32581 + Interview Questions in Mathematics

1.	The highest amount given by SAI is
Answer» The highest amount given by SAI is

Discussion

2.	Which of the following fraction(s) is/are non terminating?
Answer» Which of the following fraction(s) is/are non terminating?

Discussion

3.	In the given figure, QR is parallel to AB and DR is parallel to QB. If PD = 4 cm and PA = 9 cm, then PQ = ____.
Answer» In the given figure, QR is parallel to AB and DR is parallel to QB. If PD = 4 cm and PA = 9 cm, then PQ = ____.

3.

In the given figure, QR is parallel to AB and DR is parallel to QB. If PD = 4 cm and PA = 9 cm, then PQ = ____.

Answer»

In the given figure, QR is parallel to AB and DR is parallel to QB. If PD = 4 cm and PA = 9 cm, then PQ = ____.

Discussion

4.	Prove that, of any two chords of a circle, the greater chord is nearer to the centre.
Answer» Prove that, of any two chords of a circle, the greater chord is nearer to the centre.

Discussion

5.	tan2A-sin2A=tan2AsinA2
Answer» tan²A-sin²A=tan²AsinA²

Discussion

6.	Which of the following fraction is a terminating decimal?
Answer» Which of the following fraction is a terminating decimal?

Discussion

7.	In teh figure; PA is a tangent to the circle, PBC is secant and AD bisects angle BAC. Show that triangle PAD is an isosceles triangle. Also, show that : ∠CAD=12[∠PBA−∠PAB]
Answer» In teh figure; PA is a tangent to the circle, PBC is secant and AD bisects angle BAC. Show that triangle PAD is an isosceles triangle. Also, show that : $∠ C A D = \frac{1}{2} [∠ P B A - ∠ P A B]$

7.

In teh figure; PA is a tangent to the circle, PBC is secant and AD bisects angle BAC. Show that triangle PAD is an isosceles triangle. Also, show that : ∠CAD=12[∠PBA−∠PAB]

Answer»

In teh figure; PA is a tangent to the circle, PBC is secant and AD bisects angle BAC. Show that triangle PAD is an isosceles triangle. Also, show that :

$∠ C A D = \frac{1}{2} [∠ P B A - ∠ P A B]$

Discussion

8.	A man watches his friend swimming in his apartment swimming pool from the roof of the building which is 50 m high. When the swimmer was at one end, the angle of depression was 40∘. When the swimmer reaches the other end, the angle of depression changes to 65∘. The distance covered by the swimmer is [Tan 65∘=2.14, Tan 40∘=0.83]
Answer» A man watches his friend swimming in his apartment swimming pool from the roof of the building which is 50 m high. When the swimmer was at one end, the angle of depression was $40^{\circ}$ . When the swimmer reaches the other end, the angle of depression changes to 65 $^{\circ}$ . The distance covered by the swimmer is $[T a n 65^{\circ} = 2.14, T a n 40^{\circ} = 0.83]$

8.

A man watches his friend swimming in his apartment swimming pool from the roof of the building which is 50 m high. When the swimmer was at one end, the angle of depression was 40∘. When the swimmer reaches the other end, the angle of depression changes to 65∘. The distance covered by the swimmer is [Tan 65∘=2.14, Tan 40∘=0.83]

Answer»

A man watches his friend swimming in his apartment swimming pool from the roof of the building which is 50 m high. When the swimmer was at one end, the angle of depression was $40^{\circ}$ . When the swimmer reaches the other end, the angle of depression changes to 65 $^{\circ}$ . The distance covered by the swimmer is

$[T a n 65^{\circ} = 2.14, T a n 40^{\circ} = 0.83]$

Discussion

9.	Enter the number of points that are to be marked on a ray drawn at an acute angle to one of its sides, to construct a triangle similar to a given triangle with a scale factor 35.5
Answer» Enter the number of points that are to be marked on a ray drawn at an acute angle to one of its sides, to construct a triangle similar to a given triangle with a scale factor $\frac{3}{5}$ . 5

