Q1
mcq
1 mark
The distance between the points (a cos $\theta$, a sin $\theta$) and (a sin $\theta$, a cos $\theta$) is
- A. a
- B. $a\sqrt{2}$
- D. 2a
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Q1
mcq
1 mark
The distance between the points (a cos q, a sin q) and (a sin q, -a cos q) is
- A. a
- B. a^2
- D. 2a
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Q2
mcq
1 mark
In the given figure, tangents PA and PB to the circle centred at O, from point P are perpendicular to each other. If PA = 5 cm, then length of AB is
- A. 5 cm
- B. 5 cm
- C. 25 cm
- D. 10 cm
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Q3
mcq
1 mark
The sum of the A.P. -29, -26, -23, ....., 61 is 16 ?
- A. 11th
- B. 16th
- C. 10th
- D. 31st
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Q4
mcq
1 mark
A box contains cards numbered 6 to 55. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square, is
- A. 7/50
- B. 7/55
- C. 1/10
- D. 5/49
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Q5
mcq
1 mark
AB and CD are two chords of a circle intersecting at P. Choose the correct statement from the following :
- A. DkHD ~ DCBA
- B. DkHD ~ DBPC
- C. DkHD ~ DBCP
- D. DkHD ~ DCBP
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Q6
mcq
1 mark
Two dice are rolled together. The probability of getting the sum of the two numbers to be more than 10, is
- A. 1/9
- B. 1/6
- C. 7/12
- D. 1/12
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Q7
mcq
1 mark
After an examination, a teacher wants to know the marks obtained by most of the students in her class. She requires to calculate _____ of marks.
- A. median
- B. mode
- C. mean
- D. range
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Q8
mcq
1 mark
The roots of the quadratic equation 4x^2 - 5x + 5 = 0 are
- A. irrational
- B. rational and distinct
- C. sie and distinct
- D. real and distinct
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Q9
mcq
1 mark
The common difference of an A.P. in which a^20 - a^15 = 20, is
- A. 4
- B. 5
- C. 4d
- D. 5d
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Q10
mcq
1 mark
If value of each observation in a data is increased by 2, then median of the data
- A. increases by 2
- B. increases by 2n
- C. remains same
- D. decreases by 2
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Q11
mcq
1 mark
The perimeters of two similar triangles ABC and PQR are 56 cm and 48 cm respectively. PQ/AB is equal to
- A. 7/8
- B. 6/7
- C. 7/6
- D. 8/7
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Q12
mcq
1 mark
If a and b (a > b) are the zeroes of the polynomial -x^2 + x + (a - b) then (a - b) is equal to
- A. -10
- B. 10
- C. ±10
- D. 8
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Q12
mcq
1 mark
If $\alpha$ and $\beta$ are the zeroes of the polynomial $x^2 - 5x + k$ such that $\alpha - \beta = 1$, then the value of $k$ is equal to
- A. -10
- B. 10
- C. ±10
- D. 8
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Q13
mcq
1 mark
The value of k for which the system of equations 3x - t + 5 = 0 and 6x - ky + 16 = 0 has infinitely many solutions, is
- A. -2
- B. 2
- C. 1/2
- D. -3 1/2
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Q14
mcq
1 mark
If sin q = cos q (0° < q < 90°), then value of (sec q . sin q) is :
- A. 1/2
- B. 2
- C. 1
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Q14
mcq
1 mark
If $\sin q = \cos q$ ($0^\circ < q < 90^\circ$), then value of $(\sec q \cdot \sin q)$ is :
- A. 1/2
- B. 2
- C. 1
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Q15
mcq
1 mark
Point P divides the line segment joining the points A(4, -5) and B(1, 2) in the ratio 5:2. The coordinates of point P are
- A. (-2/3, 5/2)
- B. (0, 7/11)
- C. (0, 7/13)
- D. (7/13, 0)
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Q16
mcq
1 mark
A triangle ABC is shown. DE is parallel to BC. If AD = 5 cm, DB = 2.5 cm and BC = 12 cm, then DE is equal to
- A. 10 cm
- B. Pm
- C. Pm
- D. Gon Pm
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Q17
mcq
1 mark
If the HCF (2520, 6600) = 40 and LCM (2520, 6600) = 252 ´ k, then the value of k is
- A. 1650
- B. 1600
- C. 165
- D. 1625
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Q18
mcq
1 mark
In the given figure, AT is tangent to a circle centred at O. If ∠CAT = 40°, then ∠CBA is equal to
- A. 70°
- B. 50°
- C. 65°
- D. 40°
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Q19
short answer
1 mark
Assertions(A): If $\sin A = 1/3$, then the value of $\cos A$ is $2\sqrt{2}/3$. Reasons(R): For any angle $\theta$, $\sin^2 \theta + \cos^2 \theta = 1$.
