10th Class Important Questions Mathsl(E.M)

8/13/2019 10th Class Important Questions Mathsl(E.M)

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Tenth Class Important QuestionsMathematics Paper - I

STST AA TEM ENTS A ND SETSTEM ENTS A ND SETS

Four marks questions1) Prove that A (BC) = (A B) (AC) for any three sets A, B, C.

2) Prove that A (BC) = (A B) (AC) for any three sets A, B, C.

3) Prove that A - (BC) = (A - B) (A - C) for any three sets A, B, C.4) Prove that A - (BC) = (A - B) (A - C) for any three sets A, B, C.5) A, B are two sets of a universal set , then show that (A B)' = A' B'.6) A, B are two sets of a universal set , then show that (A B)' = A' B'.

7) If p, q are two statements, prove that (p q) = p ( q).

8) If p, q are two statements, prove that (p q) = (p) (q).

Two marks questions

1) Write disjunction and its truth table.

2) Write Conjunction and its truth table.

3) Write Implication and its truth table.

4) "If x is even then x 2 is even" prove it by direct proof.

5) "If a pair of alternate angles are equal then two lines are parallel" prove it byindirect proof.

6) Let A, B are two subsets of a universal set , show that A - B' = A B7) Show that A ' - B' = B - A.8) Prove that (A

')'

= A.

9) If A B then prove that A B = A.

10) Show that A B' = A - B.One mark questions

1) Write the converse, inverse and contrapositive of the conditional statement, ''If ina triangle ABC, AB = AC then B = C'' .

2) Define tautology and give one example.

3) Define Contradiction and give one example.


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4) Show that ( p) = p.

5) If n(A B) = 51, n(A) = 20, n(B) = 44 then find n(A B).

6) Give counter example of "All prime numbers are odd".

1 1 1 1 17) Write the set builder form of A = {1, , , , , }2 3 4 5 68) If A = {all primes less than 20}, B = {all the whole numbers less than 10}, then

find A - B.9) If A B, then show that B ' A '.10) Write the conjunction and disjunction of given statements.

5 is an odd number; 5 is positive.

11) Write the symbols of the Universal quantifier and Existential quantifier.

FUNCTIONSFUNCTIONS

Four marks questions

1) Let f, g, h be functions defined by f(x) = x, g(x) = 1 x, h(x) = x + 1, then showthat ho(gof) = (hog)of.

2) Let f, g, h be functions defined by f(x) = x + 2, g(x) = 3x 1, h(x) = 2x. Showthat ho(gof) = (hog)of.

3) f(x) = x 1, g(x) = x2 2, h(x) = x3 3 x R then show that(fog)oh = fo(goh).

4) Let A = {1, 3, 5, 7 }, B = {2, 4, 6, 8 } and C = {11, 13 }. Let f : A B andg : B C be defined by f = {(1, 2), (3, 4), (5, 2), (7, 4) },g = {(2, 11), (6, 11), (4, 13), (8, 13) }, find 'gof'.

5) If f(x) = x + 2, g(x) = x2 x 2 ( x R),g(1) + g(2) + g(3)

find f (4) + f( 2) + f(2)6) Let 'f' be given by f(x) = x + 2 and f has the domain {x : 2 x 5}. Find f 1

and its domain and range.

7) Let f : R R be defind by f(x) = 2x + 3. Find f 1(4), {f 1(x) : 2 x 3},{f 1(x) : x 5}.

8) Let f : R R, g : R R be defined by f(x) = 1 + 2x, g(x) = 3 2x. Find fog(x),gof(x), fog(3) and gof(3).


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Two marks questions

x + 1 11) If f(x) = then show that f(x) + f ( )= 0 (x 0)x 1 x

f(x + h) f(x)2) Let f(x) = x2 + 2x + 3, find (h 0)

h

x + 3 3x + 33) If f : R {3} R is defined by f(x) = , show that f ( )= x for x 1.x - 3 x - 1

2x + 1 2x + 14) f : R {2} R be defined by f(x) = , show that f ( )= x.x 2 x 2

1 - x5) If f(x) = for x 1, find f(0) + f(1).

