Q1
mcq
1 mark
The LCM of the smallest prime number and the smallest odd composite number is :
- A. 10
- B. 6
- C. 9
- D. 18
Solution hidden
Log in to view solution →
Q2
mcq
1 mark
If the mean of the first n natural numbers is 9/5n, then the value of n is :
- A. 5
- B. 4
- C. 9
- D. 10
Solution hidden
Log in to view solution →
Q3
mcq
1 mark
If 5 tan q – 12 = 0, then the value of sin q is :
- A. 12/5
- B. 13/12
- C. 13/5
- D. 5/12
Solution hidden
Log in to view solution →
Q4
mcq
1 mark
The next (4th) term of the A.P. 18, 50, 98, … is :
- A. 128
- B. 140
- C. 162
- D. 200
Solution hidden
Log in to view solution →
Q5
mcq
1 mark
In the given figure, in D ABC, DE || BC. If AD = 2·4 cm, DB = 4 cm and AE = 2 cm, then the length of AC is :
- A. 3/10 cm
- B. 10/3 cm
- C. 3/16 cm
- D. 1·2 cm
Solution hidden
Log in to view solution →
Q6
mcq
1 mark
In the given figure, RJ and RL are two tangents to the circle. If Ð RJL = 42°, then the measure of Ð JOL is :
- A. 42°
- B. 84°
- C. 96°
- D. 138°
Solution hidden
Log in to view solution →
Q7
mcq
1 mark
The perimeter of the sector of a circle of radius 21 cm which subtends an angle of 60° at the centre of circle, is :
- A. 22 cm
- B. 43 cm
- C. 64 cm
- D. 462 cm
Solution hidden
Log in to view solution →
Q8
mcq
1 mark
The ratio of the sum and product of the roots of the quadratic equation 5x2 – 6x + 21 = 0 is :
- A. 5 : 21
- B. 2 : 7
- C. 21 : 5
- D. 7 : 2
Solution hidden
Log in to view solution →
Q9
mcq
1 mark
The 14th term from the end of the A.P. – 11, – 8, – 5, ..., 49 is :
- A. 7
- B. 10
- C. 13
- D. 28
Solution hidden
Log in to view solution →
Q10
mcq
1 mark
The length of the shadow of a tower on the plane ground is 3 times the height of the tower. The angle of elevation of the Sun is :
- A. 30°
- B. 45°
- C. 60°
- D. 90°
Solution hidden
Log in to view solution →
Q11
mcq
1 mark
What is the probability that a number selected randomly from the numbers 1, 2, 3, ..., 15 is a multiple of 4 ?
- A. 4/15
- B. 6/15
- C. 3/15
- D. 5/15
Solution hidden
Log in to view solution →
Q12
mcq
1 mark
If 3/x = 2 sin A, 3/y = 2 cos A, then the value of x2 + y2 is :
- A. 36
- B. 9
- C. 6
- D. 18
Solution hidden
Log in to view solution →
Q13
mcq
1 mark
If a and b are the zeroes of the polynomial p(x) = kx2 – 30x + 45k and a + b = ab, then the value of k is :
- A. – 3/2
- B. – 2/3
- C. 2/3
- D. 3/2
Solution hidden
Log in to view solution →
Q14
mcq
1 mark
The length of an arc of a circle with radius 12 cm is 10p cm. The angle subtended by the arc at the centre of the circle, is :
- A. 120°
- B. 6°
- C. 75°
- D. 150°
Solution hidden
Log in to view solution →
Q15
mcq
1 mark
The LCM of three numbers 28, 44, 132 is :
- A. 258
- B. 231
- C. 462
- D. 924
Solution hidden
Log in to view solution →
Q16
mcq
1 mark
A chord of a circle of radius 10 cm subtends a right angle at its centre. The length of the chord (in cm) is :
- A. 5 2
- B. 10 2
- C. 2/5
- D. 5
Solution hidden
Log in to view solution →
Q17
mcq
Which out of the following type of straight lines will be represented by the system of equations 3x + 4y = 5 and 6x + 8y = 7 ?
- A. Parallel
- B. Intersecting
- C. Coincident
- D. Perpendicular to each other
Solution hidden
Log in to view solution →
Q18
mcq
The greatest number which divides 281 and 1249, leaving remainder 5 and 7 respectively, is :
- A. 23
- B. 276
- C. 138
- D. 69
Solution hidden
Log in to view solution →
Q19
mcq
Assertion (A) : Degree of a zero polynomial is not defined.
Reason (R): Degree of a non-zero constant polynomial is 0.
- A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of 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.
Solution hidden
Log in to view solution →
Q20
mcq
Assertion (A) : ABCD is a trapezium with DC || AB. E and F are points on AD and BC respectively, such that EF || AB. Then FC/BF = ED/AE .
Reason (R) : Any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally.
- A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of 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.
Solution hidden
Log in to view solution →
Q21
short answer
2 marks
The king, queen and ace of clubs and diamonds are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is randomly drawn from the remaining cards. Find the probability of getting a card of clubs.
Solution hidden
Log in to view solution →
Q22
short answer
2 marks
If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm, then find the length of each tangent.
Solution hidden
Log in to view solution →
Q23
short answer
2 marks
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Solution hidden
Log in to view solution →
Q24
short answer
2 marks
Find the ratio in which the point P(– 4, 6) divides the line segment joining the points A(– 6, 10) and B(3, – 8).
Solution hidden
Log in to view solution →
Q24
short answer
2 marks
If a, b are zeroes of the polynomial p(x) = 5x^2 – 6x + 1, then find the value of a + b + ab.
Solution hidden
Log in to view solution →
Q25
short answer
2 marks
Prove that the points (3, 0), (6, 4) and (– 1, 3) are the vertices of an isosceles triangle.