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Q20
short answer
1 mark
Assertions(A): Two cubes each of edge length 10 cm are joined together. The total surface area of newly formed cuboid is 1200 cm$^2$. Reasons(R): Area of each surface of a cube of side 10 cm is 100 cm$^2$.
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Q22
short answer
2 marks
In what ratio is the line segment joining the points (3, -5) and (-1, 6) divided by the x-axis?
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Q22
short answer
2 marks
In the given figure, AB and CD are tangents to a circle centred at O. Is $\angle BAC = \angle DCA$? Justify your answer.
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Q23
short answer
2 marks
A(3, 0), B(6, 4) and C(-1, 3) are vertices of a triangle ABC. Find length of its median BE.
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Q23
short answer
2 marks
In the given figure, a circle centred at origin O has radius 7 cm, OC is perpendicular to chord AB. If OA = 25 cm, find the length of chord AB.
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Q25
short answer
2 marks
Can $8^n$, n being a natural number, end with the digit 0? Give reasons.
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Q26
short answer
2 marks
If $A(4, -6)$, $B(3, -2)$ and $C(5, 2)$ are vertices of a triangle ABC. Find length of its median BE.
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Q26
short answer
3 marks
Prove that $\frac{\text{cosec}^2 \theta - \sec^2 \theta}{\text{cosec}^2 \theta + \sec^2 \theta} = \frac{1}{7}$.
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Q28
short answer
3 marks
Prove that $\sqrt{5}$ is an irrational number.
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Q29
short answer
2 marks
Evaluate : $2 \sin^2 30^\circ \sec 60^\circ + 3 \tan^2 60^\circ$.
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Q30
short answer
2 marks
If $2 \sin(A + B) = \sqrt{3}$ and $\cos(A - B) = 1$, then find the measures of angles A and B. $0^\circ < A + B \leq 90^\circ$.
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Q30
short answer
3 marks
A dealer sells an article for ₹ 75 and gains as much percent as the cost price of the article. Find the cost price of the article.
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Q31
short answer
In a test, the marks obtained by 100 students (out of 50) are given below: Class: 0-10, 10-20, 20-30, 30-40, 40-50. Students: 12, 23, 34, 25, 6. Find the mean marks of the students.
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Q32
short answer
5 marks
A person standing on the bank of a river observes that the angle of elevation of the top of a tower on the opposite bank is 60°. When he moves 30 m away from the bank, he finds the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the river.
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Q33
short answer
3 marks
If the sum of first m terms of an A.P. is same as sum of its first n terms ($m \neq n$), then show that the sum of its first $(m + n)$ terms is zero.
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Q33
short answer
5 marks
The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector.
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Q34
short answer
3 marks
In an A.P., the sum of three consecutive terms is 24 and the sum of their squares is 194. Find the numbers.
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Q36
short answer
3 marks
In the given figure, PQ is tangent to a circle centred at O and $\angle BAQ = 30^\circ$; show that BP = BQ.
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Q37
short answer
3 marks
In the given figure, AB, BC, CD and DA are tangents to the circle with centre O. Prove that $\angle AOB + \angle COD = 180^\circ$.
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In a survey on holidays, 120 people were asked to state which type of transport they used on their last holiday. The following pie chart shows the results of the survey.
Q42
short answer
1 mark
If one person is selected at random, find the probability that he/she travelled by bus or ship.
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Q43
short answer
1 mark
Which is most favourite mode of transport and how many people used it?
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Q44
short answer
2 marks
A person is selected at random. If the probability that the person does not use train is 4/5, find the number of people who used train.
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Q45
short answer
2 marks
The probability that randomly selected person used aeroplane is 7/60. Find the revenue collected by air company at the rate of ` 5,000 per person.
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‘circus’ has the same root as ‘circle’. In a closed circular area, various entertainment acts including human skill and animal training are presented before the crowd. A circus tent is cylindrical upto a height of 8 m and conical above it. The diameter of the base is 28 m and total height of tent is 18.5 m.
Q46
short answer
1 mark
Find slant height of the conical part.
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Q47
short answer
1 mark
Find the curved surface area of the cylindrical part.
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Q48
short answer
2 marks
Find area of the cloth used for making tent.
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Q49
short answer
2 marks
Find total volume of air inside an tent.
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A ball is thrown in the air so that $t$ seconds after it is thrown, its height $h$ metre above its starting point is given by the polynomial $h = 25t - 5t^2$. Observe the graph of the polynomial and answer the following questions :
Q50
short answer
1 mark
Write zeroes of the polynomial $h = 25t - 5t^2$.
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Q51
short answer
1 mark
Find the maximum height attained by the ball.
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Q52
short answer
2 marks
Find the time at which the ball reaches a height of 30 m.
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Q53
short answer
2 marks
Find the two possible values of $t$ when the height of the ball was 20 m.
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