Discussion

10.	On a particular day, at a crossing in a city, the various types of 240 vehicles going past during a time interval were observed as under: Type of vehicleTwo-wheelersThree-wheelersFour-wheelersFrequency846888 Out of these vehicles, one is chosen at random. What is the probability that the chosen vehicle is a two-wheeler?
Answer» On a particular day, at a crossing in a city, the various types of 240 vehicles going past during a time interval were observed as under: $\begin{matrix} Type of vehicle & Two-wheelers & Three-wheelers & Four-wheelers Frequency & 84 & 68 & 88 \end{matrix}$ Out of these vehicles, one is chosen at random. What is the probability that the chosen vehicle is a two-wheeler?

10.

On a particular day, at a crossing in a city, the various types of 240 vehicles going past during a time interval were observed as under: Type of vehicleTwo-wheelersThree-wheelersFour-wheelersFrequency846888 Out of these vehicles, one is chosen at random. What is the probability that the chosen vehicle is a two-wheeler?

Answer»

On a particular day, at a crossing in a city, the various types of 240 vehicles going past during a time interval were observed as under:
$\begin{matrix} Type of vehicle & Two-wheelers & Three-wheelers & Four-wheelers Frequency & 84 & 68 & 88 \end{matrix}$

Out of these vehicles, one is chosen at random. What is the probability that the chosen vehicle is a two-wheeler?

Discussion

11.	Question 5 The class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular lawn in the plot as shown in the figure. The students are to sow the seeds of flowering plants on the remaining area of the plot. (a) Taking A as origin, find the coordinates of the vertices of the triangle. (b) What will be the coordinates of the vertices of triangle PQR if C is the origin. (c) Also calculate the areas of the triangles in these cases. What do you observe?
Answer» Question 5 The class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular lawn in the plot as shown in the figure. The students are to sow the seeds of flowering plants on the remaining area of the plot. (a) Taking A as origin, find the coordinates of the vertices of the triangle. (b) What will be the coordinates of the vertices of triangle PQR if C is the origin. (c) Also calculate the areas of the triangles in these cases. What do you observe?

Discussion

12.	While jogging on a straight road, Ann covers 300 m towards east in 2 minutes 50 seconds. Then, she turned around and jogs for 1 minute covering a distance of 100 m. Calculate average speed and average velocity. [2 MARKS]
Answer» While jogging on a straight road, Ann covers 300 m towards east in 2 minutes 50 seconds. Then, she turned around and jogs for 1 minute covering a distance of 100 m. Calculate average speed and average velocity. [2 MARKS]

Discussion

13.	Question 2 Simplify: 7√3√10+√3−2√5√6+√5−3√2√15+3√2
Answer» Question 2 Simplify: $\frac{7 \sqrt{3}}{\sqrt{10} + \sqrt{3}} - \frac{2 \sqrt{5}}{\sqrt{6} + \sqrt{5}} - \frac{3 \sqrt{2}}{\sqrt{15} + 3 \sqrt{2}}$

Discussion

14.	The midpoint of line segment joining A(2,3) and B(4,5) lies on the curve.
Answer» The midpoint of line segment joining A(2,3) and B(4,5) lies on the curve.

Discussion

15.	Mr. Sharma has 60 shares of nominal value of ₹ 100 and he decides to sell them when they are a premium of 60 %. He invests the proceeds in shares of nominal value ₹ 50, quoted at 4 % discount, paying 18% dividend annually. Calculate : (i) the sale proceeds (ii) the number of shares he buys (iii) his annual dividend from these shares
Answer» Mr. Sharma has 60 shares of nominal value of ₹ 100 and he decides to sell them when they are a premium of 60 %. He invests the proceeds in shares of nominal value ₹ 50, quoted at 4 % discount, paying 18% dividend annually. Calculate : (i) the sale proceeds (ii) the number of shares he buys (iii) his annual dividend from these shares

15.