1 + x6) If f : R R be a function, f(x) = 3x + 5, find f 1.7) If f : R R be a function, f(x) = 2x + 3, show that 'f' is onto.8) If f : R R be a function, f(x) = x2 + 1, find f( x) + f(2x).9) If f = {(1, 3), (2, 5), (3, 7) } & g = {(3, 7), (5, 9), (7, 10) }, find gof.10) If f : R R be a function defined f(x) = 2x + 5, show that 'f' is one - one.

One mark questions

1) Write the conditions if f : A B function is inverse function.2) Give one example of onto function.

3) Define equal function.

4) Define one - one function.

5) Define constant function.

x + 1 16) If f : R {1} R be defined by f(x) = (x 1), find f ( ).x - 1 37) Define Bijection.

8) When 'gof' exists?

9) If f(x) = x + 2, g(x) = x3 3, find gof(3).10) Write the zeros of functions.

11) Write the domain and range of r = {(x, b), (y, b), (z, c) }.12) Define zero function.

13) Give the example if a function is one - one but not onto.14) If f(x) = x2 + 2x - 15 (x R), find f( 3).


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15) Write the domain and range of R = {(x, y)/ x = 2y, x, y N }POLYNOMIALS OVER INTEGERS

Five marks questions

1) Using graph of y = x2, solve x 2 4x + 3 = 02) Using graph of y = x2, solve x 2 x 6 = 03) Using graph of y = x2, solve x 2 + 4x + 4 = 0

4) Draw the graph of y = x2 5x + 6. Discuss about their roots.5) Draw the graph of y = 4x2 8x + 3

6) Draw the graph of y = x2 + 5x + 67) Using graph of y = x2, solve x 2 + 2x 15 = 0


51) Find the constant term in the expansion of (3x ____ )9.x22) Using the principle of mathematical induction, prove

1 1 1 1 n + + + ...... + = 1.2 2.3 3.4 n(n + 1) n + 1

3) Solve x 2 11x + 10 > 04) Solve x 2 + 9x 22 < 05) Factorize 4x 4 12x 3 + 7x2 + 3x 26) A play field is 100 m by 60 m, has a foot path all round it on the out side. What

is the width of the path if its area be 35

of the area of the play field?

7) The expansion ax 2 + bx + c equals 2 when x = 0, leaves a remainder 3 whendivided by (x 1) and a remainder 3 when divided by (x + 1). Find the valuesof a, b and c.

58) Find the constant term in the expansion of (6x2 ___ )8x29) A stream flows from A to B a distance of 30 km at a 2 km an hour, and a man can

row up and down in 8 hours find the rate of the man in still water.

x b10) Find the roots of the equation + x = + b.x a b a


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Two marks questions

1) State and prove Remainder theorem.

2) Find the remainder when x 4 + 4x3 5x2 6x + 7 divided by x + 2.3) Find the value of k so that x 3 3x2 + 4x + k is exactly divisible by x 2.4) Find the value of m so that x 4 2x3 + 3x2 mx + 6 is exactly divisible by x 3.5) Find the sum and the product of the roots of 3 x 2 + 9x + 6

3 = 0

6) Find the number which exceeds its reciprocal by 2 23.

7) Find the number which is less than its square by 132.

8) Find the roots of the equation x 2 + x(c b) + (c a)(a b) = 09) Find the middle terms in the expansion of (3x + 12x)7.10) Find the 5 th term in the expansion (2x + 13y )8.

One mark questions

1) State the Mathematical Induction.

2) Write the nature of equation 3x 2 7x + 2 = 0.3) Find the middle term of (x 1x)6.4) Write the quadratic equation whose roots are 3 +

5, 3 5 .

5) Expand a2 (b2 c2).6) State the Factors theorem.

