32581 + Interview Questions in Mathematics

1.	Question 11 Sum of the areas of two squares is 468m2. If the difference of their perimeters is 24 m, find the sides of the two squares.
Answer» Question 11 Sum of the areas of two squares is 468 $m^{2}$ . If the difference of their perimeters is 24 m, find the sides of the two squares.

Discussion

2.	For solving each pair of equations, use the method of eliminations by equating coefficients: 13+2y=9x 3y=7x
Answer» For solving each pair of equations, use the method of eliminations by equating coefficients: $13 + 2 y = 9 x$ $3 y = 7 x$

2.

For solving each pair of equations, use the method of eliminations by equating coefficients: 13+2y=9x 3y=7x

Answer»

For solving each pair of equations, use the method of eliminations by equating coefficients:

$13 + 2 y = 9 x$

$3 y = 7 x$

Discussion

3.	Consider a matrix A. Then (AT)T = ___
Answer» Consider a matrix A. Then $(A^{T})^{T}$ = ___

Discussion

4.	In a circle, O is the centre and ∠COD is right angle. AC = BD and CD is the tangent at P. Which of the following are true, if the radius of the circle is 1 m?
Answer» In a circle, O is the centre and $∠$ COD is right angle. AC = BD and CD is the tangent at P. Which of the following are true, if the radius of the circle is 1 m?

4.

In a circle, O is the centre and ∠COD is right angle. AC = BD and CD is the tangent at P. Which of the following are true, if the radius of the circle is 1 m?

Answer»

In a circle, O is the centre and $∠$ COD is right angle. AC = BD and CD is the tangent at P. Which of the following are true, if the radius of the circle is 1 m?

Discussion

5.	For the expression f(x) = a x2 + bx + c (a > 0), having both real roots, the condition for both real roots to be greater than a real value x0 is
Answer» For the expression f(x) = a $x^{2}$ + bx + c (a > 0), having both real roots, the condition for both real roots to be greater than a real value $x_{0}$ is

Discussion

6.	Find the value of sin2θ+cos2θ at θ=30∘ & 60∘.
Answer» $F i n d t h e v a l u e o f s i n^{2} θ + c o s^{2} θ a t θ = 30^{\circ} & 60^{\circ}$ .

Discussion

7.	In the figure given below, PAB is a secant and PR is a tangent to the circle. If PA : AB = 1 : 8, and PR = 15 cm, find the length of PB.
Answer» In the figure given below, PAB is a secant and PR is a tangent to the circle. If PA : AB = 1 : 8, and PR = 15 cm, find the length of PB.

7.

In the figure given below, PAB is a secant and PR is a tangent to the circle. If PA : AB = 1 : 8, and PR = 15 cm, find the length of PB.

Answer»

In the figure given below, PAB is a secant and PR is a tangent to the circle. If PA : AB = 1 : 8, and PR = 15 cm, find the length of PB.

Discussion

8.	Find the mean of the following distribution by step deviation method: [4 MARKS] Class intervalFrequency20−301030−40640−50850−601260−70570−809
Answer» Find the mean of the following distribution by step deviation method: [4 MARKS] $\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y 20 - 30 & 10 30 - 40 & 6 40 - 50 & 8 50 - 60 & 12 60 - 70 & 5 70 - 80 & 9 \end{matrix}$

Discussion

9.	Question 4 The product of any two irrational numbers is A) Always an irrational number B) Always a rational number C) Always an integer D) Sometimes rational, sometimes irrational
Answer» Question 4 The product of any two irrational numbers is A) Always an irrational number B) Always a rational number C) Always an integer D) Sometimes rational, sometimes irrational

Discussion

10.	Question 33 The sum of the first n terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another AP whose first term is –30 and the common difference is 8. Find n.
Answer» Question 33 The sum of the first n terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another AP whose first term is –30 and the common difference is 8. Find n.