Mr. Sharma has 60 shares of nominal value of ₹ 100 and he decides to sell them when they are a premium of 60 %. He invests the proceeds in shares of nominal value ₹ 50, quoted at 4 % discount, paying 18% dividend annually. Calculate : (i) the sale proceeds (ii) the number of shares he buys (iii) his annual dividend from these shares

Answer»

Mr. Sharma has 60 shares of nominal value of ₹ 100 and he decides to sell them when they are a premium of 60 %. He invests the proceeds in shares of nominal value ₹ 50, quoted at 4 % discount, paying 18% dividend annually. Calculate :

(i) the sale proceeds

(ii) the number of shares he buys

(iii) his annual dividend from these shares

Discussion

16.	Solve the inequation, 3x - 4 < 2x + 1 ≤ 5x + 7, x ∈ R and graph the solution set.
Answer» Solve the inequation, 3x - 4 < 2x + 1 ≤ 5x + 7, x ∈ R and graph the solution set.

16.

Solve the inequation, 3x - 4 < 2x + 1 ≤ 5x + 7, x ∈ R and graph the solution set.

Answer»

Solve the inequation,

3x - 4 < 2x + 1 ≤ 5x + 7, x ∈ R and graph the solution set.

Discussion

17.	A person deposited Rs. 5000 in his saving account. The amount is set to increase by (110)th of itself every two years. What would be the maturity amount (in Rs.) of investment after the 2nd, 4th, 6th and 8th year respectively? Are these in AP?
Answer» A person deposited Rs. 5000 in his saving account. The amount is set to increase by $(\frac{1}{10})_{t h}$ of itself every two years. What would be the maturity amount (in Rs.) of investment after the $2^{n d}$ , $4^{t h}$ , $6^{t h}$ and $8^{t h}$ year respectively? Are these in AP?

Discussion

18.	How many possibilities are depicted in the Punnett square in the F2 generation of a dihybrid cross?
Answer» How many possibilities are depicted in the Punnett square in the F2 generation of a dihybrid cross?

Discussion

19.	Given the angles of a triangle are in A.P with a common difference equal to the smallest angle. Find the value of cosA X cosB X cosC, where A, B and C are the angles of the triangle.
Answer» Given the angles of a triangle are in A.P with a common difference equal to the smallest angle. Find the value of cosA X cosB X cosC, where A, B and C are the angles of the triangle.

Discussion

20.	Question 13 In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π=3.14)
Answer» Question 13 In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. $(U s e π = 3.14)$

20.

Question 13 In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π=3.14)

Answer»

Question 13
In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. $(U s e π = 3.14)$

Discussion

21.	The positive value of 'm' for which (m + 4)x2 - 2mx + (m - 3) = 0 has equal roots is
Answer» The positive value of 'm' for which (m + 4)x² - 2mx + (m - 3) = 0 has equal roots is

Discussion

22.	Question 1 (iv) Evaluate : cosec31∘−sec59∘
Answer» Question 1 (iv) Evaluate : $c o s e c 31^{\circ} - s e c 59^{\circ}$

Discussion

23.	Question 6 In figure, ABCD is a trapezium with AB∥DC. AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. If arcs of equal radii 7 cm with centres A, B, C and D have been drawn , then find the area of the shaded region of the figure.
Answer» Question 6 In figure, ABCD is a trapezium with $A B ∥ D C$ . AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. If arcs of equal radii 7 cm with centres A, B, C and D have been drawn , then find the area of the shaded region of the figure.

Discussion

24.	For determining median from ogive curves , S1 : one can use less than type curve. S2 : one can use more than type curve.
Answer» For determining median from ogive curves , S1 : one can use less than type curve. S2 : one can use more than type curve.

24.

For determining median from ogive curves , S1 : one can use less than type curve. S2 : one can use more than type curve.

Answer»

For determining median from ogive curves ,

S1 : one can use less than type curve.

S2 : one can use more than type curve.

