Q1
mcq
1 mark
The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ – b cos θ) is
- A. sqrt(a^2 + b^2)
- B. a^2 - b^2
- C. sqrt(a^2 - b^2)
- D. a^2 + b^2
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Q2
mcq
1 mark
An ice-cream cone of radius r and height h is completely filled by two spherical scoopes of ice-cream. If radius of each spherical scoop is r/2, then h : 2r equals
- A. 1 : 8
- B. 1 : 2
- C. 1 : 1
- D. 2 : 1
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Q3
mcq
1 mark
The value of k for which the system of linear equations kx – y – 2 = 0 and 6x – 2y – 3 = 0 has infinitely many solutions, is
- A. 1/2
- B. 3
- C. 4
- D. Not exist
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Q4
mcq
1 mark
A circle is divided into 16 identical sectors. If radius of the circle is 7 cm, area of each sector is
- A. 77/4 cm2
- B. 77 cm2
- C. 154 cm2
- D. 77/8 cm2
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Q5
mcq
1 mark
Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is
- A. 34
- B. 43
- C. 38.5
- D. 41.5
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Q6
mcq
1 mark
Three tennis balls are just packed in a cylindrical jar. If radius of each ball is r, volume of air inside the jar is
- A. 2πr3
- B. 3πr3
- C. 5πr3
- D. 4πr3
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Q7
mcq
1 mark
Observe the graph of polynomial p(x). The zeroes of the polynomial are
- A. –2, 0, 2.5
- B. –2, 2.5
- C. 0, 4
- D. –2, 0
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Q8
mcq
1 mark
From an external point P, a tangent PT has been drawn to a circle with centre at O and radius 3 cm, intersecting its concentric circle at A and B. If AB = 8 cm and OA = AP, the length PQ equals.
- A. 8 cm
- B. 10 cm
- C. 9 cm
- D. 12 cm
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Q9
mcq
1 mark
sin A / (sec A – 1)^2 is same as
- A. cos2 A
- B. sec2 A
- C. –sec2 A
- D. cot2 A
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Q10
mcq
1 mark
PQ is tangent to a circle with centre O. If POR = 65º, then mPTR is
- A. 65º
- B. 58.5º
- C. 57.5º
- D. 45º
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Q11
mcq
1 mark
In the given figure, a circle is centred at (1, 2). The diameter of the circle is
- A. 4
- B. 2 2
- C. 5
- D. 2 5
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Q12
mcq
1 mark
In the given figure, DE || BC. If AD/DB = 1/3 and AC = 6 cm, then length AE is
- A. 1.5 cm
- B. 1 cm
- C. 2 cm
- D. 3 cm
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Q13
mcq
1 mark
It is given that ABC ~ EDF. Which of the following is not true ?
- A. Perimeter of ABC / Perimeter of EDF = AB/ED
- B. AB/ED = AC/EF
- C. ∠A = ∠D, ∠C = ∠F
- D. (AB + BC)/AC = (DE + DF)/EF
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Q14
mcq
1 mark
If the quadratic equation 9x2 + 8kx + 16 = 0 has real and equal roots, then the value of k is
- A. 3
- B. –3
- C. –4
- D. 2/3
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Q15
mcq
1 mark
1/(1+cot^2 A) + 1/(1+tan^2 A) equals to :
- A. tan2 A
- B. –1
- C. – tan2 A
- D. cot2 A
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Q16
mcq
1 mark
If in an A.P. the sum of first ten terms is zero whose first term is a and common difference is d, then which of the following relations is true?
- A. 10a + 9d = 0
- B. 2a = 9d
- C. a10 = –a
- D. a10 = a
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Q16
mcq
If sum of first ten terms of an A.P. is zero with a as the first term and d, the common difference, which of the following relation is true ?
- A. 10a + 9d = 0
- B. 2a = 9d
- C. a10 = -a
- D. a10 = a
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Q17
mcq
1 mark
Two dice are thrown together. The probability of obtaining the sum of numbers as maximum 12 is
- A. 1
- C. 1/2
- D. 35/36
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Q17
mcq
Two dice are rolled together. The probability that sum of the numbers obtained is atmost 12, is
- A. 1
- C. 1/2
- D. 35/36
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Q18
mcq
Arc PQ subtends an angle θ at the centre of the circle with radius 6.3 cm. If PQ = 11 cm, then the value of θ is
- A. 10º
- B. 60º
- C. 45º
- D. 100º
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Q19
mcq
Assertion (A) : If probability of happening of an event is 0.2p, p > 0, then p can’t be more than 5. Reason (R) : P( E ) = 1 – P(E) for an event E.
- A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
- C. Assertion (A) is true, but Reason (R) is false.
- D. Assertion (A) is false, but Reason (R) is true.
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Q20
mcq
Assertion (A) : (sqrt(3) + sqrt(5)) is an irrational number. Reason (R) : Sum of the any two irrational numbers is always irrational.
- A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
- C. Assertion (A) is true, but Reason (R) is false.
- D. Assertion (A) is false, but Reason (R) is true.
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Q22
short answer
2 marks
α and β are the zeroes of the polynomial 5x^2 – 16x – 10. Find the value of α/β + β/α.
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Q23
short answer
2 marks
Prove that: ((1+cot^2 θ)/(1+tan^2 θ)) = 2 sin θ cos θ.
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Q23
short answer
In the given figure, DEFG is a square. ABC is right angle triangle with A = 90º. Prove that AG DG = AF DB.