7) One root of a equation x 2 + 5x k = 0 is 3. Find the second root and k value.8) Write the quadratic equation whose roots are 1 +

2, 1

2 .

9) Find the roots of the equation 2x 2 + 7x + 3 = 0.

10) Write the general form of a quadratic expression in single variable 'x'.

LINEAR PROGRAMMINGLINEAR PROGRAMMING

Five marks questions1) Maximise f = x + 4y subject to the constraints

8x + 5y 40, 4x + 3y 12, x 0, y 0.2) Minimise f = 5x + 7y subject to the conditions

i) x 0 ii) y 0 iii) 2x + 3y 12 iv) 3x + y 12.3) Maximise f = 2x + 3y subject to the conditions

x 0, y 0, x + y 5 & 3x + y 9.4) Minimise f = 4x + y subject to the conditions

x + y 6, 2x + y 8, x 0 & y 0.


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5) Maximise f = 2x + 3y subject to the conditions

5x + 8y 40, 5x + 4y 30, x 0 & y 0.


1) A shop keeper sells not more than 30 shirts of each colour. Atleast twice as manywhite ones are sold as green ones. If the profit on each of the white be Rs.20 andthat of green be Rs.25. How many of each kind to sold to give him a maximumprofit? (Write only conditions, objective functions)

2) A certain manufacturer has 75 kg of cashew and 120 kg of ground nuts. These areto be mixed in 1 kg packets as follows. A low grade mixture 250 grams of cashewand 750 grams of ground nuts, where as in a high grade mixture 500 gms of

cashew and 500 grams of ground nuts. If the profit on the low grade mixture isRs.2 per package and that of high grade mixture is Rs.3 per package. How manypackages of each mixture be made for a maximum profit? (Write only conditions,objective functions)

3) A sweet shop makes gift packet of sweet combines two special types of sweetsA & B which weigh 7 kg. Atleast 3 kg of 'A' and no more than 5 kg of 'B' shouldbe used. The shop makes a profit of Rs.15 on A and Rs.20 on B per kg. Determinethe product mix so as to obtain maximum profit. (Write objective functions andconditions)

Two marks questions

1) Draw 4x + 3y 12.2) Draw 2x + 3y 6.3) Indicate the polygonal region represented by the system of inequations

x 1, y 1, x 3, y 3.4) A points (vertices) of a closed convex one (0, 0), (6, 0), (4, 2 1

2), (0, 5). Maximise

f = 3x + 2y.

5) A vertices of a closed convex A(0, 0), B(3, 0), C(2, 3) & D(0, 5). Maximisef = 2x + 3y.

6) Indicate the polygonal region of x 0, y 0, x + y 1.7) At which point A (2, 4), B (0, 8), f = 4x + y is maximum?

One mark questions

1) Define convex set.

2) Define objective function.


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3) Define Feasible region.

4) Define Feasible solution.

5) Define isoprofit lines.

6) Define open convex polygon.

7) At which point (0, 120), (80, 40), F = 14 x +3

20 y is maximum?

8) Define linear programming problem.

REAL NUM BERS


1) If a1 / 3 + b

1 / 3 + c1 / 3 = 0, show that (a + b + c) 3 = 27 abc.

12) If y = 3

3 + then show that 3y 3 9y = 10.

3 3

3) If a x 1 = bc, b y 1 = ca, c z 1 = ab, show that xy + yz + zx = xyz.

1 1 1 14) If a x = b y = c z = d w and ab = cd, then show that + = + .

x y z w1

5) If lmn = 1 then show that = 11 + l + m 16) If x = 0.1, find the value of [1 (1 (1 x3)1)1]

1 / 3.

b c y 2z7) If a x = b y = c z and = , show that = .

a b x x + zLt 1 2 3

8) Show that x 2 [ ]= x 2 x(x 1)(x 2) 2(1 + x) 4 1

9) Evaluate Lt x 0 (1 + x) 3 1

110) If a = x +

x2 + 1 then show that x = (a a1).