Discussion

25.	If √2 & −√2 are zeroes of x4−11x2+18 find the other zeroes. [3 MARKS]
Answer» If $\sqrt{2} & - \sqrt{2}$ are zeroes of $x^{4} - 11 x^{2} + 18$ find the other zeroes. [3 MARKS]

Discussion

26.	Question 2 The point P(- 4, 2) lies on the line segment joining the points A(-4, 6) and B(-4,-6).
Answer» Question 2 The point P(- 4, 2) lies on the line segment joining the points A(-4, 6) and B(-4,-6).

Discussion

27.	If a line segment is drawn between the points (5,-3) and (5,4) then find the coordinates of the point on the same segment which is 3 units from (5,4)
Answer» If a line segment is drawn between the points (5,-3) and (5,4) then find the coordinates of the point on the same segment which is 3 units from (5,4)

Discussion

28.	If x=0.¯¯¯¯¯¯18, which of the following statements are true? (i) 100x=18.¯¯¯¯¯¯18 (ii) 100x−x=17.¯¯¯¯¯¯18 (iii) 99x=18
Answer» If $x = 0. ¯ ¯¯¯¯ ¯ 18$ , which of the following statements are true? (i) $100 x = 18. ¯ ¯¯¯¯ ¯ 18$ (ii) $100 x - x = 17. ¯ ¯¯¯¯ ¯ 18$ (iii) $99 x = 18$

Discussion

29.	Question 7 If two positive integers p and q can be expressed as p = ab2 and q=a3b; where a, b being prime numbers, then LCM (p, q) is equal to A) ab B) a2b2 C) a3b2 D) a3b3
Answer» Question 7 If two positive integers p and q can be expressed as p = $a b^{2} a n d q = a^{3} b$ ; where a, b being prime numbers, then LCM (p, q) is equal to A) $a b$ B) $a^{2} b^{2}$ C) $a^{3} b^{2}$ D) $a^{3} b^{3}$

Discussion

30.	Two parallel lines touch a circle at points A and B respectively. The area of the circle is 25π cm2, then the distance between the lines is
Answer» Two parallel lines touch a circle at points A and B respectively. The area of the circle is 25 $π$ ${c m}^{2}$ , then the distance between the lines is

Discussion

31.	Question 42(i) At a fete, cards bearing numbers 1 to 1000, one number on one card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square greater than 500, the player wins a prize. What is the probability that the first player wins a prize?
Answer» Question 42(i) At a fete, cards bearing numbers 1 to 1000, one number on one card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square greater than 500, the player wins a prize. What is the probability that the first player wins a prize?

Discussion

32.	It is 260 km from Patna to Ranchi by air and 320 km by road. An airplane takes 30 minutes to go from Patna to Ranchi whereas a deluxe bus takes 8 hours. Find the average speed of the plane in km/hr.
Answer» It is $260 km$ from Patna to Ranchi by air and $320 km$ by road. An airplane takes 30 minutes to go from Patna to Ranchi whereas a deluxe bus takes 8 hours. Find the average speed of the plane in $km/hr$ .

Discussion

33.	From a thin metallic piece, in the shape of a trapezium ABCD, in which AB∥CD and ∠BCD=90∘, a quarter circle BEFC is removed. Given AB = BC = 3.5 cm and DE = 2 cm, calculate the area of the remaining piece of the metal sheet.
Answer» From a thin metallic piece, in the shape of a trapezium ABCD, in which $A B ∥ C D$ and $∠ B C D = 90^{\circ}$ , a quarter circle BEFC is removed. Given AB = BC = 3.5 cm and DE = 2 cm, calculate the area of the remaining piece of the metal sheet.

33.

From a thin metallic piece, in the shape of a trapezium ABCD, in which AB∥CD and ∠BCD=90∘, a quarter circle BEFC is removed. Given AB = BC = 3.5 cm and DE = 2 cm, calculate the area of the remaining piece of the metal sheet.

