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.
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
What is the common difference of an AP in
which a18– a14= 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
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,
Find the value of k if the points A(2, 3), B(4, k) and C(6, –3) are
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
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:
Find the mean, mode and median for the following frequency distribution.
Draw less than and more than ogive for the following frequency
No. of students
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
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 2x² – kx + k = 0 has equal roots is
Solve the quadratic equation using factorization method: x – 21x + 108 = 0.
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 5x² + 13x + 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.
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 .
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 ….