43030 + Interview Questions in Mathematics

1.	Let f(x)=sin x ∫x0cos t dt+2∫x0t dt+cos2 x−x2. Then area bounded by x f(x) and ordinate x = 0 and x = 5 with x-axis is
Answer» Let $f (x) = sin x \int_{0}^{x} cos t dt + 2 \int_{0}^{x} t dt + {cos}^{2} x - x^{2}$ . Then area bounded by $x f (x)$ and ordinate x = 0 and x = 5 with x-axis is

Discussion

2.	The value of 50∑r=0(−1)r 50Crr+2 is equal to
Answer» The value of $50 \sum r = 0 (- 1)^{r} \frac{^{50} C_{r}}{r + 2}$ is equal to

Discussion

3.	Differentiate the following functions with respect to x : 2xcot x√x
Answer» Differentiate the following functions with respect to x : $\frac{2^{x} c o t x}{\sqrt{x}}$

3.

Differentiate the following functions with respect to x : 2xcot x√x

Answer»

Differentiate the following functions with respect to x :

$\frac{2^{x} c o t x}{\sqrt{x}}$

Discussion

4.	In an even n-sided polygon, the sides are painted blue and red alternatively. The vertices of the polygon are joined to form triangles with one side in common with the polygon. Find the number of such triangles with one blue side.
Answer» In an even $n$ -sided polygon, the sides are painted blue and red alternatively. The vertices of the polygon are joined to form triangles with one side in common with the polygon. Find the number of such triangles with one blue side.

Discussion

5.	The angle between the lines represented by the equation 4x2−24xy+11y2=0are
Answer» The angle between the lines represented by the equation $4 x^{2} - 24 x y + 11 y^{2} = 0$ are

Discussion

6.	A fair dice is tossed eight times. Probability that on the eighth throw a third six is observed is
Answer» A fair dice is tossed eight times. Probability that on the eighth throw a third six is observed is

Discussion

7.	The line segment joining the points (−3, −4) and (1, −2) is divided by y-axis in the ratio
Answer» The line segment joining the points $(- 3, - 4)$ and $(1, - 2)$ is divided by y-axis in the ratio

Discussion

8.	If F(n+1)=2F(n)+12 for n=1,2,… and F(1)=2, then F(101) equals
Answer» If $F (n + 1) = \frac{2 F (n) + 1}{2}$ for $n = 1, 2, \dots$ and $F (1) = 2$ , then $F (101)$ equals

Discussion

9.	What is means of gross vectors?
Answer» What is means of gross vectors?

Discussion

10.	Write the converse of the statement 'x is an even number implies that x is divisible by 4'
Answer» Write the converse of the statement 'x is an even number implies that x is divisible by 4'

Discussion

11.	Let f(x) be a function satisfying f(x)+f(x−1)=x2∀x∈R. If f(0) =20, then remainder when f(50) is divided by 1000, is
Answer» Let f(x) be a function satisfying $f (x) + f (x - 1) = x^{2} \forall x \in R$ . If f(0) =20, then remainder when f(50) is divided by 1000, is

Discussion

12.	Why we add c while doing integration .can u explain me with the help of an example
Answer» Why we add c while doing integration .can u explain me with the help of an example

Discussion

13.	In the expansion of (1+x)n(1+y)n(1+z)n, the sum of coefficients of the terms of degree ‘r’ is
Answer» In the expansion of $(1 + x)^{n} (1 + y)^{n} (1 + z)^{n}$ , the sum of coefficients of the terms of degree ‘r’ is

Discussion

14.	If the absolute term (independent of x) in the expansion of (√x−kx2)10 is 405 then k =
Answer» If the absolute term (independent of x) in the expansion of ${(\sqrt{x} - \frac{k}{x^{2}})}^{10}$ is 405 then k =

Discussion

15.	If \|A X B\|=(3)^1/2 A.B, then the value of \|A+B\| is
Answer» If \|A X B\|=(3)^1/2 A.B, then the value of \|A+B\| is

Discussion

16.	The number of ways in which 3 children can distribute 10 tickets out of 15 consecutively numbered tickets among themselves such that they get consecutive blocks of 5, 3 and 2 tickets is
Answer» The number of ways in which 3 children can distribute 10 tickets out of 15 consecutively numbered tickets among themselves such that they get consecutive blocks of 5, 3 and 2 tickets is

Discussion

17.	If f:R→R be defined by f(x)=x2+1, then find f−1{17} and f−1{−3}.
Answer» If $f : R \to R$ be defined by $f (x) = x^{2} + 1$ , then find $f^{- 1} {17}$ and $f^{- 1} {- 3}$ .

