32581 + Interview Questions in Mathematics Page 225 InterviewSolution

11201.	5 cos260∘+4 sec230∘−tant245∘sin230∘+cos230∘
Answer» $\frac{5 c o s^{2} 60^{\circ} + 4 s e c^{2} 30^{\circ} - t a n t^{2} 45^{\circ}}{s i n^{2} 30^{\circ} + c o s^{2} 30^{\circ}}$

Discussion

11202.	In the figure below, O is the centre of the circle.Prove that x + y = 90°
Answer» In the figure below, O is the centre of the circle. Prove that x + y = 90°

11202.

In the figure below, O is the centre of the circle.Prove that x + y = 90°

Answer»

In the figure below, O is the centre of the circle.

Prove that x + y = 90°

Discussion

11203.	In each of the following find the value of ‘k’, for which the points are collinear.(i) (7, − 2), (5, 1), (3, − k) (ii) (8, 1), (k, − 4), (2, − 5)
Answer» In each of the following find the value of ‘k’, for which the points are collinear. (i) (7, − 2), (5, 1), (3, − k) (ii) (8, 1), (k, − 4), (2, − 5)

11203.

In each of the following find the value of ‘k’, for which the points are collinear.(i) (7, − 2), (5, 1), (3, − k) (ii) (8, 1), (k, − 4), (2, − 5)

Answer»

In each of the following find the value of ‘k’, for which the points are collinear.

(i) (7, − 2), (5, 1), (3, − k) (ii) (8, 1), (k, − 4), (2, − 5)

Discussion

11204.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula: x2+6x−(a2+2a−8)=0
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $x^{2} + 6 x - (a^{2} + 2 a - 8) = 0$

Discussion

11205.	Simplify and solve the following linear equation.15(y−4)−2(y−9)+5(y+6)=0
Answer» Simplify and solve the following linear equation. $15 (y - 4) - 2 (y - 9) + 5 (y + 6) = 0$

Discussion

11206.	The perimeter of a circle is 17.5 cm. Find the area of the sector enclosed by two radii and an arc 44 cm in length.
Answer» The perimeter of a circle is 17.5 cm. Find the area of the sector enclosed by two radii and an arc 44 cm in length.

Discussion

11207.	cosec θ(cosec θ−1)+cosec θ(cosec θ+1)=
Answer» $\frac{c o s e c θ}{(c o s e c θ - 1)} + \frac{c o s e c θ}{(c o s e c θ + 1)} =$

Discussion

11208.	Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle
Answer» Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle

Discussion

11209.	If x and y are the roots of the equation 4k2+5k+6=0, then match the following with their values.
Answer» If $x$ and $y$ are the roots of the equation $4 k^{2} + 5 k + 6 = 0$ , then match the following with their values.

Discussion

11210.	A cricketer scores the following runs in eight innings: 58, 76, 40, 35, 46, 45, 0, 100 Find the mean score.
Answer» A cricketer scores the following runs in eight innings: 58, 76, 40, 35, 46, 45, 0, 100 Find the mean score.

Discussion

11211.	Solve and find the numbers of positive integral solutions of the following inequation. 2x−3<x+2≤3x+5, xϵR
Answer» Solve and find the numbers of positive integral solutions of the following inequation. $2 x - 3 < x + 2 \leq 3 x + 5, x ϵ R$

11211.

Solve and find the numbers of positive integral solutions of the following inequation. 2x−3<x+2≤3x+5, xϵR

Answer»

Solve and find the numbers of positive integral solutions of the following inequation.

$2 x - 3 < x + 2 \leq 3 x + 5, x ϵ R$

Discussion

11212.	There is a circle with center O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?
Answer» There is a circle with center O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?

Discussion

11213.	Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
Answer» Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

Discussion

11214.	Solve the following quadratic equation for x:x2-4ax-b2+4a2=0
Answer» Solve the following quadratic equation for x: $x^{2} - 4 a x - b^{2} + 4 a^{2} = 0$

Discussion

11215.	The coordinates of the point which is equidistant from the vertices of the triangle formed by the points O(0, 0), A(a, 0) and B(0, b), are _________.
Answer» The coordinates of the point which is equidistant from the vertices of the triangle formed by the points O(0, 0), A(a, 0) and B(0, b), are _________.

Discussion

11216.	A jar contains 54 marbles, each of which some are blue, some are green and some are white. The probability of selecting a blue marble at random is 13 and the probability of selecting a green marble at random is 49. How many white marbles does the jar contain?
Answer» A jar contains 54 marbles, each of which some are blue, some are green and some are white. The probability of selecting a blue marble at random is $\frac{1}{3}$ and the probability of selecting a green marble at random is $\frac{4}{9}$ . How many white marbles does the jar contain?