Answer»

From a thin metallic piece, in the shape of a trapezium ABCD, in which $A B ∥ C D$ and $∠ B C D = 90^{\circ}$ , a quarter circle BEFC is removed. Given AB = BC = 3.5 cm and DE = 2 cm, calculate the area of the remaining piece of the metal sheet.

Discussion

34.	A number is selected at random from the numbers 1 to 30. What is the probability that the selected nummber is a prime number ? (a) 23 (b) 916 (c) 13 (d) 1130
Answer» A number is selected at random from the numbers 1 to 30. What is the probability that the selected nummber is a prime number ? (a) $\frac{2}{3}$ (b) $9 \frac{1}{6}$ (c) $\frac{1}{3}$ (d) $\frac{11}{30}$

Discussion

35.	Question 41(ii) A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at random. What is the probability that it is white?
Answer» Question 41(ii) A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at random. What is the probability that it is white?

Discussion

36.	In triangle ABC, right angled at B, if ∠A is made larger and larger till it becomes 90∘, find the value of Sin A and Cos A.
Answer» In triangle ABC, right angled at B, if $∠$ A is made larger and larger till it becomes $90^{\circ}$ , find the value of Sin A and Cos A.

Discussion

37.	The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is (a) 7 (b) 14 (c) 21 (d) 28
Answer» The probability of getting a bad egg in a lot of $400$ is $0.035$ . The number of bad eggs in the lot is (a) $7$ (b) $14$ (c) $21$ (d) $28$

Discussion

38.	Using componendo and dividendo find out the value of x. √3x+4+√3x−5√3x+4−√3x−5=9
Answer» Using componendo and dividendo find out the value of x. $\frac{\sqrt{3 x + 4} + \sqrt{3 x - 5}}{\sqrt{3 x + 4} - \sqrt{3 x - 5}} = 9$

Discussion

39.	Given that HCF (26 , 91) = 13, then LCM of (26 , 91) is :
Answer» Given that HCF (26 , 91) = 13, then LCM of (26 , 91) is :

Discussion

40.	From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and of base radius 7 cm is drilled out. Find the volume and the total surface of the remaining solid. [4 MARKS]
Answer» From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and of base radius 7 cm is drilled out. Find the volume and the total surface of the remaining solid. [4 MARKS]

Discussion

41.	Question 7 Using Basic proportionality theorem, prove that a line drawn through the mid-points of one side of a triangle parallel to another side bisects the third side.
Answer» Question 7 Using Basic proportionality theorem, prove that a line drawn through the mid-points of one side of a triangle parallel to another side bisects the third side.

Discussion

42.	One of the diagonals of a rhombus of side 20 cm is 24 cm. The length of other diagonal is equal to
Answer» One of the diagonals of a rhombus of side 20 cm is 24 cm. The length of other diagonal is equal to

Discussion

43.	If A(5, 3), B(11, -5) and P(12, y) are the vertices of a right triangle, right angled at P, then y is equal to
Answer» If A(5, 3), B(11, -5) and P(12, y) are the vertices of a right triangle, right angled at P, then y is equal to

Discussion

44.	A(h,-6) , B(2,3) and C(-6,k) are co-ordinates of vertices of a triangle whose centroid is G(1,5). What is the values of (h - k)?-11
Answer» A(h,-6) , B(2,3) and C(-6,k) are co-ordinates of vertices of a triangle whose centroid is G(1,5). What is the values of (h - k)? -11

Discussion

45.	Calculate the median from the following data: Height135−140140−145145−150150−155155−160160−165165−170170−175(in cm)No. of6101822201563boys
Answer» Calculate the median from the following data: $\begin{matrix} Height & 135 - 140 & 140 - 145 & 145 - 150 & 150 - 155 & 155 - 160 & 160 - 165 & 165 - 170 & 170 - 175 (in cm) No. of & 6 & 10 & 18 & 22 & 20 & 15 & 6 & 3 boys \end{matrix}$

Discussion

46.	ABCD is a rectangle having length 30 cm and breadth 25 cm. P, Q, R and S are the midpoints of line segments AB, BC, CD and AD respectively. What is the area of the shaded part?
Answer» ABCD is a rectangle having length 30 cm and breadth 25 cm. P, Q, R and S are the midpoints of line segments AB, BC, CD and AD respectively. What is the area of the shaded part?

