43030 + Interview Questions in Mathematics

1.	The value of x∈R for which vectors →a=(1,−2,1),→b=(−2,3,−4),→c=(1,−1,x) form a linearly dependent system, is equal to
Answer» The value of $x \in R$ for which vectors $\to a = (1, - 2, 1), \to b = (- 2, 3, - 4), \to c = (1, - 1, x)$ form a linearly dependent system, is equal to

Discussion

2.	Algebraic sum of the intercepts made by the plane x + 3y - 4z + 6 = 0 on the axes is
Answer» Algebraic sum of the intercepts made by the plane x + 3y - 4z + 6 = 0 on the axes is

Discussion

3.	(3) Stee The length of an elastic string is X m when the tension is 8 N, and Y m when the tension is 10 N in metres when the tension is 18 N is (1) 4X- 5Y (3) 9x-4Y . The length (2) 5Y-4X 4) 4Y-9x
Answer» (3) Stee The length of an elastic string is X m when the tension is 8 N, and Y m when the tension is 10 N in metres when the tension is 18 N is (1) 4X- 5Y (3) 9x-4Y . The length (2) 5Y-4X 4) 4Y-9x

Discussion

4.

Match the following functions satisfying particular functional relationship Column-I (A) f(x+y)=f(x)+f(y) (B) f(xy)=f(x)+f(y) (C) f(x+y)=f(x)⋅f(y) (D) f(X)+f(y)=f(x+y1−xy) Column-II (p) log3x (q) tan−1x (r) 3x (s) 3x (t) A transcendental function

Answer» Match the following functions satisfying particular functional relationship

	Column-I
(A)	$f (x + y) = f (x) + f (y)$
(B)	$f (x y) = f (x) + f (y)$
(C)	$f (x + y) = f (x) \cdot f (y)$
(D)	$f (X) + f (y) = f (\frac{x + y}{1 - x y})$

	Column-II
(p)	${log}_{3} x$
(q)	$t a n^{- 1} x$
(r)	$3 x$
(s)	$3^{x}$
(t)	A transcendental function

Discussion

5.	The acute angle of intersection of the curves y=[\|sinx\|+\|cosx\|] and x2+y2=5 (where [.] denotes the greatest integer function) is tan−1(k) then k is
Answer» The acute angle of intersection of the curves $y = [\| sin x \| + \| cos x \|]$ and $x^{2} + y^{2} = 5$ (where $[.]$ denotes the greatest integer function) is ${tan}^{- 1} (k)$ then $k$ is

Discussion

6.	11.4+14.7+17.10+...
Answer» $\frac{1}{1.4} + \frac{1}{4.7} + \frac{1}{7.10} + . . .$

Discussion

7.	If x∈R, then the range of log5/4(5x2−8x+4) is
Answer» If $x \in R$ , then the range of ${log}_{5 / 4} (5 x^{2} - 8 x + 4)$ is

Discussion

8.	An urn contains 5 red and 2 black balls. Two balls are randomly drawn, without replacement. Let X represent the number of black balls. Drawn. What are the possible values of X? Is X a random variable ? If yes, find the mean and variance of X.
Answer» An urn contains 5 red and 2 black balls. Two balls are randomly drawn, without replacement. Let X represent the number of black balls. Drawn. What are the possible values of X? Is X a random variable ? If yes, find the mean and variance of X.

Discussion

9.	If A={x∶x is a multiple of 3} and B={x∶x is a multiple of 5}, then A−B=
Answer» If $A = {x ∶ x is a multiple of 3}$ and $B = {x ∶ x is a multiple of 5}$ , then $A - B =$

Discussion

10.	The figure formed by the lines ax±by±c=0 is
Answer» The figure formed by the lines $a x \pm b y \pm c = 0$ is

Discussion

11.	Find the general solution of the equation sinx+sin3x+sin5x=0
Answer» Find the general solution of the equation $sin x + sin 3 x + sin 5 x = 0$

Discussion

12.	In ΔABC, the median AD divides ∠BAC such that ∠BAD:∠CAD=2:1. Then cos(A3) is equal to
Answer» In $Δ A B C$ , the median $A D$ divides $∠ B A C$ such that $∠ B A D : ∠ C A D = 2 : 1.$ Then $cos (\frac{A}{3})$ is equal to

Discussion

13.	If sin x= cos x and x is acute, state the value of x
Answer» If sin x= cos x and x is acute, state the value of x

Discussion

14.	If tanα=2tt2−1, what is t?
Answer» If $t a n α = \frac{2 t}{t^{2} - 1}$ , what is t?

Discussion

15.	Write the solution set of the inequation x+1x≥2
Answer» Write the solution set of the inequation $x + \frac{1}{x} \geq 2$