Discussion

11217.	Rationalize 2+√34+√3
Answer» Rationalize $\frac{2 + \sqrt{3}}{4 + \sqrt{3}}$

Discussion

11218.	Calculate mode from following data:Class Interval5−1415−2425−3435−4444−5455−64Frequency81015254020.
Answer» Calculate mode from following data: $\begin{matrix} Class Interval & 5 - 14 & 15 - 24 & 25 - 34 & 35 - 44 & 44 - 54 & 55 - 64 Frequency & 8 & 10 & 15 & 25 & 40 & 20 \end{matrix}$ .

11218.

Calculate mode from following data:Class Interval5−1415−2425−3435−4444−5455−64Frequency81015254020.

Answer»

Calculate mode from following data:

$\begin{matrix} Class Interval & 5 - 14 & 15 - 24 & 25 - 34 & 35 - 44 & 44 - 54 & 55 - 64 Frequency & 8 & 10 & 15 & 25 & 40 & 20 \end{matrix}$ .

Discussion

11219.	In each of the pictures below, draw aangle, according to the specifications:(i) At the point A(ii) At the point A with one side along OA(iii) At the point A one side along AB
Answer» In each of the pictures below, draw aangle, according to the specifications: (i) At the point A (ii) At the point A with one side along OA (iii) At the point A one side along AB

11219.

In each of the pictures below, draw aangle, according to the specifications:(i) At the point A(ii) At the point A with one side along OA(iii) At the point A one side along AB

Answer»

In each of the pictures below, draw aangle, according to the specifications:

(i) At the point A

(ii) At the point A with one side along OA

(iii) At the point A one side along AB

Discussion

11220.	if polynomial p(x)=x^200 - 2x^199 + x^50 - 2x^49 + x² + x + 1 id divided by (x-1)(x-2) then the remainder is
Answer» if polynomial p(x)=x^200 - 2x^199 + x^50 - 2x^49 + x² + x + 1 id divided by (x-1)(x-2) then the remainder is

Discussion

11221.	Find the area of a parallelogram ABCD if three of its vertices are A(2, 4), B(2 + 3, 5) and C(2, 6). [CBSE 2013]
Answer» Find the area of a parallelogram ABCD if three of its vertices are A(2, 4), B(2 + $\sqrt{3}$ , 5) and C(2, 6). [CBSE 2013]

Discussion

11222.	In the right △ABC, right angled at B, which of the following is true?
Answer» In the right $△$ ABC, right angled at B, which of the following is true?

Discussion

11223.	Question 9 In given figure, ABC is a triangle right angled at B and BD⊥AC. If AD =4 cm and CD = 5cm, then find BD and AB.
Answer» Question 9 In given figure, ABC is a triangle right angled at B and $B D ⊥ A C$ . If AD =4 cm and CD = 5cm, then find BD and AB.

Discussion

11224.	In the given figure, there are two concentric circles with centre O of radii 5 cm and 3 cm. From an external point P, tangent PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP.
Answer» In the given figure, there are two concentric circles with centre O of radii 5 cm and 3 cm. From an external point P, tangent PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP.

Discussion

11225.	Let p(x) be a polynomial of degree more than 2. When p(x) is divided by x-2, it leaves remainder 1 and when it is divided by x-3, it leaves remainder 3. Find the remainder, when p(x) is divided by (x-2)(x-3).
Answer» Let p(x) be a polynomial of degree more than 2. When p(x) is divided by x-2, it leaves remainder 1 and when it is divided by x-3, it leaves remainder 3. Find the remainder, when p(x) is divided by (x-2)(x-3).

Discussion

11226.	The 4th term of an AP is zero . Prove that its 25th term is triple its 11th term.
Answer» The 4th term of an AP is zero . Prove that its 25th term is triple its 11th term.