2Two marks questions

x + a

2a

1) Evaluate Lt x a x a

1 + x + x 2 1

2) Evaluate Lt x 0 x2x 1

3) Solve 13


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x4) Solve 2 4

3

5) If a x = b, b y = c, c z = a then show that xyz = 1.

4x 36) Show that Lt = 2.

x 2x + 37) If a + b + c = 0, show that x a

2b1c1 . x a1b2c1

. x a1b1c2

= x 3.

x3 a38) Evaluate Lt

x a x 2 a2

7 x9) Solve = 10210) Simplify a x(y + z) . a y(z + x) . az(x + y)

One mark questions

1) If a 2 = 0.04, find a 3.

2) If x1 / 2 = 0.2, find x

3/2.

3) Find the value of 16 1.25

4) Simplify a2 / 3 (a1 / 3 (a1 / 4)4)

x + 125) Evaluate Lt x 4 4

2x + 36) Evaluate Lt

x 3x + 5x2 + 5x

7) Evaluate Lt x 0 x

8) If (x2 / 3)p = x 2, find 'p'.9) Simplify a

x(y z). a

y(z x). a

z(x y)

10) Find the value of x, x x = x

x, (x > 0)

PROGRESSIONSPROGRESSIONS

Four marks questions1) If 7 times the 7 th term of an AP is equal to 11 times of the 11 th term, prove that

18th term of it is zero.

2) Insert 4 arithmetic means between 3 and 23.

3) The product of two numbers is 91 and their arithmetic mean is 10. Find the two


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numbers.

4) If the sum of the first 'n' natural numbers is S 1 and that of their squares S 2 andcubes S 3, show that 9S 2

2 = S 3(1 + 8S 1).

15) Insert 5 geometric means between , 243.

3

6) If the A.M. and G.M. of two numbers are 13 and 12 respectively, find thenumbers.

7) Find the sum of 'n' terms of the series 0.5 + 0.55 + 0.555 + .... n terms.

8) Find the sum of 'n' terms of the progression 7, 77, 777, .....

9) If the mth, nth and pth terms of a G.P. form three consecutive terms of ageometric sequence, prove that m, n & p form three consecutive terms of anarithmetic sequence.

1 110) In a H.P., the 3 rd term is and the 7 th term is then show that the 15 th term

7 5

is 1.1 1 1

11) (b + c), (c + a), (a + b) are in H.P., show that , , will also be in H.P.a2 b2 c2

12) The A.M., G.M. and H.M. of two numbers are A, G, H respectively, show that

A G H.13) The sum of 6 terms which form an A.P. is 345. The difference between the first

and last term is 55. Find the 6 terms.

2 214) Insert 6 HM's between and .

3 31

15) Find the sum to n terms in the series 1.2 + 2.3 + 3.4 + ....

Two marks questions

1) If g 1, g 2, g 3 are 3 geometric means between m & n, show that g 1g3 = g22

.2) Determine k so that k + 2, 4k 6 and 3k 2 are the three consecutive terms of

an A.P.

3) Determine the 12 th term of a G.P. whose 8 th term is 192 and common ratio is 2.

4) The first term of a G.P. is 50 and the 4 th term is 1350. Determine its 5 th term.

5) Which term in the A.P., 5, 2, 1, .... is 22?6) Find the sum of all the natural numbers between 1 & 100 which are multiples of 3.

7) If a, b, c are 3 consecutive terms of an A.P., then prove that k a, k b, k c are 3

consecutive terms of a G.P., where k is positive.


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- 4 808) The common ratio of a G.P. is __ and the sum of infinity is __ . Find the5 9

first term.

9)In A.P. first term is

2 & 10

thterm is 16, then find the 15

thterm.

10) Find the sum to 'n' terms of the progression

1, 1, 1, 1, 1, .... ( 1)n + 1

One mark questions

4x 5x1) In A.P. x, , , 2x, ...., find t 12 .3 32) Evaluate

3

n = 1(n2 + 1).