Discussion

11.	Question 10 In Δ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.
Answer» Question 10 In $Δ$ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

Discussion

12.	There is a cardboard of area 52 cm2. If, a cuboid of breadth 4 cm and height 3 cm has to be created using the board, then what will be the length of the cuboid formed?
Answer» There is a cardboard of area $52 c m^{2}$ . If, a cuboid of breadth $4 c m$ and height $3 c m$ has to be created using the board, then what will be the length of the cuboid formed?

Discussion

13.	Question 6 If n is an odd integer, then show that n2−1 is divisible by 8.
Answer» Question 6 If n is an odd integer, then show that $n^{2} - 1$ is divisible by 8.

Discussion

14.	A square is inscribed in the circle x2+y2−2x+4y−93=0 with its sides parallel to the coordinate axes. The coordinates of its vertices are
Answer» A square is inscribed in the circle $x^{2} + y^{2} - 2 x + 4 y - 93 = 0$ with its sides parallel to the coordinate axes. The coordinates of its vertices are

Discussion

15.	The graphs of the equations 5x-15y=8 and 3x-9y=245 are two lines which are (a) coincident (b) parallel (c) intersecting exactly at one point (d) perpendicular to each other
Answer» The graphs of the equations 5x-15y=8 and 3x-9y= $\frac{24}{5}$ are two lines which are (a) coincident (b) parallel (c) intersecting exactly at one point (d) perpendicular to each other

15.

The graphs of the equations 5x-15y=8 and 3x-9y=245 are two lines which are (a) coincident (b) parallel (c) intersecting exactly at one point (d) perpendicular to each other

Answer»

The graphs of the equations 5x-15y=8 and 3x-9y= $\frac{24}{5}$ are two lines which are

(a) coincident

(b) parallel

(c) intersecting exactly at one point

(d) perpendicular to each other

Discussion

16.	Give an example of two irrationals whose product is rational.
Answer» Give an example of two irrationals whose product is rational.

Discussion

17.	The angle of depression of a car parked on the road from the top of a 150-m-high tower is 30∘. The distance of the car from the tower is (a) 50√3 m (b) 150√3 m (c) 150√2 m (d) 75 m
Answer» The angle of depression of a car parked on the road from the top of a 150-m-high tower is $30^{\circ}$ . The distance of the car from the tower is (a) $50 \sqrt{3}$ m (b) $150 \sqrt{3}$ m (c) $150 \sqrt{2}$ m (d) 75 m

17.

The angle of depression of a car parked on the road from the top of a 150-m-high tower is 30∘. The distance of the car from the tower is (a) 50√3 m (b) 150√3 m (c) 150√2 m (d) 75 m

Answer»

The angle of depression of a car parked on the road from the top of a 150-m-high tower is $30^{\circ}$ . The distance of the car from the tower is

(a) $50 \sqrt{3}$ m

(b) $150 \sqrt{3}$ m

(c) $150 \sqrt{2}$ m

(d) 75 m

Discussion

18.	(i) Find the values of k for which the quadratic equation (3k+1)x2+2(k+1)x+1=0 has real and equal roots. (ii) Find the value of k for which the equations x2+k(2x+k−1)+2=0 has real and equal roots.
Answer» (i) Find the values of k for which the quadratic equation $(3 k + 1) x^{2} + 2 (k + 1) x + 1 = 0$ has real and equal roots. (ii) Find the value of k for which the equations $x^{2} + k (2 x + k - 1) + 2 = 0$ has real and equal roots.

Discussion

19.	A cylindrical tub of radius 5 cm and length 9.8 cm is full of water.A solid in the form of a right circular cone mounted on a hemisphere is immersed in the tub. If the radius of the hemisphere is 3.5 cm and height of the cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.(Take π=22/7)
Answer» A cylindrical tub of radius 5 cm and length 9.8 cm is full of water.A solid in the form of a right circular cone mounted on a hemisphere is immersed in the tub. If the radius of the hemisphere is 3.5 cm and height of the cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.(Take $π = 22 / 7$ )

Discussion

20.	Equal circles with centres O and O' touch each other at X. OO' produced to meet a circle with centre O', at A. AC is a tangent to the circle whose centre is O. O' D is perpendicular to AC. Find the value of DO′CO
Answer» Equal circles with centres O and O' touch each other at X. OO' produced to meet a circle with centre O', at A. AC is a tangent to the circle whose centre is O. O' D is perpendicular to AC. Find the value of $\frac{D O^{'}}{C O}$

Discussion

21.	When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4. And, when 6 is added to numerator and the denominator is multipled by 3, it becomes 2/3. Find the fraction.
Answer» When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4. And, when 6 is added to numerator and the denominator is multipled by 3, it becomes 2/3. Find the fraction.

