CBSE Class 10 Basic MATHS 110 Important Questions :**110 Important Questions For Mathematics-Basic **

CBSE Class 10 Mathematics Basic Section A Quiz 1

- 32 marks are allotted to questions which require remembering facts, terms, concepts and answers.
- 28 marks are allotted for questions which would demonstrate a student’s understanding of concepts.
- Application based questions will carry 12 marks in basic Mathematics paper.
- Questions which require analyzing, evaluation and compiling of information will carry 8 marks in Basic Maths paper.

### 32 marks

- Using Euclid’s algorithm, find the HCF of (i) 405 and 2520 (ii) 504 and 1188 (iii) 960 and 1575.
- Using prime factorization, find the HCF and LCM of (i) 72, 84 (ii) 23, 31 (iii)96, 404 (iv)144,198 (v) 396, 1080 (vi)1152, 1664
- The HCF of two numbers is 18 and their product is 12960. Find their LCM.
- Prove that 2+ 5
**√**3 is an irrational number. - The decimal expansion of 93/1500 will be (a)terminating (b) non-terminating (c) non-terminating repeating (d) non-terminating non-repeating.
- (a) Find the zeroes of the quadratic polynomial 6x^2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.(b) Find the zeroes of polynomial p(x) = (x – 1)(x – 2)
- Find a quadratic polynomial, whose zeroes are – 4 and 1, respectively.
- Find a quadratic polynomial, the sum and product of whose zeroes are – 5 and 3, respectively.
- The value of k for which (–4) is a zero of the polynomial x2 – x – (2k +2) is
- The number of zeroes of the polynomial from the graph is

- (a) A quadratic polynomial can have at most …….. zeroes. (b)A cubic polynomial can have at most …….. zeroes.
- On comparing the ratios a1/a2, b1/b2 and c1/c2 find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:(i) 5x – 4y + 8 = 0 and 7x + 6y – 9 = 0 (ii) 9x + 3y + 12 = 0 and 18x + 6y + 24 = 0 (iii) 6x – 3y + 10 = 0 and 2x – y + 9 = 0.
- (a)Find the value of k so that the following system of equations has no solution:3x – y – 5 = 0, 6x – 2y + k = 0 (b) Find the value of k so that the following system of equation has infinite solutions: 3x – y – 5 = 0, 6x – 2y + k = 0 (c) For which values of p, does the pair of equations given below has unique solution: 4x + py + 8 = 0 and 2x + 2y + 2 = 0
- Solve the following pair of linear equations: 21x + 47y = 110 ; 47x + 21y = 162
- If x = a, y = b is the solution of the equations x – y = 2 and x + y = 4, then the values of a and b are ….
- Is the pair of equations x + 2y – 3 = 0 and 6y + 3x – 9 = 0 consistent?
- Solve by elimination :3x = y + 5 ; 5x – y = 11
- The product of the zeroes of the polynomial 2×2 – 8x + 6 is
- The following figure shows the graph of y = f(x), where f(x) is a polynomial with variable x.The number of zeroes of the polynomial f(x) is

- The 10th term of the AP: 5, 8, 11, 14, … is
- The 21st term of the AP whose first two terms are –3 and 4 is
- If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?
- What is the common difference of an AP in
which
*a*18–*a*14= 32? - If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is
- Is 0 a term of the AP: 31, 28, 25, …?
- Find the value of the middle most term (s) of the AP : –11, –7, –3,…, 49.
- Find a, b and c such that the following numbers are in AP: a, 7, b, 23, c.
- The sum of the 5th and the 7th terms of an AP is 52 and the 10th term is 46. Find the AP.
- In below figure, DE || BC, the value of AD is

- In the fig., P and Q are points on the sides AB and AC respectively of ΔABC such that AP = 3.5cm, PB = 7 cm, AQ = 3 cm and QC = 6 cm. I f PQ = 4.5 cm, find BC.

- In the fig., PQ || BC and AP : PB = 1 : 2. Find
*ar(*△*APQ)/ ar(*△*ABC)*

- The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of first triangle is 9 cm., what is the corresponding side of the other triangle ?
- Find a point on the y-axis which is equidistant from the points A(6, 5) and B(– 4, 3).
- Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 10 units.
- Find the point on x-axis which is equidistant from (7, 6) and (–3, 4).
- Find the coordinates of the point which divides the line segment joining the points (4, – 3) and (8, 5) in the ratio 3 : 1 internally.
- Find the area of a triangle formed by the points A(5, 2), B(4, 7) and C (7, – 4).
- Find the value of k if the points A(2, 3), B(4, k) and C(6, –3) are collinear.
- The distance of the point P(4, –3) from the origin is
- What is the midpoint of a line with endpoints (–3, 4) and (10, –5)?
- If cot θ = 2 , find the value of all T– ratios of θ .
- Express cot 85° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.
- If tan A = cot B, prove that A + B = 90°.
- The value of sin 60° cos 30° + sin 30° cos 60° is
- (a)Find the value of sin 25° cos 65° + cos 25° sin 65° (b) Find the value of 9 sec² A – 9 tan² A.
- The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.
- A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.
- PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length TP.
- If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠POA is equal to
- From a point P, 10 cm away from the centre of a circle, a tangent PT of length 8 cm is drawn. Find the radius of the circle.
- The common point of a tangent to a circle with the circle is called _________
- Find the area of circle whose circumference is 22cm.
- To divide a line segment AB in the ratio 5:7, first a ray AX is drawn so that ∠BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is
- If the area of a circle is 154 cm², then its perimeter is
- Find the diameter of the circle whose area is equal to the sum of the areas of the two circles of diameters 20 cm and 48 cm.
- Find the diameter of the circle whose area is equal to the sum of the areas of the two circles of diameters 20 cm and 48 cm.
- Find the mean of the following data:

Class Interval | 10-25 | 25-40 | 40-55 | 55-70 | 70-85 | 85-100 |

Frequency | 2 | 3 | 7 | 6 | 6 | 6 |

- Find the mean, mode and median for the following frequency distribution.

Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | Total |

Frequency | 8 | 16 | 36 | 34 | 6 | 100 |

- Draw less than and more than ogive for the following frequency distribution:

Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |

No. of students | 8 | 5 | 10 | 6 | 6 | 6 |

Also find the median from the graph.

- For a frequency distribution, mean, median and mode are connected by the relation (a) mode = 3mean – 2median (b) mode = 2median – 3mean (c) mode = 3median – 2mean (d) mode = 3median + 2mean
- Draw a line segment of length 8 cm and divide it in the ratio 2:3
- A lot of 25 bulbs contain 5 defective ones. One bulb is drawn at random from the lot. What is the probability that the bulb is good.
- Two dice are thrown simultaneously at random. Find the probability of getting a sum of eight.
- A dice is thrown once. Find the probability of getting a prime number.
- One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (i) a king of red color (ii) a face card (iii) a red face card (iv) the jack of hearts (v) a spade (vi) the queen of diamonds
- Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is (i) 6 (ii) 12 (iii) 7
- A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (i) red ? (ii) white ?(iii) not green?
- Two dice are thrown simultaneously at random. Find the probability of getting the sum of 8.
- Two coins are tossed simultaneously. Find the probability of getting 2 heads.
- Show that tan 48° tan 23° tan 42° tan 67° = 1

### 28 marks

- Find the area of the shaded region in above right sided figure, where ABCD is a square of side 14 cm.

- Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are 4/3 times the corresponding sides of Δ ABC.
- Draw a line segment of length 7.6 cm and divide it in the ratio 3 : 4.
- From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.
- Prove that “The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.”
- State and prove Basic Proportionality theorem.
- If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.
- State and prove the Pythagoras theorem.
- Prove that the lengths of tangents drawn from an external point to a circle are equal.
- If the sum of first 14 terms of an A.P. is 1050 and its first term is 10, find the 20 th term.
- The first term of an A.P. is 5, the last term is 45 and sum is 400. Find the number of terms and the common difference.
- Solve 2x + 3y = 11 and x − 2y = −12 algebraically and hence find the value of ‘m’ for which y = mx + 3.
- Find two consecutive positive integers sum of whose squares is 365.
- An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march ?
- Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
- A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
- If tan2A = cot(A + 60°), find the value of A, where 2A is an acute angle
- Draw the graphs of the pair of linear equations x – y + 2 = 0 and 4x – y – 4 = 0 . Calculate the area of the triangle formed by the lines so drawn and the x-axis.
- Values of
*k*for which the quadratic equation 2*x*² –*kx*+*k*= 0 has equal roots is - Solve the quadratic equation using factorization method: x – 21x + 108 = 0.

### 12 marks

- For what value of k, the following system of equations 2x + ky = 1, 3x – 5y = 7 has (i) a unique solution (ii) no solution
- The cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and a pencil box.
- In a competitive examination, one mark is awarded for each correct answer while ½ mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?
- Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now?
- There are some students in the two examination halls A and B. To make the number of students equal in each hall, 10 students are sent from A to B. But if 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in the two halls.
- Find the roots of the quadratic equation using 5
*x*² + 13*x*+ 8 = 0 the quadratic formula. - Which term of the AP: 53, 48, 43,… is the first negative term?
- Find the sum of last ten terms of the AP: 8, 10, 12,—, 126.
- The fourth vertex D of a parallelogram ABCD whose three vertices are A (–2, 3), B (6, 7) and C (8, 3) is
- If the point A (2, – 4) is equidistant from P (3, 8) and Q (–10, y), find the values of y. Also find distance PQ.

### 8 marks

- Find the coordinates of the point R on the line segment joining the points P (–1, 3) and Q (2, 5) such that PR=(3/5)PQ .
- Prove that: (cosA-sinA+1)/ (cosA+ sinA-1)= cosecA + cotA
- sec A (1 – sin A)(sec A + tan A) = 1.
- The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.
- The decorative block is shown in figure made of two solids — a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block.

- A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
- A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.
- A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18m of uniform thickness. Find the thickness of the wire.
- A shuttle cock used for playing badminton has the shape of the combination of (A) a cylinder and a sphere (B) a cylinder and a hemisphere (C) a sphere and a cone (D) frustum of a cone and a hemisphere.
- Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is ….