the length of AQ is :
- A. 2·8 cm
- B. 5·8 cm
- C. 3·8 cm
- D. 4·8 cm
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Q10
mcq
1 mark
The line represented by the equation x y = 0 is :
- A. parallel to x-axis
- B. parallel to y-axis
- C. passing through the origin
- D. passing through the point (3, 2)
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Q11
mcq
1 mark
The points ( 5, 0), (5, 0) and (0, 4) are the vertices of a triangle which is a/an :
- A. right-angled triangle
- B. isosceles triangle
- C. equilateral triangle
- D. scalene triangle
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Q12
mcq
1 mark
The 10th term of the AP 5, , ,
- A. A
- B. B
- C. C
- D. D
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Q13
mcq
1 mark
In the given figure, RS is the tangent to the circle at the point L and MN is the diameter. If NML = 30 , then RLM is :
- A. 30
- B. 60
- C. 90
- D. 120
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Q14
mcq
The coordinates of the end points of a diameter of a circle are (5, 2) and (5, 2). The length of the radius of the circle is :
- A. ± 2
- B. ± 4
- C. 4
- D. 2
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Q15
mcq
Which of the following statements is incorrect ?
- A. Two congruent figures are always similar.
- B. A square and a rhombus of the same area are always similar.
- C. Two equilateral triangles are always similar.
- D. Two similar triangles need not be congruent.
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Q16
mcq
The least number which is a perfect square and is divisible by each of 16, 20 and 50, is :
- A. 1200
- B. 100
- C. 3600
- D. 2400
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Q17
mcq
If sin 30 tan 45 = , then the value of k is :
- A. 4
- B. 3
- C. 2
- D. 1
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Q18
mcq
The quadratic equation whose roots are 7 and is :
- A. 7x2 50x + 7 = 0
- B. 7x2 50x + 1 = 0
- C. 7x2 + 50x 7 = 0
- D. 7x2 + 50x 1 = 0
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Q19
short answer
Assertion (A) : Common difference of the AP : 5, 1, 3, Reason (R): Common difference of the AP : a1, a2, a3 an is obtained by d = an an 1.
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Q20
short answer
Assertion (A) : The pair of linear equations px +3y+59=0 and 2x + 6y + 118 = 0 will have infinitely many solutions if p = 1. Reason (R): If the pair of linear equations px +3y+19=0 and 2x + 6y + 157 = 0 has a unique solution, then p 1.
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Q21
short answer
2 marks
In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and AOB = 90 . If AO = OB = 42 cm, then find the perimeter of the top of the table.
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Q22
short answer
2 marks
In the given figure, three sectors of a circle of radius 5 cm, making angles 35 , 50 and 95 at the centre are shaded. Find the area of the shaded region. [Use = ]
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Q22
short answer
2 marks
At point A on the diameter AB of a circle of radius 10 cm, tangent XAY is drawn to the circle. Find the length of the chord CD parallel to XY at a distance of 16 cm from A.
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Q23
short answer
2 marks
If p and q are zeroes of the polynomial p(y) = 21y2 y 2, then find the value of (1 p) . (1 q).
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Q24
short answer
2 marks
If tan A = ; where A is an acute angle, then find the value of .
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Q26
short answer
2 marks
In the given figure, and PST = PRQ. Prove that PQR is an isosceles triangle.
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Q27
short answer
2 marks
In the given figure, ABE ACD. Prove that ADE ABC.
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Q27
short answer
3 marks
Find the sum of all 3-digit natural numbers which are divisible by 11.
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Q28
short answer
3 marks
The length of the hour hand of a clock is 10 cm. Find the area of the minor sector swept by the hour hand of the clock between 5 a.m. to 8 a.m. Also, find the area of the major sector.
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Q29
short answer
3 marks
If cosec = x + , prove that cosec + cot = 2x or .
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Q30
short answer
3 marks
If the mid-point of the line segment joining the points A(3, 4) and B(k, 6) is P(x, y) and x + y 10 = 0, then find the value of k.
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Q31
short answer
3 marks
Prove that is an irrational number.
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Q32
short answer
3 marks
Prove that the parallelogram circumscribing a circle is a rhombus.
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Q32
long answer
5 marks
Prove that a line drawn parallel to one side of a triangle to intersect the other two sides in distinct points divides the other two sides in the same ratio. Hence, in the figure given below, prove that = where LM || CB and LN || CD.
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Q33
short answer
3 marks
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
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Q34
long answer
5 marks
Find the Mean and Mode of the following data: Classes 4-8 (2), 8-12 (12), 12-16 (15), 16-20 (25), 20-24 (18), 24-28 (12), 28-32 (13), 32-36 (3).
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Q37
long answer
5 marks
Two ships are sailing in the sea on either side of a lighthouse. The angles of depression to the two ships as observed from the top of the lighthouse are 60 and 45 , respectively. If the distance between the ships is 100 m, then find the height of the lighthouse.
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Q38
long answer
5 marks
The angles of depression of the top and the bottom of an 8 m tall building from the top of another multistoried building are 30 and 45 , respectively. Find the height of the multistoried building and the distance between the two buildings.
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Q40
long answer
5 marks
The numerator of a fraction is 3 less than its denominator. If 2 is added to both numerator and denominator, then the sum of the new fraction and the original fraction is 9 1/20. Find the original fraction.
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Q41
long answer
5 marks
A train travelling at a uniform speed for 360 km would have taken 48 minutes less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train.
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A skilled carpenter decided to craft a special rolling pin for the local baker. He carefully joined three cylindrical pieces of wood two small ones on the ends and one larger in the centre to create a perfect tool. The baker loved the rolling pin, as it rolled out the smoothest dough for breads and pastries. The length of the bigger cylindrical part is 12 cm and diameter is 7 cm and the length of each smaller cylindrical part is 5 cm and diameter is 2·1 cm.
Q42
short answer
1 mark
Find the volume of the bigger cylindrical part.
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Q43
short answer
1 mark
Find the curved surface area of the bigger cylindrical part.
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Q44
short answer
2 marks
Find the ratio of the volume of the bigger cylindrical part to the total volume of the two smaller (identical) cylindrical parts.
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Q45
short answer
2 marks
Find the sum of the curved surface areas of the two identical smaller cylindrical parts.
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A school is organizing a grand cultural event to show the talent of its students. To accommodate the guests, the school plans to rent chairs and tables from a local supplier. It finds that rent for each chair is 50 and for each table is 200. The school spends 30,000 for renting the chairs and tables. Also, the total number of items (chairs and tables) rented are 300.
Q46
short answer
1 mark
Write down the pair of linear equations representing the given information.
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Q47
short answer
2 marks
Find the number of chairs and number of tables rented by the school.
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Q48
short answer
2 marks
If the school wants to spend a maximum of 27,000 on 300 items (tables and chairs), then find the number of chairs and tables it can rent.
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Q49
short answer
1 mark
What is maximum number of tables that can be rented in 30,000 if no chairs are rented ?
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Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from 10 to 74. Before each match, he draws a card from the jar. If the card bears an even number, the team wins. If the number is even and divisible by 5, they win by a big margin. If the number is an odd number less than 30, they win by a small margin. And if the number is a prime number between 50 and 74, they lose. Answer the following questions if Rahul draws a card today :
Q50
short answer
1 mark
What is the probability that Rahul draws a card with an even number ?
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Q51
short answer
2 marks
What is the probability that Rahul draws a card with a prime number between 50 and 74 ?
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