Discussion

47.	The height of hill is 150 metres. From the top of the hill the angle of depression of two objects lying towards east of the hill are 45∘ and 30∘. Find the distance between the objects.
Answer» The height of hill is 150 metres. From the top of the hill the angle of depression of two objects lying towards east of the hill are $45^{\circ} a n d 30^{\circ}$ . Find the distance between the objects.

Discussion

48.	A circle of radius R is circumscribing a triangle ABC, having ∠A=30∘, & BC = 20 cm. Then the radius 'R' is equal to [sin 30∘=0.5]
Answer» A circle of radius R is circumscribing a triangle ABC, having $∠ A = 30^{\circ}$ , & BC = 20 cm. Then the radius 'R' is equal to $[s i n 30^{\circ} = 0.5]$

48.

A circle of radius R is circumscribing a triangle ABC, having ∠A=30∘, & BC = 20 cm. Then the radius 'R' is equal to [sin 30∘=0.5]

Answer»

A circle of radius R is circumscribing a triangle ABC, having $∠ A = 30^{\circ}$ , & BC = 20 cm. Then the radius 'R' is equal to $[s i n 30^{\circ} = 0.5]$

Discussion

49.	Question 7 A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.
Answer» Question 7 A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

Discussion

50.	Find the length of altitude AD of an isosceles ΔABC in which AB = AC = 2a units and BC = a units.
Answer» Find the length of altitude AD of an isosceles $Δ A B C$ in which AB = AC = 2a units and BC = a units.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The highest amount given by SAI is

Which of the following fraction(s) is/are non terminating?

In the given figure, QR is parallel to AB and DR is parallel to QB. If PD = 4 cm and PA = 9 cm, then PQ = ____.

Prove that, of any two chords of a circle, the greater chord is nearer to the centre.

tan2A-sin2A=tan2AsinA2

Which of the following fraction is a terminating decimal?

In teh figure; PA is a tangent to the circle, PBC is secant and AD bisects angle BAC. Show that triangle PAD is an isosceles triangle. Also, show that : ∠CAD=12[∠PBA−∠PAB]

Enter the number of points that are to be marked on a ray drawn at an acute angle to one of its sides, to construct a triangle similar to a given triangle with a scale factor 35.5

While jogging on a straight road, Ann covers 300 m towards east in 2 minutes 50 seconds. Then, she turned around and jogs for 1 minute covering a distance of 100 m. Calculate average speed and average velocity. [2 MARKS]

Question 2 Simplify: 7√3√10+√3−2√5√6+√5−3√2√15+3√2

The midpoint of line segment joining A(2,3) and B(4,5) lies on the curve.

Solve the inequation, 3x - 4 &lt; 2x + 1 ≤ 5x + 7, x ∈ R and graph the solution set.

A person deposited Rs. 5000 in his saving account. The amount is set to increase by (110)th of itself every two years. What would be the maturity amount (in Rs.) of investment after the 2nd, 4th, 6th and 8th year respectively? Are these in AP?

How many possibilities are depicted in the Punnett square in the F2 generation of a dihybrid cross?

Given the angles of a triangle are in A.P with a common difference equal to the smallest angle. Find the value of cosA X cosB X cosC, where A, B and C are the angles of the triangle.

Question 13 In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π=3.14)

The positive value of 'm' for which (m + 4)x2 - 2mx + (m - 3) = 0 has equal roots is

Question 1 (iv) Evaluate : cosec31∘−sec59∘

Question 6 In figure, ABCD is a trapezium with AB∥DC. AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. If arcs of equal radii 7 cm with centres A, B, C and D have been drawn , then find the area of the shaded region of the figure.

