Q1
mcq
The distance between the points P (5, 3/11) and Q (5, 3/2) is :
- A. 6 units
- B. 4 units
- C. 2 units
- D. 3 units
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Q2
mcq
In the given figure, AB = BC = 10 cm. If AC = 7 cm, then the length of BP is :
- A. 3·5 cm
- B. 7 cm
- C. 6·5 cm
- D. 5 cm
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Q3
mcq
Water in a river which is 3 m deep and 40 m wide is flowing at the rate of 2 km/h. How much water will fall into the sea in 2 minutes?
- A. 800 m^3
- B. 4000 m^3
- C. 8000 m^3
- D. 2000 m^3
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Q4
mcq
If the mean and the mode of a distribution are 15 and 18 respectively, then the median of the distribution is :
- A. 17
- B. 15
- C. 16
- D. 18
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Q5
mcq
The 11th term from the end of the A.P. : 10, 7, 4, ......., 62 is :
- A. 25
- B. 16
- C. 32
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Q6
mcq
One card is drawn at random from a well shuffled pack of 52 playing cards. The probability that the drawn card is a queen, is :
- A. 4/13
- B. 4/52
- C. 2/13
- D. 1/26
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Q7
mcq
PQ is tangent to a circle centered at O. If the radius of the circle is 5 cm, then the length of the tangent PQ is :
- A. √35 cm
- B. √3/10 cm
- C. 10 cm
- D. √3/5 cm
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Q8
mcq
Which of the following numbers cannot be the probability of happening of an event ?
- B. 1.07
- C. 0.07
- D. 0.07/3
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Q9
mcq
If $\sec \theta + \tan \theta = 3$, then the value of $(\sec \theta - \tan \theta)$ is :
- A. 4/3
- B. 2/3
- C. 1/3
- D. 3
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Q10
mcq
A quadratic equation whose roots are $(3 - \sqrt{2})$ and $(3 + \sqrt{2})$ is :
- A. $x^2 - 6x + 7 = 0$
- B. $x^2 + 6x + 7 = 0$
- C. $9x^2 - 2 = 0$
- D. $x^2 - 7 = 0$
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Q11
mcq
If every term of the statistical data consisting of n terms is decreased by 2, then the mean of the data :
- A. decreases by 2
- B. remains unchanged
- C. decreases by 2n
- D. decreases by 1
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Q12
mcq
The number of polynomials having zeroes -3 and 5 is :
- A. only one
- B. infinite
- C. exactly two
- D. at most two
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Q13
mcq
The solution of the pair of equations $x + y = a + b$ and $ax - by = a^2 - b^2$ is :
- A. x = b, y = a
- B. x = a, y = b
- C. x = a, y = -b
- D. x = -a, y = b
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Q14
mcq
The common difference of the A.P. whose $n^{th}$ term is given by $a_n = 3n + 7$, is :
- A. 7
- B. 3
- C. 3n
- D. 1
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Q15
mcq
In the given figure, DE || BC. The value of x is :
- A. 6
- B. 12.5
- C. 8
- D. 10
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Q16
mcq
In triangles ABC and DEF, $\frac{FD}{BC} = \frac{DE}{AB}$. Which of the following makes the two triangles similar ?
- A. \angle A = \angle D
- B. \angle B = \angle D
- C. \angle B = \angle E
- D. \angle A = \angle F
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Q17
mcq
$\frac{2 \tan 30^\circ}{1 + \tan^2 30^\circ}$ is equal to :
- A. \sin 60^\circ
- B. \cos 60^\circ
- C. \tan 60^\circ
- D. \sin 30^\circ
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Q18
mcq
In the given figure, AB is a tangent to the circle centered at O. If OA = 6 cm and \angle OAB = 30^\circ, then the radius of the circle is :
- A. 3 cm
- B. 3\sqrt{3} cm
- C. 2 cm
- D. \sqrt{3} cm
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Q19
short answer
1 mark
Assertion (A) : The number $5^n$ cannot end with the digit 0, where n is a natural number. Reason (R): Prime factorisation of 5 has only two factors, 1 and 5.
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Q20
short answer
1 mark
Assertion (A) : If the points A(4, 3) and B(x, 5) lie on a circle with centre O(2, 3), then the value of x is 2. Reason (R) : Centre of a circle is the mid-point of each chord of the circle.
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Q21
short answer
2 marks
Find the greatest 3-digit number which is divisible by 18, 24 and 36.
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Q22
short answer
2 marks
(a) If $a \cos + b \sin = m$ and $a \sin - b \cos = n$, then prove that $a^2 + b^2 = m^2 + n^2$.
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Q23
short answer
2 marks
(b) Prove that: $1/(\sec A - 1) + 1/(\sec A + 1) = 2 \csc^2 A$
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Q23
short answer
2 marks
Find the ratio in which y-axis divides the line segment joining the points (5, 6) and ( 1, 4).