20 803) In a G.P., 5, , , ....., find S .7 492 7

4) , x, are in G.P., find x.7 2

5) Find the sum of 100 terms in A.P., 2, 4, 6, 8, .....

4 3 126) Write the next two terms in the series , , , .....

3 2 7

7) 'n'th term in the A.P. is (3n + 1), then find the sum of 'n' terms.

8) Find the 'n'th term in the G.P., 100, 110, 121, ......1 19) In G.P., 1, , , ......, find S .3 9

10) Find the value of 0.234

.

W W riter: P riter: P . V . V enu Gopal enu Gopal


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Tenth Class Important QuestionsMathematics Paper - II

GEOMETRY

5 Marks Questions1) Construct the circumcircle of the triangle ABC, when BC = 6 cm, B = 55 ,

C = 70 .

2) Construct a cyclic quadrilateral ABCD in which AB = 3 cm, BC = 6 cm,AC = 4 cm and AD = 2 cm.

3) Construct the circumcircle of the triangle ABC, when AB = 4 cm, BC = 4 cm,

AC = 6 cm.4) Construct a triangle ABC in which BC = 5 cm, A = 70 and median AD

through A = 3.5 cm.

5) Construct a triangle ABC in which BC = 4 cm, A = 50 and altitude throughA = 3 cm.

6) Construct a triangle ABC in which BC = 7 cm, A = 70 and foot of theperpendicular D on BC from A is 4.5 cm away from B.

7) Construct a triangle ABC in which AB = 4.4 cm, C = 65 and median throughC = 2.7 cm.

8) Construct a cyclic quadrilateral ABCD in which AC = 4 cm, ABC = 57 .

4 Marks Questions

1) State and prove Pythagorean theorem.

2) State and prove Converse of Pythagorean theorem.

3) State and prove Thales theorem.

4) State and prove Converse of Thales theorem.

5) State and prove Vertical Angle Bisector theorem.

6) State and prove Alternate Segment theorem.

7) Prove that the ratio of the areas of two similar triangles is equal to the squaresof any two corresponding sides of the triangle.

2 Marks Questions

1) The lengths of the two tangents drawn from an external point to a circle are equal.

2) If PAB is a secant to a circle intersecting the circle of A and B and PT is atangent segment then show that PA . PB = PT 2.


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3) In a equilateral triangle with side 'a', prove that the area of the triangle is

3 a2 sq.units.4

4) ABC is a triangle in which AB = AC and 'D' is any point on BC prove thatAB 2 AD 2 = BD . CD

5) Two poles of the heights 6 m and 11 m stand vertically on a plane ground. If the

distance between their feet is 12 m. Determine the distance between their tops.

6) A ladder is placed in such a way that its foot is at a distance of 5 m from a wall

and its tip reaches a window 12 m above the ground. Determine the length of

the ladder.

7) In a ABC, AD is drawn perpendicular to BC. Prove thatAB 2 BD 2 = AC 2 CD 2.

8) ABCD is a rhombus, prove that AB 2 + BC 2 + CD 2 + DA 2 = AC 2 + BD 2.

9) Two circles are of radii 3 cm and 1 cm. The distance between their centres is

5 cm. Find the length of their transverse common tangent.

3

10) Show that altitude of a equilateral triangle is times of its side.2

1 Mark Questions1) Two circles of radii 5 cm and 12 cm touch externally. Then find the distance

between their centres.

2) There is a circle of radius 3 from a point P which is at a distance of 5 cm from

the centre of the circle, a tangent is drawn to the circle. Then find the length of

the tangent.

3) Write the properties of similar triangles.

4)Write the Converse of Pythagorean theorem.

5) Write the Thales theorem.

6) Two circles of radii 5 cm, 7 cm having 3 tangents. Then find the distance

between their centres.

7) A man goes 4 m due east and then 12 m due north. How far is be from the

starting point?