Discussion

18.	The maximum number of points of intersection of 8 straight lines is
Answer» The maximum number of points of intersection of $8$ straight lines is

Discussion

19.	If a straight line passing through the point P(−3,4) is such that its intercepted portion between the coordinate axes is bisected at P, the its equation is :
Answer» If a straight line passing through the point $P (- 3, 4)$ is such that its intercepted portion between the coordinate axes is bisected at $P$ , the its equation is :

Discussion

20.	At what values of parameter 'a' are there values of n such that the numbers 5^(1+x)+5^(1-x),a/2, 25^(x)+25^(-x) form an AP.
Answer» At what values of parameter 'a' are there values of n such that the numbers 5^(1+x)+5^(1-x),a/2, 25^(x)+25^(-x) form an AP.

Discussion

21.	Find the greater number in 300! and √300300
Answer» Find the greater number in 300! and $\sqrt{300^{300}}$

Discussion

22.	∫sin3xcos4x dx is equal to.
Answer» $\int {sin}^{3} x {cos}^{4} x d x$ is equal to.

Discussion

23.	One angle of a triangle is 23x grades and another is 32x degrees while the third is πx75 radians. Express all the angles in degrees.
Answer» One angle of a triangle is $\frac{2}{3} x$ grades and another is $\frac{3}{2} x$ degrees while the third is $\frac{π x}{75}$ radians. Express all the angles in degrees.

Discussion

24.	A solution is to be kept between 86∘ and 95∘ F.What is the range of temperature in degree Celsius,if the Celsius(C)/Fahrenheit (F) conversion formula is given by F=95 C+32..
Answer» A solution is to be kept between $86^{\circ} a n d 95^{\circ} F$ .What is the range of temperature in degree Celsius,if the Celsius(C)/Fahrenheit (F) conversion formula is given by $F = \frac{9}{5} C + 32.$ .

Discussion

25.	In a triangle ABC, 2ca sinA−B+C2 is equal to
Answer» In a triangle ABC, $2 c a s i n \frac{A - B + C}{2}$ is equal to

Discussion

26.	If x+y=π/4 ,prove that(1+tanx)(1+tany)=2
Answer» If x+y=π/4 ,prove that(1+tanx)(1+tany)=2

Discussion

27.	Using integration, find the area of the triangle whose vertices are (2,3),(3,5), and (4,4).
Answer» Using integration, find the area of the triangle whose vertices are $(2, 3), (3, 5),$ and $(4, 4) .$

Discussion

28.	The suffix ‘-mony’ refers to
Answer» The suffix ‘-mony’ refers to

Discussion

29.	Let f, g : R → R be defined, respectively by f(x) = x + 1, g(x) = 2x - 3. Find f + g, f - g and fg.
Answer» Let f, g : R $\to$ R be defined, respectively by f(x) = x + 1, g(x) = 2x - 3. Find f + g, f - g and $\frac{f}{g}$ .

Discussion

30.	If (√2)4×43=2x×2√2,then x=?
Answer» If ${(\sqrt{2})}^{4} \times 4^{3} = 2^{x} \times 2 \sqrt{2}, t h e n x = ?$

Discussion

31.	If the straight line 4y – 3x + 18 = 0 cuts the parabola y2=4ax in P and Q.Then the angle subtended by PQ at the vertex of the parabola is
Answer» If the straight line 4y – 3x + 18 = 0 cuts the parabola $y^{2} = 4 a x$ in P and Q.Then the angle subtended by PQ at the vertex of the parabola is

Discussion

32.	If a matrix B is obtained from matrix A by an elementary row or column transformation then B is said to be ______ of A
Answer» If a matrix B is obtained from matrix A by an elementary row or column transformation then B is said to be ______ of A

Discussion

33.	If ∣∣∣→a⋅→b∣∣∣=∣∣∣→a×→b∣∣∣, then the acute angle between →a and →b is (a) 30∘ (b) 45∘ (c) 60∘ (d) 90∘
Answer» If $∣ ∣ ∣ \to a \cdot \to b ∣ ∣ ∣ = ∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣,$ then the acute angle between $\to a$ and $\to b$ is $(a) 30^{\circ} (b) 45^{\circ}$ $(c) 60^{\circ} (d) 90^{\circ}$

Discussion

34.	Evaluate:∫π−π(1−x2)sin xcos2x dx
Answer» $Evaluate : \int_{- π}^{π} (1 - x^{2}) sin x {cos}^{2} x d x$

Discussion

35.	The letters of the word 'SURITI' are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word 'SURITI'.
Answer» The letters of the word 'SURITI' are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word 'SURITI'.