Discussion

22.	If two points are given in a cordinate plain……then how can we the linear equation for It?
Answer» If two points are given in a cordinate plain……then how can we the linear equation for It?

Discussion

23.	The value of p for which the points (–1, 3), (2, p), (5, –1) are collinear is ____.
Answer» The value of p for which the points (–1, 3), (2, p), (5, –1) are collinear is ____.

Discussion

24.	The three points (-2,2), (8,-2) and (-4, -3) are the vertices of
Answer» The three points (-2,2), (8,-2) and (-4, -3) are the vertices of

Discussion

25.	In △ABC, the medians BE and CF intersect at G. AGD is a line meeting BC at D. If GD is 1.5 cm, then AD is equal to -
Answer» In $△$ ABC, the medians BE and CF intersect at G. AGD is a line meeting BC at D. If GD is 1.5 cm, then AD is equal to -

25.

In △ABC, the medians BE and CF intersect at G. AGD is a line meeting BC at D. If GD is 1.5 cm, then AD is equal to -

Answer»

In $△$ ABC, the medians BE and CF intersect at G. AGD is a line meeting BC at D. If GD is 1.5 cm, then AD is equal to -

Discussion

26.	A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to a point on the ground which is at a certain distance from the foot of the pole. The height of the pole, if the angle made by the rope with the ground level is 30∘ is ___ m.
Answer» A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to a point on the ground which is at a certain distance from the foot of the pole. The height of the pole, if the angle made by the rope with the ground level is $30^{\circ}$ is ___ m.

Discussion

27.	Which of the following is/are a measure of central tendency?
Answer» Which of the following is/are a measure of central tendency?

Discussion

28.	If the ratio of mean and median of a certain data is 2:3, then find the ratio of its mode and mean.
Answer» If the ratio of mean and median of a certain data is 2:3, then find the ratio of its mode and mean.

Discussion

29.	If ∠BCD=50∘, then ∠BAD = ___.
Answer» If $∠ B C D = 50^{\circ},$ then $∠ B A D$ = ___.

Discussion

30.	Two pipes running together can fill a tank in 100\9 minutes, if one pipe takes 5 minutes more than other to fill the tank find the time in which each pipe would fill the tank.
Answer» Two pipes running together can fill a tank in 100\9 minutes, if one pipe takes 5 minutes more than other to fill the tank find the time in which each pipe would fill the tank.

Discussion

31.	x2−12x+45=0, find the product of the roots of the equation.
Answer» $x^{2} - 12 x + 45 = 0$ , find the product of the roots of the equation.

Discussion

32.	Which of the following shows the correct histogram for the given data: Class interval20−2525−3030−3535−4040−4545−50Frequency3024522846100
Answer» Which of the following shows the correct histogram for the given data: $\begin{matrix} Class interval & 20 - 25 & 25 - 30 & 30 - 35 & 35 - 40 & 40 - 45 & 45 - 50 Frequency & 30 & 24 & 52 & 28 & 46 & 100 \end{matrix}$

Discussion

33.	150 spherical marbles, each of diameter 1.4cm, are dropped in the cylindrical vessel of diameter term containing some water, which are completely immerged in water. Find the rise in the level of water in vessel.
Answer» 150 spherical marbles, each of diameter 1.4cm, are dropped in the cylindrical vessel of diameter term containing some water, which are completely immerged in water. Find the rise in the level of water in vessel.

Discussion

34.	If a and b are two odd positive integers such that a>b then prove that one of the two numbers a+b÷2 and a-b÷2 is odd and the other is even.
Answer» If a and b are two odd positive integers such that a>b then prove that one of the two numbers a+b÷2 and a-b÷2 is odd and the other is even.