Discussion

11227.	Question 10In figure. If PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and ∠BQR=70∘ , then ∠AQB is equal to(A) 20°(B) 40°(C) 35°(D) 45°
Answer» Question 10 In figure. If PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and $∠ B Q R = 70^{\circ}$ , then $∠$ AQB is equal to (A) 20° (B) 40° (C) 35° (D) 45°

Discussion

11228.	Factorise X square + 4 x + 9
Answer» Factorise X square + 4 x + 9

Discussion

11229.	Question 1 (iv)Evaluate the following:(iv) (sin30∘+tan45∘−cosec60∘)(sec30∘+cos60∘+cot45∘)
Answer» Question 1 (iv) Evaluate the following: (iv) $\frac{(s i n 30^{\circ} + t a n 45^{\circ} - c o s e c 60^{\circ})}{(s e c 30^{\circ} + c o s 60^{\circ} + c o t 45^{\circ})}$

Discussion

11230.	Evaluate each of the following: sin260∘ + sin245∘ + sin260∘ + sin290∘
Answer» Evaluate each of the following: $s i n^{2} 60^{\circ}$ + $s i n^{2} 45^{\circ}$ + $s i n^{2} 60^{\circ}$ + $s i n^{2} 90^{\circ}$

11230.

Evaluate each of the following: sin260∘ + sin245∘ + sin260∘ + sin290∘

Answer»

Evaluate each of the following:

$s i n^{2} 60^{\circ}$ + $s i n^{2} 45^{\circ}$ + $s i n^{2} 60^{\circ}$ + $s i n^{2} 90^{\circ}$

Discussion

11231.	Which of the following trigonometric ratios will have the same value as cot 53∘?
Answer» Which of the following trigonometric ratios will have the same value as cot $53^{\circ}$ ?

Discussion

11232.	The area of the largest triangle that can be inscribed in a semi-circle of radius r is(a) 2r2 sq. units(b) r2 sq. units(c) 12r2 sq. units(d) √2r2 sq. units
Answer» The area of the largest triangle that can be inscribed in a semi-circle of radius $r$ is (a) $2 r^{2}$ sq. units (b) $r^{2}$ sq. units (c) $\frac{1}{2} r^{2}$ sq. units (d) $\sqrt{2} r^{2}$ sq. units

Discussion

11233.	Question 3 (v)Form the pair of linear equations for the following problems and find their solution by substitution method:A fraction becomes 911, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 56. Find the fraction.
Answer» Question 3 (v) Form the pair of linear equations for the following problems and find their solution by substitution method: A fraction becomes $\frac{9}{11}$ , if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes $\frac{5}{6}$ . Find the fraction.

Discussion

11234.	A takes 3 hours more than B to walk a distance of 30 km. But, if A doubles his pace (speed) he is ahead of B by 112 hours. Find the speeds of A and B.
Answer» A takes 3 hours more than B to walk a distance of 30 km. But, if A doubles his pace (speed) he is ahead of B by 1 $\frac{1}{2}$ hours. Find the speeds of A and B.

Discussion

11235.	Question 3The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically.
Answer» Question 3 The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically.

Discussion

11236.	In △ABC , D,E and F are mid points of sides AB , BC and AC respectively.How many pairs of similar triangles are there in the figure formed after joining D,E,F ?
Answer» In $△ A B C$ , D,E and F are mid points of sides AB , BC and AC respectively.How many pairs of similar triangles are there in the figure formed after joining D,E,F ?

Discussion

11237.	To find the sum of the 1st 24 terms of an AP whose nth term is given by an=3+2n, what is the best approach to solve this question?
Answer» To find the sum of the $1^{s t}$ 24 terms of an AP whose $n^{t h}$ term is given by $a_{n} = 3 + 2 n$ , what is the best approach to solve this question?

Discussion

11238.	Find the largest number which will divide 445, 542,699 leaving the reminder 6 in each case.
Answer» Find the largest number which will divide 445, 542,699 leaving the reminder 6 in each case.

Discussion

11239.	52 The angle of elevation of top of a vertical tower PQ from a point X on the ground is 60^° . At a point Y, 40 m vertically above X, the angle of elevation of the top is 45^° . Calculate the height of the tower.
Answer» 52 The angle of elevation of top of a vertical tower PQ from a point X on the ground is 60^° . At a point Y, 40 m vertically above X, the angle of elevation of the top is 45^° . Calculate the height of the tower.

Discussion

11240.	If each edge of a cube is doubled, how many times will its surface area increase?
Answer» If each edge of a cube is doubled, how many times will its surface area increase?

Discussion

11241.	If 35 is removed from the data: 30, 34, 35, 36, 37, 38, 39, 40, then the median increased by(a) 2(b) 1.5(c) 1(d) 0.5
Answer» If 35 is removed from the data: 30, 34, 35, 36, 37, 38, 39, 40, then the median increased by (a) 2 (b) 1.5 (c) 1 (d) 0.5

Discussion

11242.	In the Euclid's Division Lemma, if divident is 42, divisor is 5 and remainder is 2 times of its quotient then, find the quotient.
Answer» In the Euclid's Division Lemma, if divident is 42, divisor is 5 and remainder is 2 times of its quotient then, find the quotient.