8) The perpendicular AD on the base BC of a ABC intersects at D so thatDB = 3 CD. Prove that 2 AB 2 = 2 AC 2 + BC 2.


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ANALYTICAL GEOMETRY

4 Marks Questions

1) Find the equation of a line passing through the point (5, 3) and whose sum ofthe intercepts on the coordinate axes is 5 6 .

2) Find the equation of the line which passes through the point (1, 6) and whoseproduct of the intercepts on the coordinate axis is 1.

3) Find the equation of the line that cuts off intercepts 'a' and 'b' on the X andY - axes such that a + b = 3, ab = 2.

4) Find the area of the triangle enclosed between the coordinate axes and the line

passing through (8, 3) and ( 4, 12).5) Find the equation of a line whose slope is 4 5 and which bisects the line join-

ing the points P(1, 2) and Q(4, 3).6) Find the equation of the line passing through (4, 3) and is perpendicular to the

line 2x - 5y + 4 = 0.7) Find the equation of a line passing through (4, 3) and making intercepts on the

coordinate axes whose sum is equal to -1.

3 7 58) If the three points A

(2,

)B

(3,

)C

(x,

)are collinear.

2 , 2 , 2Find the value of x.

9) If the area of the triangle formed with the vertices (t, 2t), ( 2, 6), (3, 1) is5 sq.units. Find t?

10) Show that the points A(1, 2), B( 3, 4), C(7, 1) are collinear and find the ratioin which A divides BC.

11) Find the coordinates of the points of trisection of a segment joining A( 3, 2)and B(9, 5).

12) If the three points A(p, 2), B( 3, 4) and C(7, 1) are collinear. Find the value of p.

13) If the distance between (4, 0) and (a, b) is twice the distance between (0, 0) and(a, b). Find the relation between a and b.

14) Show that ( 3, 4), (12, 5), (14, 12), ( 1, 3) are the vertices of a parallelogram.15) The point (1, 4) is the centroid of a triangle, two of whose vertices are (4, 8)

and ( 9, 7). Find the area of the triangle.


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2 Marks Questions

1) In what ratio is the segment joining the points ( - 3, 2) and (6, 1) divided byY - axis.

2) Find the intercepts made by 3x + 4y = 12 on the coordinate axes.

3) Find the coordinates of the centroid of the triangle whose vertices are

(4, 4), ( 2, 2) and (6, 12).4) Find the equation of the line passing through the point (3, 5) and whose

7slope is .

3

5) Find the point on X - aixs that is equidistant from (2, 3) & (4, 2).6) In what ratio does P (4, 6) divide the join of A( 2, 3) & B(6, 7).7) If A = (2, 5), B = (x, 7), find the possible values of x so that AB = 13.8) Find the area of the triangle enclosed between the coordinate axes and the line

joining points (4, 0) and (0, 5).

9) If P(6, 1), Q(1, 3), R(x, 8), find the value of x, so that PQ = QR.10) Find the equation of the line passing through the points (4, 7) and (1, 5).

Determine the intercepts made by this line on coordinate axes.

11) Find the equation of the line passing through (1, 2) and is parallel to

4x 5y + 3 = 0.1 Mark Questions

1) If A (7, 5), B (2, 4), C (6, 10) then show that AB = AC.

2) Find the coordinates of the centre of the circle having the points (9, 3) and(1, 1) as the end points of the diameter.

3) Find the point of intersection of the medians of a triangle whose vertices are(1, 0), (5, 2) and (8, 2).

4) Find the equation of a line which makes an angle 135 with the positivedirection of X - axis and making an intercept of 3 units on Y - axis.

5) Find the equation of the line making an angle 150 with positive direction ofX - axis and having Y - intercept 3.

6) A straight line makes intercepts 4 and 7 on X and Y - axis. What is theequation of that line?

7) One end of the diameter of a circle is (2, 3) and the centre is ( 2, 5). Find thecoordinates of the other end of the diameter.