Solution hidden
Log in to view solution →
Q25
short answer
2 marks
Evaluate: (2 tan^2 30° + sec^2 60° - tan^2 45°) / (1 - sin^2 60°)
Solution hidden
Log in to view solution →
Q26
short answer
3 marks
Prove that: (sin q + cos q) / (tan q - cot q) = sec^2 q - cosec^2 q
Solution hidden
Log in to view solution →
Q27
short answer
3 marks
A sector is cut from a circle of radius 21 cm. The central angle of the sector is 150°. Find the length of the arc of this sector and the area of the sector.
Solution hidden
Log in to view solution →
Q30
short answer
3 marks
Prove that √3 is an irrational number.
Solution hidden
Log in to view solution →
Q30
short answer
3 marks
Prove that the parallelogram circumscribing a circle is a rhombus.
Solution hidden
Log in to view solution →
Q31
short answer
3 marks
Prove that (2 + √3) is an irrational number, given that √6 is an irrational number.
Solution hidden
Log in to view solution →
Q32
short answer
3 marks
Three unbiased coins are tossed simultaneously. Find the probability of getting at least one head.
Solution hidden
Log in to view solution →
Q34
short answer
3 marks
If the sum of the first 14 terms of an A.P. is 1050 and the first term is 10, then find the 20th term and the nth term.
Solution hidden
Log in to view solution →
Q34
long answer
5 marks
From a window 15 metres high above the ground in a street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are 30° and 45° respectively. Find the height of the opposite house. (Use 3 = 1·732)
Solution hidden
Log in to view solution →
Q35
short answer
3 marks
The first term of an A.P. is 5, the last term is 45 and the sum of all the terms is 400. Find the number of terms and the common difference of the A.P.
Solution hidden
Log in to view solution →
Q35
long answer
A juice seller was serving his customers using glasses as shown in the figure. The inner diameter of the cylindrical glass was 5·6 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of the glass was 10 cm, find the apparent capacity and the actual capacity of the glass.
Solution hidden
Log in to view solution →
Q36
long answer
5 marks
In the given figure, △FEC ≅ △GDB and ∠1 = ∠2. Prove that △ADE ~ △ABC.
Solution hidden
Log in to view solution →
Q37
long answer
5 marks
Sides AB and AC and median AD of a △ABC are respectively proportional to sides PQ and PR and median PM of another △PQR. Show that △ABC ~ △PQR.
Solution hidden
Log in to view solution →
Q38
long answer
5 marks
Find the value of ‘k’ for which the quadratic equation (k + 1)x^2 – 6(k + 1)x + 3(k + 9) = 0, k ≠ – 1 has real and equal roots.
Solution hidden
Log in to view solution →
Q39
long answer
5 marks
The age of a man is twice the square of the age of his son. Eight years hence, the age of the man will be 4 years more than three times the age of his son. Find their present ages.
Solution hidden
Log in to view solution →
Q40
long answer
5 marks
In the given figure, D FEC @ D GDB and Ð 1 = Ð 2. Prove that D ADE ~ D ABC.
Solution hidden
Log in to view solution →Reading Passage
A garden is in the shape of a square. The gardener grew saplings of Ashoka tree on the boundary of the garden at the distance of 1 m from each other. He wants to decorate the garden with rose plants. He chose a triangular region inside the garden to grow rose plants. In the above situation, the gardener took help from the students of class 10. They made a chart for it which looks like the given figure.
Q43
short answer
1 mark
If A is taken as origin, what are the coordinates of the vertices of D PQR ?
Solution hidden
Log in to view solution →
Q45
short answer
2 marks
Find the coordinates of the point which divides the line segment joining points P and R in the ratio 2 : 1 internally.
Solution hidden
Log in to view solution →
Q46
short answer
1 mark
Find out if D PQR is an isosceles triangle.
Solution hidden
Log in to view solution →
Q47
short answer
2 marks
(ii) (a) Find distances PQ and QR.
Solution hidden
Log in to view solution →Reading Passage
Activities like running or cycling reduce stress and the risk of mental disorder like depression. Running helps build endurance. Children develop stronger bones and muscles and are less prone to gain weight. The physical education teacher of a school has decided to conduct an inter school running tournament in his school premises. The time taken by a group of students to run 100 m, was noted as follows : Time (in seconds) 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 Number of students 8 10 13 6 3
Q48
short answer
1 mark
(i) What is the median class of the above given data ?
Solution hidden
Log in to view solution →Reading Passage
Essel World is one of India’s largest amusement parks that offers a diverse range of thrilling rides, water attractions and entertainment options for visitors of all ages. The park is known for its iconic ‘‘Water Kingdom’’ section, making it a popular destination for family outings and fun-filled adventure. The ticket charges for the park are 150 per child and 250 per adult. On a day, the cashier of the park found that 300 tickets were sold and an amount of 55,000 was collected.
Q49
short answer
2 marks
(ii) (a) Find the mean time taken by the students to finish the race.
Solution hidden
Log in to view solution →
Q50
short answer
2 marks
(ii) (b) Find the mode of the above given data.
Solution hidden
Log in to view solution →
Q51
short answer
1 mark
(iii) How many students took time less than 60 seconds ?
Solution hidden
Log in to view solution →
Q52
short answer
1 mark
(i) If the number of children visited be x and the number of adults visited be y, then write the given situation algebraically.
Solution hidden
Log in to view solution →
Q53
short answer
2 marks
(ii) (a) How many children visited the amusement park that day ?
Solution hidden
Log in to view solution →
Q54
short answer
1 mark
(iii) How much amount will be collected if 250 children and 100 adults visit the amusement park ?
Solution hidden
Log in to view solution →