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Q24
short answer
2 marks
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
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Q26
short answer
2 marks
(a) The line segment joining the points A(4, 5) and B(4, 5) is divided by the point P such that AP : AB = 2 : 5. Find the coordinates of P.
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Q27
short answer
2 marks
(b) Point P(x, y) is equidistant from points A(5, 1) and B(1, 5). Prove that x = y.
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Q27
short answer
3 marks
A fraction becomes 1/3 when 1 is subtracted from the numerator. It becomes 1/4 when 8 is added to the denominator. Find the fraction.
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Q28
short answer
3 marks
(a) In the given figure, CD is the perpendicular bisector of AB. EF is perpendicular to CD. AE intersects CD at G. Prove that DG/FG = CD/CF.
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Q28
short answer
Prove that: $\frac{\sec A + 1}{\tan A} + \frac{\tan A}{\sec A + 1} = 2 \operatorname{cosec} A$
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Q29
short answer
3 marks
(b) In the given figure, ABCD is a parallelogram. BE bisects CD at M and intersects AC at L. Prove that EL = 2BL.
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Q29
short answer
3 marks
Find the mean of the following frequency distribution : Classes 25-30, 30-35, 35-40, 40-45, 45-50, 50-55, 55-60
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Q31
short answer
Find the common difference of an A.P. whose first term is 8, the last term is 65 and the sum of all its terms is 730.
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Q33
short answer
Prove that $\sqrt{3}$ is an irrational number.
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Q33
long answer
5 marks
A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope. Find the area of that part of the field in which the horse can graze. Also, find the increase in grazing area if length of rope is increased to 10 m. (Use $\pi = 3.14$)
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Q34
short answer
The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change together next?
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Q35
long answer
5 marks
Two pillars are standing on either side of a 80 m wide road. Height of one pillar is 20 m more than the height of the other pillar. From a point on the road between the pillars, the angle of elevation of the higher pillar is 60°, whereas that of the other is 30°. Find the distance of the point from the pillars and the height of each pillar. (Use $\sqrt{3} = 1.73$)
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Q36
long answer
5 marks
A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the journey, what was its first average speed?
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Q37
long answer
5 marks
Two pipes together can fill a tank in $8/15$ hours. The pipe with larger diameter takes 2 hours less than the pipe with smaller diameter to fill the tank separately. Find the time in which each pipe can fill the tank separately.
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Q39
long answer
5 marks
A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 10 cm and 8 cm respectively. Find the lengths of the sides AB and AC, if it is given that the area of ABC is 90 $cm^2$.
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Q40
long answer
5 marks
Two circles with centres O and O' of radii 6 cm and 8 cm, respectively intersect at two points P and Q such that OP and O'P are tangents to the two circles. Find the length of the common chord PQ.
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In a pool at an aquarium, a dolphin jumps out of the water travelling at 20 cm per second. Its height above water level after t seconds is given by $h = 20t - 16t^2$.
Q42
short answer
1 mark
Find zeroes of polynomial $p(t) = 20t - 16t^2$.
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Q43
short answer
1 mark
Which of the following types of graph represents $p(t)$?
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Q44
short answer
2 marks
What would be the value of h at $t = 2/3$? Interpret the result.
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Q45
short answer
2 marks
How much distance has the dolphin covered before hitting the water level again?
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A golf ball is spherical with about 300-500 dimples that help increase its velocity while in play. Golf balls are traditionally white but available in colours also. In the given figure, a golf ball has diameter 4.2 cm and the surface has 315 dimples (hemi-spherical) of radius 2 mm.
Q46
short answer
1 mark
Find the surface area of one such dimple.
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Q47
short answer
1 mark
Find the volume of the material dug out to make one dimple.
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Q48
short answer
2 marks
Find the total surface area exposed to the surroundings.
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Q49
short answer
2 marks
Find the volume of the golf ball.
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A middle school decided to run the following spinner game as a fund-raiser on Christmas Carnival. Making Purple : Spin each spinner once. Blue and red make purple. So, if outcome...
Q50
short answer
1 mark
List all possible outcomes of the game.
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Q51
short answer
1 mark
Find the probability of making a purple colour.
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A middle school decided to run the following spinner game as a fund-raiser on Christmas Carnival. Making Purple : Spin each spinner once. Blue and red make purple. So, if outcome Based on the above, answer the following questions :
Q52
short answer
2 marks
For each win, a participant gets < 10, but if he/she loses, he/she has to pay < 5 to the school. If 99 participants played, calculate how much fund could the school have collected.
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Q53
short answer
2 marks
If the same amount of < 5 has been decided for winning or losing the game, then how much fund had been collected by school ? (Number of participants = 99)
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