8) Find the slope of a line perpendicular to 5x - 2y + 4 = 0.


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15 15 cot + 17 sin 6) If sin = , evaluate

17 8 tan + 16 sec cos 2 cos 2

7) Show that tan2

tan2

=

.cos 2 . cos 2 cos cos

8) Solve + = 4.1 sin 1 + sin cos 2 3 cos + 2

9) Solve = 1.sin2

2 Marks Questions

m + n1) If sec = then find sin .2 mn2) Eliminate ' ' from x = a sec , y = b tan .

43) If cos = then find the value of sec tan .

5

4) Show that sec 2 + cosec 2 = sec 2 . cose 2 5) Find the value of sin 420 .

3

6) If cos = then find 4 sin 2 + tan 2 .2

1 17) If tan(A B) = , sin A = , find B in circular measure.

3

2

8) Find the value of cos 0 + sin 90 + 2 sin 45 .

9) If 5 sin A = 3, find the value of sec 2 A tan2 A.

10) Show that tan 2 + cot 2 + 2 = sec 2 . cosec 2

1 Mark Questions

1) Find the value of cot 240 .

2) Eliminate from x = a sin , y = b tan 12

3) If sin = then find cos .13

4) Find the value of sin 2 30 + cos 2 60.

5) Find the value of tan 2 45 + 2 tan 2 60.

6) The angle of depression of a point 100 mts from the foot of the tree is 60 . Find

the height of the tree.


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1 tan2 307) Show that = cos 60 .

1 + tan 2 30

8) Find the value of cos 45 . sin 30 + sin 45 . cos 30

9) Eliminate ' ' from x = cosec + cot , y = cosec - cot .10) Change the 270 into circular measure.

11) Show tan interms of cos .

STATISTICS

4 Marks Questions

1) Calculate the A.M. of the following distribution by short - cut method.

CI 0 - 19 20 - 39 40 - 59 60 - 79 80 - 99 100 - 119

f 9 16 24 15 4 2

2) The mean of the following frequency table is 50. But the frequencies f 1 & f 2 inclasses 20 - 40 & 60 - 80 are missing.

Find the missing frequencies.

CI 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 Total

f 17 f 1 32 f 2 19 100

3) Find the median of the marks scored by 50 students in 50 marks test.

Marks 1 - 10 11 - 20 21 - 30 31 - 40 41 - 50

Students 3 12 16 14 5

4) Find the mode of the frequency distribution given below.

CI 30 - 39 40 - 49 50 - 59 60 - 69 70 - 79 80 - 89

f 2 3 20 17 10 4

2 Marks Questions1) The mean of 11 observations is 17.5. If an observation 15 is deleted. Find the

mean of the remaining observations.

2) Write the merits of A.M.

3) The mean of 10 observations is 16.3. By an error, one observation is registered as32 instead of 23. Find the correct mean.

4) Observations of some data are x4

, x, x5

, x3,x2

(x > 0). If the median of the datais 5. Find the value of x.


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5) Find the mean of 25

, 53

, 13

, 56

& 16

.

6) The mean and median of a unimodal grouped data are 39 & 38. Find the mode of the data.

7) Write the formula of grouped data of median and explain.

8) Find the median of 15 23

, 15.03, 15, 15 13

, 15.3.

1 Mark Questions

1) Find the range of first 'n' natural numbers.

2) Find the mean of first 'n' natural numbers.

3) Write the empirical relationship between Mean, Median and Mode.

4) The sum of 15 observations of a data is 420. Find the mean.5) Mean of 9, 11, 13, P, 18, 19 is P, then find P?

6) The observations of an ungrouped data are x, y & 2x and x < y < 2x. If the Meanand Median of the data are each equal to 6. Find the observations of the data.

7) Find the Mode of 3, 8, 6, 3, 4, 5, 3, 6, 7, 8, 3.