Discussion

11243.	If 5^2x-1 - 25^x-1 =2500, find the value of x
Answer» If 5^2x-1 - 25^x-1 =2500, find the value of x

Discussion

11244.	Find the common root of the given quadratic equations.x2−4=0 and x2−5x+6=02
Answer» Find the common root of the given quadratic equations. $x^{2} - 4 = 0 a n d x^{2} - 5 x + 6 = 0$ 2

Discussion

11245.	Show that 5 + 7 is an irrational number.
Answer» Show that 5 + $\sqrt{7}$ is an irrational number.

Discussion

11246.

Find the mean of the following frequency distribution using a suitable method. Class 20−30 30−40 40−50 50−60 60−70 Frequency 25 40 42 33 10

Answer»

Find the mean of the following frequency distribution using a suitable method.

Class	20−30	30−40	40−50	50−60	60−70
Frequency	25	40	42	33	10

Discussion

11247.	If the third and the ninth terms of an AP are 4 and -8 respectively, which term of this AP is zero?
Answer» If the third and the ninth terms of an AP are 4 and -8 respectively, which term of this AP is zero?

Discussion

11248.	The LCM and HCF of two rational numbers are equal, then the numbers must be(a) prime(b) co-prime(c) composite(d) equal
Answer» The LCM and HCF of two rational numbers are equal, then the numbers must be (a) prime (b) co-prime (c) composite (d) equal

Discussion

11249.	From a window A, 10 m above the ground the angle of elevation of the top C of a tower is x0, where tan x0=5/2 and the angle of depression of the foot D of the tower is y0,where tany0=14.Calculate the height CD of the tower in metres.
Answer» $F r o m a w i n d o w A, 10 m a b o v e t h e g r o u n d t h e a n g l e o f e l e v a t i o n o f t h e t o p C o f a t o w e r i s x^{0}, w h e r e t a n x^{0} = 5 / 2 a n d t h e a n g l e o f d e p r e s s i o n o f t h e f o o t D o f t h e t o w e r i s y^{0}, w h e r e t a n y^{0} = \frac{1}{4} . C a l c u l a t e t h e h e i g h t C D o f t h e t o w e r i n m e t r e s .$

11249.

From a window A, 10 m above the ground the angle of elevation of the top C of a tower is x0, where tan x0=5/2 and the angle of depression of the foot D of the tower is y0,where tany0=14.Calculate the height CD of the tower in metres.

Answer»

$F r o m a w i n d o w A, 10 m a b o v e t h e g r o u n d t h e a n g l e o f e l e v a t i o n o f t h e t o p C o f a t o w e r i s x^{0}, w h e r e t a n x^{0} = 5 / 2 a n d t h e a n g l e o f d e p r e s s i o n o f t h e f o o t D o f t h e t o w e r i s y^{0}, w h e r e t a n y^{0} = \frac{1}{4} . C a l c u l a t e t h e h e i g h t C D o f t h e t o w e r i n m e t r e s .$

Discussion

11250.	Find the equation of the line through (–2,3) with slope –4.
Answer» Find the equation of the line through $(- 2, 3)$ with slope $- 4$ .

Discussion

Explore topic-wise InterviewSolutions in .

5 cos260∘+4 sec230∘−tant245∘sin230∘+cos230∘

In the figure below, O is the centre of the circle.Prove that x + y = 90°

In each of the following find the value of ‘k’, for which the points are collinear.(i) (7, − 2), (5, 1), (3, − k) (ii) (8, 1), (k, − 4), (2, − 5)

Find the roots of each of the following equations, if they exist, by applying the quadratic formula: x2+6x−(a2+2a−8)=0

Simplify and solve the following linear equation.15(y−4)−2(y−9)+5(y+6)=0

The perimeter of a circle is 17.5 cm. Find the area of the sector enclosed by two radii and an arc 44 cm in length.

cosec θ(cosec θ−1)+cosec θ(cosec θ+1)=

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle

If x and y are the roots of the equation 4k2+5k+6=0, then match the following with their values.

A cricketer scores the following runs in eight innings: 58, 76, 40, 35, 46, 45, 0, 100 Find the mean score.