Discussion

35.	Salman buys 50 shares of face value Rs 100 available at Rs 132. (i) What is his investment ? (ii) If the dividend is 7.5 %, what will be his annual income? (iii) If he wants to increase his annual income by Rs 150, how many extra shares should he buy?
Answer» Salman buys 50 shares of face value Rs 100 available at Rs 132. (i) What is his investment ? (ii) If the dividend is 7.5 %, what will be his annual income? (iii) If he wants to increase his annual income by Rs 150, how many extra shares should he buy?

35.

Salman buys 50 shares of face value Rs 100 available at Rs 132. (i) What is his investment ? (ii) If the dividend is 7.5 %, what will be his annual income? (iii) If he wants to increase his annual income by Rs 150, how many extra shares should he buy?

Answer»

Salman buys 50 shares of face value Rs 100 available at Rs 132.

(i) What is his investment ?

(ii) If the dividend is 7.5 %, what will be his annual income?

(iii) If he wants to increase his annual income by Rs 150, how many extra shares should he buy?

Discussion

36.	If a and b are 2 positive integers such that a>b, then prove that one of the (a+b)÷2 and (a-b)÷2 is odd and the other is even.
Answer» If a and b are 2 positive integers such that a>b, then prove that one of the (a+b)÷2 and (a-b)÷2 is odd and the other is even.

Discussion

37.	The 9th term of an AP is equal to 7 times the second term and 12 term exceeds 5 times the third term by 3 find the first term and the common difference
Answer» The 9th term of an AP is equal to 7 times the second term and 12 term exceeds 5 times the third term by 3 find the first term and the common difference

Discussion

38.	An arc ACB subtends ∠AOB at the centre of the circle. If 2 arcs are drawn with A and B as centre with a fixed radius such that they intersect at point P, then line OP will ___________ ∠AOB.
Answer» An arc ACB subtends $∠ A O B$ at the centre of the circle. If 2 arcs are drawn with A and B as centre with a fixed radius such that they intersect at point P, then line OP will ___________ $∠ A O B$ .

Discussion

39.	Find the quadratic polynomial whose zeroes are 5 +-√2.
Answer» Find the quadratic polynomial whose zeroes are 5 +-√2.

Discussion

40.	The line segment joining the points A (3, -4) and B (-2, 1) is divided in the ratio 1:3 at point P in it. Find the co-ordinates of P. Also, find the equation of the line through P and perpendicular to the line 5x - 3y = 4.
Answer» The line segment joining the points A (3, -4) and B (-2, 1) is divided in the ratio 1:3 at point P in it. Find the co-ordinates of P. Also, find the equation of the line through P and perpendicular to the line 5x - 3y = 4.

40.

The line segment joining the points A (3, -4) and B (-2, 1) is divided in the ratio 1:3 at point P in it. Find the co-ordinates of P. Also, find the equation of the line through P and perpendicular to the line 5x - 3y = 4.

Answer»

The line segment joining the points A (3, -4) and B (-2, 1) is divided in the ratio 1:3 at point P in it. Find the co-ordinates of P.

Also, find the equation of the line through P and perpendicular to the line 5x - 3y = 4.

Discussion

41.	Prove that the parallelogram circumscribing a circle is a rhombus. OR Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
Answer» Prove that the parallelogram circumscribing a circle is a rhombus. OR Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Discussion

42.	Which of the following is NOT the length of a median in triangle ABC with vertices A(-1,3), B(1,1) and C(5,1)?
Answer» Which of the following is NOT the length of a median in triangle ABC with vertices A(-1,3), B(1,1) and C(5,1)?

Discussion

43.	ABC is a triangle whose vertices are (1, 3), (–2, –1) and (4, 0) respectively. G is its centroid and BGCH is a parallelogram. Find the coordinates of the vertex H.
Answer» ABC is a triangle whose vertices are (1, 3), (–2, –1) and (4, 0) respectively. G is its centroid and BGCH is a parallelogram. Find the coordinates of the vertex H.