8) Find the Median of 3, 5, 8, 0, 3, 2, 10.9) Find the value of x, if Median of arranged in ascending order is 12, 15, x, 19, 25

is 18.10) Find the range of 10, 18, 37, 42, 3, 12, 15, 26.

MATRICES

4 Marks Questions

1) Solve the simultaneous equations using matrix inverse method

2x + 5y = 11, 4x 3y = 92) Solve a 1x + b1y + c1 = 0, a 2x + b2y + c2 = 0 using matrix inverse method.

3) Solve 3x + 4y 5 = 0, x 2y + 6 = 0 using matrix inverse method.7 3y

4) Solve x = , y = 13 6x by using matrix inverse method.2

5) Solve x + 5y = 17, 5x + y = 13 using Cramer's method.

6) Solve 2x 3y + 4 = 0, 6x + y + 8 = 0 using Cramer's method.a b 1 0

7) If A = ( ), I = ( )then show that A 2 (a + d) A = (bc ad)I.c d 0 12 4 - 2 5 1 2

8) If A = ( ), B = ( )C = ( )then show that A(B + C) = AB + AC.3 0 6 1 3 0


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2 1 2 09) If A = ( ), B = ( ), find (i) (AB) 1 (ii) B 1 A1. What do you infer?3 1 5 31 4 2 m

10) If A = ( ), B = ( ), AB = BA then find m.0 1 0 1 21 1 a 111) Given that A = ( ), B = ( )and (A + B)2 = A2 + B2, find a & b.2 1 b 1

2 Marks Questions2 31) Find the value of x & y if (x y) ( )= (6 10).0 1

1 22) If M

( )= (2 3) find the order of M and determine the matrix M.

0 51 2

3) If A = ( )then show that A + A1 = 4I.1 31 3 2 p4) If ( ) ( )= ( )then find p.0 1 1 1

3 15) Find X, given that X + 2I = ( )1 22 4 2 5 1 26) If A =

( ), B =

( ), C =

( )find A 2 + BC.

3 6 6 1 3 07 47) If A = ( ), find A 1 & show that AA 1 = A1 A = I.5 30 0 1 08) If A = ( ), B = ( ), find AB & BA.1 0 0 0

1 Mark Questions1 3

1) If A = ( )then find A 2.2 11 4

2) If A = ( )then show that A = A1.0 11 33) If A = ( )then find A + AT.5 6

2a 54) If = 0 then find a.6 3


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d 2 55) If = 0, find d.4 2

2 4 4 36) If A = ( ), B = ( )then find 3A + 2B.6 5 5 73 4 a b 1 0

7) If ( )= ( ) ( ), find the values of a, b, c, d.2 5 c d 0 112 7 48) If A = ( ), B = ( )& AP = B then find P.1 8 11 29) If A = ( )then find A + A1.0 3

10) Define Singular Matrix.COMPUTING

4 Marks Questions1) Gopal purchased a radio set for Rs. 500 and sold it for Rs. 600. Execute flow chart

using this data to determine loss or gain.

2) Execute flow chart for P = Rs. 2000, r = 10%, n = 5 years, find compoundinterest.

3) Draw flow chart for solving an equation ax 2 + bx + c = 0 by considering allpossible cases.

4) Draw a flow chart to pick the largest of the three given numbers.

5) Draw a flow chart to compute the sum of the first 100 natural numbers.

2 Marks Questions

1) Write the historic development of computers.

2) Explain the structure of a computer by means of a block diagram.

3) List the essential components of a computer.

4) Write the characteristics of a computer.

5) Define Algorithm.

6) Define flow chart.

7) What are the different boxes used in a flow chart?

8) What should be kept in mind while writing an algorithm?


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1 Mark Questions1) In flow chart what is the decision box shape?

2) In flow chart, what is the shape of end box?

3) Write any 4 computer languages.

4) Expand CPU.

5) Write the parts in CPU.

6) What is meant by Hardware.

1P P .. V EN U G O P V EN U G O P A LA L

10th Class Important Questions Mathsl(E.M)

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