For determining median from ogive curves , S1 : one can use less than type curve. S2 : one can use more than type curve.

If √2 &amp; −√2 are zeroes of x4−11x2+18 find the other zeroes. [3 MARKS]

Question 2 The point P(- 4, 2) lies on the line segment joining the points A(-4, 6) and B(-4,-6).

If a line segment is drawn between the points (5,-3) and (5,4) then find the coordinates of the point on the same segment which is 3 units from (5,4)

If x=0.¯¯¯¯¯¯18, which of the following statements are true? (i) 100x=18.¯¯¯¯¯¯18 (ii) 100x−x=17.¯¯¯¯¯¯18 (iii) 99x=18

Question 7 If two positive integers p and q can be expressed as p = ab2 and q=a3b; where a, b being prime numbers, then LCM (p, q) is equal to A) ab B) a2b2 C) a3b2 D) a3b3

Two parallel lines touch a circle at points A and B respectively. The area of the circle is 25π cm2, then the distance between the lines is

It is 260 km from Patna to Ranchi by air and 320 km by road. An airplane takes 30 minutes to go from Patna to Ranchi whereas a deluxe bus takes 8 hours. Find the average speed of the plane in km/hr.

From a thin metallic piece, in the shape of a trapezium ABCD, in which AB∥CD and ∠BCD=90∘, a quarter circle BEFC is removed. Given AB = BC = 3.5 cm and DE = 2 cm, calculate the area of the remaining piece of the metal sheet.

A number is selected at random from the numbers 1 to 30. What is the probability that the selected nummber is a prime number ? (a) 23 (b) 916 (c) 13 (d) 1130

Question 41(ii) A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at random. What is the probability that it is white?

In triangle ABC, right angled at B, if ∠A is made larger and larger till it becomes 90∘, find the value of Sin A and Cos A.

The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is (a) 7 (b) 14 (c) 21 (d) 28

Using componendo and dividendo find out the value of x. √3x+4+√3x−5√3x+4−√3x−5=9

Given that HCF (26 , 91) = 13, then LCM of (26 , 91) is :

From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and of base radius 7 cm is drilled out. Find the volume and the total surface of the remaining solid. [4 MARKS]

Question 7 Using Basic proportionality theorem, prove that a line drawn through the mid-points of one side of a triangle parallel to another side bisects the third side.

One of the diagonals of a rhombus of side 20 cm is 24 cm. The length of other diagonal is equal to

If A(5, 3), B(11, -5) and P(12, y) are the vertices of a right triangle, right angled at P, then y is equal to

A(h,-6) , B(2,3) and C(-6,k) are co-ordinates of vertices of a triangle whose centroid is G(1,5). What is the values of (h - k)?-11

Calculate the median from the following data: Height135−140140−145145−150150−155155−160160−165165−170170−175(in cm)No. of6101822201563boys

ABCD is a rectangle having length 30 cm and breadth 25 cm. P, Q, R and S are the midpoints of line segments AB, BC, CD and AD respectively. What is the area of the shaded part?

The height of hill is 150 metres. From the top of the hill the angle of depression of two objects lying towards east of the hill are 45∘ and 30∘. Find the distance between the objects.

A circle of radius R is circumscribing a triangle ABC, having ∠A=30∘, &amp; BC = 20 cm. Then the radius 'R' is equal to [sin 30∘=0.5]

Question 7 A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

Find the length of altitude AD of an isosceles ΔABC in which AB = AC = 2a units and BC = a units.

Solve the inequation, 3x - 4 < 2x + 1 ≤ 5x + 7, x ∈ R and graph the solution set.

If √2 & −√2 are zeroes of x4−11x2+18 find the other zeroes. [3 MARKS]

A circle of radius R is circumscribing a triangle ABC, having ∠A=30∘, & BC = 20 cm. Then the radius 'R' is equal to [sin 30∘=0.5]