Discussion

44.	The figure alongside represents the lines y = x + 3 and √3y = x - 2
Answer» The figure alongside represents the lines y = x + 3 and √3y = x - 2

Discussion

45.	Tap on the region in which the probability of finding a crashed plane is 19.
Answer» Tap on the region in which the probability of finding a crashed plane is $\frac{1}{9} .$

Discussion

46.	For an A.P the sum of first 30 terms is -1155,the common difference is -3and the thirtieth term is -82. What is the first term?
Answer» For an A.P the sum of first 30 terms is -1155,the common difference is -3and the thirtieth term is -82. What is the first term?

Discussion

47.	If x is the length of perpendicular CD drawn on the diameter AB and given that AC = 32 cm, BC = 18 cm, then x = ___ cm.
Answer» If x is the length of perpendicular CD drawn on the diameter AB and given that AC = 32 cm, BC = 18 cm, then x = ___ cm.

47.

If x is the length of perpendicular CD drawn on the diameter AB and given that AC = 32 cm, BC = 18 cm, then x = ___ cm.

Answer»

If x is the length of perpendicular CD drawn on the diameter AB and given that AC = 32 cm, BC = 18 cm, then x = ___ cm.

Discussion

48.	A sum of ₹ 2000 is invested at 4% simple interest per year. If the total interest at the end of each year forms an AP, then the interest at the end of the 30th year will be
Answer» A sum of ₹ 2000 is invested at 4% simple interest per year. If the total interest at the end of each year forms an AP, then the interest at the end of the 30th year will be

Discussion

49.	The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7 : 15. Find the numbers.
Answer» The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7 : 15. Find the numbers.

Discussion

50.	If x = 3 is one of the roots of a quadratic equation x2−2kx−6=0, then find the value of k.
Answer» If x = 3 is one of the roots of a quadratic equation $x^{2} - 2 k x - 6 = 0$ , then find the value of k.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Question 11 Sum of the areas of two squares is 468m2. If the difference of their perimeters is 24 m, find the sides of the two squares.

For solving each pair of equations, use the method of eliminations by equating coefficients: 13+2y=9x 3y=7x

Consider a matrix A. Then (AT)T =​ ___

In a circle, O is the centre and ∠COD is right angle. AC = BD and CD is the tangent at P. Which of the following are true, if the radius of the circle is 1 m?

For the expression f(x) = a x2 + bx + c (a &gt; 0), having both real roots, the condition for both real roots to be greater than a real value x0 is

Find the value of sin2θ+cos2θ at θ=30∘ &amp; 60∘.

In the figure given below, PAB is a secant and PR is a tangent to the circle. If PA : AB = 1 : 8, and PR = 15 cm, find the length of PB.

Find the mean of the following distribution by step deviation method: [4 MARKS] Class intervalFrequency20−301030−40640−50850−601260−70570−809

Question 4 The product of any two irrational numbers is A) Always an irrational number B) Always a rational number C) Always an integer D) Sometimes rational, sometimes irrational

Question 33 The sum of the first n terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another AP whose first term is –30 and the common difference is 8. Find n.

Question 10 In Δ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

There is a cardboard of area 52 cm2. If, a cuboid of breadth 4 cm and height 3 cm has to be created using the board, then what will be the length of the cuboid formed?

Question 6 If n is an odd integer, then show that n2−1 is divisible by 8.

A square is inscribed in the circle x2+y2−2x+4y−93=0 with its sides parallel to the coordinate axes. The coordinates of its vertices are

The graphs of the equations 5x-15y=8 and 3x-9y=245 are two lines which are (a) coincident (b) parallel (c) intersecting exactly at one point (d) perpendicular to each other

Give an example of two irrationals whose product is rational.

The angle of depression of a car parked on the road from the top of a 150-m-high tower is 30∘. The distance of the car from the tower is (a) 50√3 m (b) 150√3 m (c) 150√2 m (d) 75 m

(i) Find the values of k for which the quadratic equation (3k+1)x2+2(k+1)x+1=0 has real and equal roots. (ii) Find the value of k for which the equations x2+k(2x+k−1)+2=0 has real and equal roots.