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Q24
short answer
2 marks
Evaluate: sin^2 60º / (1 - 2 tan^2 30º - sec^2 45º)
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Q24
short answer
Verify that roots of the quadratic equation (p – q)x 2 + (q – r)x + (r – p) = 0 are equal when q + r = 2p.
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Q28
short answer
Prove that 2 + 3 5 is an irrational number given that 5 is irrational number.
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Q28
short answer
3 marks
Find the greatest number which divides 764 and 1198, leaving remainders 8 and 10 respectively.
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Q29
short answer
If the HCF of 210 and 55 is expressed as 210 5 + 55m, then find the value of m.
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Q30
short answer
3 marks
To protect plants from heat, a shed of iron rods covered with green cloth is made. The lower part of the shed is a cuboid mounted by semi-cylinder as shown in the figure. Find the area of the cloth required to make this shed, if dimensions of the cuboid are 14 m 25 m 16 m
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Q30
short answer
Chord AB subtends an angle of 120º at the centre O of the circle with radius 21 cm. Find the perimeter of shaded segment ACB. (Use 3 = 1.7)
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Q31
short answer
3 marks
The internal and external radii of a hollow hemisphere are 5 2 cm and 10 cm respectively. A cone of height 5 7 cm and radius 5 2 cm is surmounted on the hemisphere as shown in the figure. Find the total surface area of the object in terms of . (Use 2 = 1.4)
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Q31
short answer
If sec + tan = m, show that m 1 m – 1 2 2 = sin .
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Q32
short answer
3 marks
A bag contains 30 balls out of which ‘m’ number of balls are blue in colour. Find the probability that a ball drawn at random from the bag is not blue.
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Q32
long answer
5 marks
A kite is flying at a height of 60 m above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as 30º. From the bottom of the same building, the angle of elevation of kite is 45º. Find the length of the string and height of roof from the ground. (Use 3 = 1.73)
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Q33
short answer
3 marks
If 6 more blue balls are added in the bag, then the probability of drawing a blue ball will be 4/5 times the probability of drawing a blue ball in the first case. Find the value of m.
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Q35
short answer
3 marks
In a class test, Veer scored 6 more than twice as many marks as Kevin scored. If one of them had scored 4 more marks, their total score would have been 40. Find the marks obtained by Veer and Kevin.
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Q36
short answer
3 marks
Solve the linear equations 3x + y = 14 and y = 2 graphically.
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Q40
long answer
5 marks
A person on tour has 5,400 for his expenses. If he extends his tour by 5 days, he has to cut down his daily expenses by 180. Find the original duration of the tour and daily expense.
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Q41
long answer
5 marks
The total cost of certain piece of cloth was 2,100. During special sale time, the shopkeeper offered 2 m extra cloth for free thus reducing the price of cloth per metre by 120. What was the original per metre price of cloth and its length ?
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Q42
long answer
5 marks
Find mean and mode of the following frequency distribution : Class : 10–30 30–50 50–70 70–90 90–110 110–130 130–150 Frequency : 6 8 12 10 14 11 9
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Q43
long answer
5 marks
If the median of the distribution given below is 28.5, find the values of x and y. Class : 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 Total Frequency : 5 x 20 15 y 5 60
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In the given figure, TP and TQ are tangents to a circle with centre M, touching another circle with centre N at A and B respectively. It is given that MQ = 13 cm, NB = 8 cm, BQ = 35 cm and TP = 80 cm.
Q45
short answer
1 mark
Is MN parallel to PA ? Justify your answer.
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‘Kolam’ is a decorative art which is made with rice flour in South Indian States. It is drawn on grid pattern of dots. One such art work is shown below. Observe the given figure carefully. There are 4 dots in first square, 8 dots in second square, 12 dots in third square and so on.
Q47
short answer
1 mark
Show that number of dots given above form an A.P. Write the first term and common difference.
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Q48
short answer
1 mark
Write nth term of the A.P. formed.
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Q49
short answer
2 marks
The pattern is expanded on a large ground. If total 220 dots are used, then find the number of squares formed.
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Q50
short answer
Is it possible to complete n number of squares using 100 dots ? If yes, then find the value of n.
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Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some places are given below : Point A : (–4, 2) Rajasthan High Court Point B : (4, –4) Birla Mandir Point C : (4, 3) Heera Bagh Point D : (–5, –2) Amar Jawan Jyoti
Q51
short answer
1 mark
Advocate Rehana stays at Heera Bagh. How much distance she has to cover daily to go to the court and coming back home ?
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Q52
short answer
1 mark
There is a crossing on X-axis which divides AD in a certain ratio. Find the ratio.
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Q53
short answer
2 marks
Is Birla Mandir equidistant from Heera Bagh and Amar Jawan Jyoti ? Justify your answer.
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Q54
short answer
Using section formula, show that points A, O and B are not collinear.
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Carom board is a very popular game. The board is a square of side length 65 cm. It has circular pockets in each corner. Ansh strikes a disc, kept at position P with a striker. The disc, hits the boundary of the board at R and goes straight to pocket at corner C. It is given that PS = 9 cm, PQ = 35 cm, BR = x, PRQ = and CRB = .
Q55
short answer
1 mark
Using law of reflection i.e. PRT = CRT, prove that = .
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Q56
short answer
1 mark
Prove that PQR ~ CBR given that PQ is perpendicular to AB.
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Q57
short answer
2 marks
Find the value of x using similarity of triangles.
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Q58
short answer
If Area PQR / Area CBR = (CB/PQ)^2, then find the value of x.
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