Discussion

36.	Five persons A,B,C,D and E are seated in a circular arrangement. If each of them is given a hat of one of the three colours red, blue and green, then number of ways of distributing the hats such that the persons seated in adjacent seats get different coloured hats is
Answer» Five persons $A, B, C, D$ and $E$ are seated in a circular arrangement. If each of them is given a hat of one of the three colours red, blue and green, then number of ways of distributing the hats such that the persons seated in adjacent seats get different coloured hats is

Discussion

37.	The distance of the point P(-2, 3, 1) from the line QR which passes through the point Q(-3, 6, 2) and makes equal angles with the axes is
Answer» The distance of the point P(-2, 3, 1) from the line QR which passes through the point Q(-3, 6, 2) and makes equal angles with the axes is

Discussion

38.	According to the passage, which of the following behaviours of people are better explained by behavioural science than by economics?
Answer» According to the passage, which of the following behaviours of people are better explained by behavioural science than by economics?

Discussion

39.	Let * be a binary operation defined on set of rational numbers, by a * b =ab10. Find the identity element.
Answer» Let * be a binary operation defined on set of rational numbers, by a * b = $\frac{a b}{10}$ . Find the identity element.

Discussion

40.	A rectangle is inscribed in a circle with a diameter lying along the line 3y=x+7. If the two adjacent vertices of the rectangle are (−8,5) and (6,5), then the area of the rectangle (in sq. units) is :
Answer» A rectangle is inscribed in a circle with a diameter lying along the line $3 y = x + 7$ . If the two adjacent vertices of the rectangle are $(- 8, 5)$ and $(6, 5)$ , then the area of the rectangle (in sq. units) is :

Discussion

41.	For an equilateral triangle, one side lies on x+y=6 and the 3rd vertex is mirror image of the origin in the mirror x+y=6. Then the coordinates of other two vertices are
Answer» For an equilateral triangle, one side lies on $x + y = 6$ and the $3^{r d}$ vertex is mirror image of the origin in the mirror $x + y = 6$ . Then the coordinates of other two vertices are

Discussion

42.	If a, b, c are in G.P., prove that 1logam, 1logbm, 1logcm are in A.P.,
Answer» If a, b, c are in G.P., prove that $\frac{1}{l o g_{a} m}, \frac{1}{l o g_{b} m}, \frac{1}{l o g_{c} m}$ are in A.P.,

Discussion

43.	The solution set of inequality log5(x−3)+12log53<12log5(2x2−6x+7) is
Answer» The solution set of inequality ${log}_{5} (x - 3) + \frac{1}{2} {log}_{5} 3 < \frac{1}{2} {log}_{5} (2 x^{2} - 6 x + 7)$ is

Discussion

44.	The value of cot10°(cot40°−cot50°) is equal to
Answer» The value of $cot 10 ° (cot 40 ° - cot 50 °)$ is equal to

Discussion

45.	The equation of the common tangent to the curves is y2=8x and xy=−1 is
Answer» The equation of the common tangent to the curves is $y^{2} = 8 x a n d x y = - 1$ is

Discussion

46.	Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.
Answer» Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

Discussion

47.	Find the height of a cylinder whose volume is 1.54 m cubed. and diameter of the base is 140 cm ?
Answer» Find the height of a cylinder whose volume is 1.54 m cubed. and diameter of the base is 140 cm ?

Discussion

48.	A man is known to speak truth 3 out of 4 times. He throws a dice and reports that it is a six. Find the probability that it is actually a six.
Answer» A man is known to speak truth 3 out of 4 times. He throws a dice and reports that it is a six. Find the probability that it is actually a six.

Discussion

49.	Find the two numbers whose A.M. is 25 and GM is 20.
Answer» Find the two numbers whose A.M. is 25 and GM is 20.

Discussion

50.	-(x-3)+4 < 5 - 2x
Answer» -(x-3)+4 < 5 - 2x

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Let f(x)=sin x ∫x0cos t dt+2∫x0t dt+cos2 x−x2. Then area bounded by x f(x) and ordinate x = 0 and x = 5 with x-axis is

The value of 50∑r=0(−1)r 50Crr+2 is equal to

Differentiate the following functions with respect to x : 2xcot x√x

In an even n-sided polygon, the sides are painted blue and red alternatively. The vertices of the polygon are joined to form triangles with one side in common with the polygon. Find the number of such triangles with one blue side.