Equal circles with centres O and O' touch each other at X. OO' produced to meet a circle with centre O', at A. AC is a tangent to the circle whose centre is O. O' D is perpendicular to AC. Find the value of DO′CO

When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4. And, when 6 is added to numerator and the denominator is multipled by 3, it becomes 2/3. Find the fraction.

If two points are given in a cordinate plain……then how can we the linear equation for It?

The value of p for which the points (–1, 3), (2, p), (5, –1) are collinear is ____.

The three points (-2,2), (8,-2) and (-4, -3) are the vertices of

In △ABC, the medians BE and CF intersect at G. AGD is a line meeting BC at D. If GD is 1.5 cm, then AD is equal to -

A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to a point on the ground which is at a certain distance from the foot of the pole. The height of the pole, if the angle made by the rope with the ground level is 30∘ is ___ m.

Which of the following is/are a measure of central tendency?

If the ratio of mean and median of a certain data is 2:3, then find the ratio of its mode and mean.

If ∠BCD=50∘, then ∠BAD = ___.

Two pipes running together can fill a tank in 100\9 minutes, if one pipe takes 5 minutes more than other to fill the tank find the time in which each pipe would fill the tank.

x2−12x+45=0, find the product of the roots of the equation.

Which of the following shows the correct histogram for the given data: Class interval20−2525−3030−3535−4040−4545−50Frequency3024522846100

150 spherical marbles, each of diameter 1.4cm, are dropped in the cylindrical vessel of diameter term containing some water, which are completely immerged in water. Find the rise in the level of water in vessel.

If a and b are two odd positive integers such that a>b then prove that one of the two numbers a+b÷2 and a-b÷2 is odd and the other is even.

Salman buys 50 shares of face value Rs 100 available at Rs 132. (i) What is his investment ? (ii) If the dividend is 7.5 %, what will be his annual income? (iii) If he wants to increase his annual income by Rs 150, how many extra shares should he buy?

If a and b are 2 positive integers such that a>b, then prove that one of the (a+b)÷2 and (a-b)÷2 is odd and the other is even.

The 9th term of an AP is equal to 7 times the second term and 12 term exceeds 5 times the third term by 3 find the first term and the common difference

An arc ACB subtends ∠AOB at the centre of the circle. If 2 arcs are drawn with A and B as centre with a fixed radius such that they intersect at point P, then line OP will ___________ ∠AOB.

Find the quadratic polynomial whose zeroes are 5 +-√2.

The line segment joining the points A (3, -4) and B (-2, 1) is divided in the ratio 1:3 at point P in it. Find the co-ordinates of P. Also, find the equation of the line through P and perpendicular to the line 5x - 3y = 4.

Prove that the parallelogram circumscribing a circle is a rhombus. OR Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Which of the following is NOT the length of a median in triangle ABC with vertices A(-1,3), B(1,1) and C(5,1)?

ABC is a triangle whose vertices are (1, 3), (–2, –1) and (4, 0) respectively. G is its centroid and BGCH is a parallelogram. Find the coordinates of the vertex H.

The figure alongside represents the lines y = x + 3 and √3y = x - 2

Tap on the region in which the probability of finding a crashed plane is 19.

For an A.P the sum of first 30 terms is -1155,the common difference is -3and the thirtieth term is -82. What is the first term?

If x is the length of perpendicular CD drawn on the diameter AB and given that AC = 32 cm, BC = 18 cm, then x = ___ cm.

A sum of ₹ 2000 is invested at 4% simple interest per year. If the total interest at the end of each year forms an AP, then the interest at the end of the 30th year will be

The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7 : 15. Find the numbers.

If x = 3 is one of the roots of a quadratic equation x2−2kx−6=0, then find the value of k.

Consider a matrix A. Then (AT)T = ___

For the expression f(x) = a x2 + bx + c (a > 0), having both real roots, the condition for both real roots to be greater than a real value x0 is

Find the value of sin2θ+cos2θ at θ=30∘ & 60∘.