Solve and find the numbers of positive integral solutions of the following inequation. 2x−3&lt;x+2≤3x+5, xϵR

There is a circle with center O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

Solve the following quadratic equation for x:x2-4ax-b2+4a2=0

The coordinates of the point which is equidistant from the vertices of the triangle formed by the points O(0, 0), A(a, 0) and B(0, b), are _________.

A jar contains 54 marbles, each of which some are blue, some are green and some are white. The probability of selecting a blue marble at random is 13 and the probability of selecting a green marble at random is 49. How many white marbles does the jar contain?

Rationalize 2+√34+√3

Calculate mode from following data:Class Interval5−1415−2425−3435−4444−5455−64Frequency81015254020.

In each of the pictures below, draw aangle, according to the specifications:(i) At the point A(ii) At the point A with one side along OA(iii) At the point A one side along AB

if polynomial p(x)=x^200 - 2x^199 + x^50 - 2x^49 + x² + x + 1 id divided by (x-1)(x-2) then the remainder is

Find the area of a parallelogram ABCD if three of its vertices are A(2, 4), B(2 + 3, 5) and C(2, 6). [CBSE 2013]

In the right △ABC, right angled at B, which of the following is true?

Question 9 In given figure, ABC is a triangle right angled at B and BD⊥AC. If AD =4 cm and CD = 5cm, then find BD and AB.

In the given figure, there are two concentric circles with centre O of radii 5 cm and 3 cm. From an external point P, tangent PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP.

Let p(x) be a polynomial of degree more than 2. When p(x) is divided by x-2, it leaves remainder 1 and when it is divided by x-3, it leaves remainder 3. Find the remainder, when p(x) is divided by (x-2)(x-3).

The 4th term of an AP is zero . Prove that its 25th term is triple its 11th term.

Question 10In figure. If PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and ∠BQR=70∘ , then ∠AQB is equal to(A) 20°(B) 40°(C) 35°(D) 45°

Factorise X square + 4 x + 9

Question 1 (iv)Evaluate the following:(iv) (sin30∘+tan45∘−cosec60∘)(sec30∘+cos60∘+cot45∘)

Evaluate each of the following: sin260∘ + sin245∘ + sin260∘ + sin290∘

Which of the following trigonometric ratios will have the same value as cot 53∘?

The area of the largest triangle that can be inscribed in a semi-circle of radius r is(a) 2r2 sq. units(b) r2 sq. units(c) 12r2 sq. units(d) √2r2 sq. units

Question 3 (v)Form the pair of linear equations for the following problems and find their solution by substitution method:A fraction becomes 911, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 56. Find the fraction.

A takes 3 hours more than B to walk a distance of 30 km. But, if A doubles his pace (speed) he is ahead of B by 112 hours. Find the speeds of A and B.

Question 3The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically.

In △ABC , D,E and F are mid points of sides AB , BC and AC respectively.How many pairs of similar triangles are there in the figure formed after joining D,E,F ?

To find the sum of the 1st 24 terms of an AP whose nth term is given by an=3+2n, what is the best approach to solve this question?

Find the largest number which will divide 445, 542,699 leaving the reminder 6 in each case.

52 The angle of elevation of top of a vertical tower PQ from a point X on the ground is 60^° . At a point Y, 40 m vertically above X, the angle of elevation of the top is 45^° . Calculate the height of the tower.

If each edge of a cube is doubled, how many times will its surface area increase?

If 35 is removed from the data: 30, 34, 35, 36, 37, 38, 39, 40, then the median increased by(a) 2(b) 1.5(c) 1(d) 0.5

In the Euclid's Division Lemma, if divident is 42, divisor is 5 and remainder is 2 times of its quotient then, find the quotient.

If 5^2x-1 - 25^x-1 =2500, find the value of x

Find the common root of the given quadratic equations.x2−4=0 and x2−5x+6=02

Show that 5 + 7 is an irrational number.

Find the mean of the following frequency distribution using a suitable method. Class 20−30 30−40 40−50 50−60 60−70 Frequency 25 40 42 33 10

If the third and the ninth terms of an AP are 4 and -8 respectively, which term of this AP is zero?

The LCM and HCF of two rational numbers are equal, then the numbers must be(a) prime(b) co-prime(c) composite(d) equal

From a window A, 10 m above the ground the angle of elevation of the top C of a tower is x0, where tan x0=5/2 and the angle of depression of the foot D of the tower is y0,where tany0=14.Calculate the height CD of the tower in metres.

Find the equation of the line through (–2,3) with slope –4.

Solve and find the numbers of positive integral solutions of the following inequation. 2x−3<x+2≤3x+5, xϵR