The angle between the lines represented by the equation 4x2−24xy+11y2=0are

A fair dice is tossed eight times. Probability that on the eighth throw a third six is observed is

The line segment joining the points (−3, −4) and (1, −2) is divided by y-axis in the ratio

If F(n+1)=2F(n)+12 for n=1,2,… and F(1)=2, then F(101) equals

What is means of gross vectors?

Write the converse of the statement 'x is an even number implies that x is divisible by 4'

Let f(x) be a function satisfying f(x)+f(x−1)=x2∀x∈R. If f(0) =20, then remainder when f(50) is divided by 1000, is

Why we add c while doing integration .can u explain me with the help of an example

In the expansion of (1+x)n(1+y)n(1+z)n, the sum of coefficients of the terms of degree ‘r’ is

If the absolute term (independent of x) in the expansion of (√x−kx2)10 is 405 then k =

If |A X B|=(3)^1/2 A.B, then the value of |A+B| is

The number of ways in which 3 children can distribute 10 tickets out of 15 consecutively numbered tickets among themselves such that they get consecutive blocks of 5, 3 and 2 tickets is

If f:R→R be defined by f(x)=x2+1, then find f−1{17} and f−1{−3}.

The maximum number of points of intersection of 8 straight lines is

If a straight line passing through the point P(−3,4) is such that its intercepted portion between the coordinate axes is bisected at P, the its equation is :

At what values of parameter 'a' are there values of n such that the numbers 5^(1+x)+5^(1-x),a/2, 25^(x)+25^(-x) form an AP.

Find the greater number in 300! and √300300

∫sin3xcos4x dx is equal to.

One angle of a triangle is 23x grades and another is 32x degrees while the third is πx75 radians. Express all the angles in degrees.

A solution is to be kept between 86∘ and 95∘ F.What is the range of temperature in degree Celsius,if the Celsius(C)/Fahrenheit (F) conversion formula is given by F=95 C+32..

In a triangle ABC, 2ca sinA−B+C2 is equal to

If x+y=π/4 ,prove that(1+tanx)(1+tany)=2

Using integration, find the area of the triangle whose vertices are (2,3),(3,5), and (4,4).

The suffix ‘-mony’ refers to

Let f, g : R → R be defined, respectively by f(x) = x + 1, g(x) = 2x - 3. Find f + g, f - g and fg.

If (√2)4×43=2x×2√2,then x=?

If the straight line 4y – 3x + 18 = 0 cuts the parabola y2=4ax in P and Q.Then the angle subtended by PQ at the vertex of the parabola is

If a matrix B is obtained from matrix A by an elementary row or column transformation then B is said to be ______ of A

If ∣∣∣→a⋅→b∣∣∣=∣∣∣→a×→b∣∣∣, then the acute angle between →a and →b is (a) 30∘ (b) 45∘ (c) 60∘ (d) 90∘

Evaluate:∫π−π(1−x2)sin xcos2x dx

The letters of the word 'SURITI' are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word 'SURITI'.

Five persons A,B,C,D and E are seated in a circular arrangement. If each of them is given a hat of one of the three colours red, blue and green, then number of ways of distributing the hats such that the persons seated in adjacent seats get different coloured hats is

The distance of the point P(-2, 3, 1) from the line QR which passes through the point Q(-3, 6, 2) and makes equal angles with the axes is

According to the passage, which of the following behaviours of people are better explained by behavioural science than by economics?

Let * be a binary operation defined on set of rational numbers, by a * b =ab10. Find the identity element.

A rectangle is inscribed in a circle with a diameter lying along the line 3y=x+7. If the two adjacent vertices of the rectangle are (−8,5) and (6,5), then the area of the rectangle (in sq. units) is :

For an equilateral triangle, one side lies on x+y=6 and the 3rd vertex is mirror image of the origin in the mirror x+y=6. Then the coordinates of other two vertices are

If a, b, c are in G.P., prove that 1logam, 1logbm, 1logcm are in A.P.,

The solution set of inequality log5(x−3)+12log53&lt;12log5(2x2−6x+7) is

The value of cot10°(cot40°−cot50°) is equal to

The equation of the common tangent to the curves is y2=8x and xy=−1 is

Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

Find the height of a cylinder whose volume is 1.54 m cubed. and diameter of the base is 140 cm ?

A man is known to speak truth 3 out of 4 times. He throws a dice and reports that it is a six. Find the probability that it is actually a six.

Find the two numbers whose A.M. is 25 and GM is 20.

-(x-3)+4 &lt; 5 - 2x

The solution set of inequality log5(x−3)+12log53<12log5(2x2−6x+7) is

-(x-3)+4 < 5 - 2x