Discussion

16.	Find x if cos3x+sin(2x-7/6)=-2
Answer» Find x if cos3x+sin(2x-7/6)=-2

Discussion

17.	Evaluate the following:a+xyzxa+yzxya+z
Answer» Evaluate the following: $\|\begin{matrix} a + x & y & z \\ x & a + y & z \\ x & y & a + z \end{matrix}\|$

Discussion

18.	81.Three symmetrical dices are thrown .The probability that the same number will appear on each of them is? options: (a)1/216 (b)1/36 (c)35/36 (d)1/35
Answer» 81.Three symmetrical dices are thrown .The probability that the same number will appear on each of them is? options: (a)1/216 (b)1/36 (c)35/36 (d)1/35

Discussion

19.	If parabola touches the x axis at one point then there will be one zero or two overlapping zeros?
Answer» If parabola touches the x axis at one point then there will be one zero or two overlapping zeros?

Discussion

20.	What is the condition for a function y = f(x) to be a monotonically increasing function
Answer» What is the condition for a function y = f(x) to be a monotonically increasing function

Discussion

21.	Let (1−x+x4)10=a0+a1x+a2x2+⋯+a40x40. Then which of the following options is CORRECT?
Answer» Let ${(1 - x + x^{4})}^{10} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{40} x^{40} .$ Then which of the following options is CORRECT?

Discussion

22.	If 2 sin θ + 3 cos θ = 2, then 3 sin θ – 2 cos θ = _________.
Answer» If 2 sin θ + 3 cos θ = 2, then 3 sin θ – 2 cos θ = _________.

Discussion

23.	{ If }l_1=∫_0^{mπ}f(\vert\operatorname{cos}x\vert)dx and }l_2=∫_0^{5π}f(\vert\operatorname{cos}x\vert)dx} then
Answer» { If }l_1=∫_0^{mπ}f(\vert\operatorname{cos}x\vert)dx and }l_2=∫_0^{5π}f(\vert\operatorname{cos}x\vert)dx} then

Discussion

24.	An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known: P(A fails) = 0.2 P(B fails alone) = 0.15 P(A and B fail) = 0.15 Evaluate the following probabilities (i) P(A fails\| B has failed) (ii) P(A fails alone)
Answer» An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known: P(A fails) = 0.2 P(B fails alone) = 0.15 P(A and B fail) = 0.15 Evaluate the following probabilities (i) P(A fails\| B has failed) (ii) P(A fails alone)

Discussion

25.	23.At far off distant places, electricity is supplied with high voltage and low current. Explain why
Answer» 23.At far off distant places, electricity is supplied with high voltage and low current. Explain why

Discussion

26.	The value of 1∫−1x√1−x2⋅sin−1(2x√1−x2)dx is equal to
Answer» The value of $1 \int - 1 \frac{x}{\sqrt{1 - x^{2}}} \cdot {sin}^{- 1} (2 x \sqrt{1 - x^{2}}) d x$ is equal to

Discussion

27.	If f(x) = exg(x), g(0) = 2, g'(0) = 1, then f'(0) = __________________.
Answer» If f(x) = e^xg(x), g(0) = 2, g'(0) = 1, then f'(0) = __________________.

Discussion

28.	Hybridisation of Xe in XeF4 molecule isXeF4 अणु में Xe का संकरण क्या है?
Answer» Hybridisation of Xe in XeF₄ molecule is XeF₄ अणु में Xe का संकरण क्या है?

Discussion

29.	The sum of all values of x for which the matrix [3x2xx+1x−1] is NOT invertible, is[2 marks]
Answer» The sum of all values of $x$ for which the matrix $[\begin{matrix} 3 x & 2 x x + 1 & x - 1 \end{matrix}]$ is NOT invertible, is [2 marks]

Discussion

30.	The differential equation that represents the family of curves y=12x2−c, where c is an arbitrary constant is
Answer» The differential equation that represents the family of curves $y = \frac{1}{2 x^{2} - c},$ where $c$ is an arbitrary constant is

Discussion

31.	Solve the given inequality for real x:
Answer» Solve the given inequality for real x:

Discussion

32.	The value of the determinant ∆=sec2θtan2θ1tan2θsec2θ-122202 is _____________.
Answer» The value of the determinant $∆ = \|\begin{matrix} \sec^{2} θ & \tan^{2} θ & 1 \\ \tan^{2} θ & \sec^{2} θ & - 1 \\ 22 & 20 & 2 \end{matrix}\|$ is _____________.

Discussion

33.	Find the intervals in which the following functions are increasing or decreasing.(i) f(x) = 10 − 6x − 2x2(ii) f(x) = x2 + 2x − 5(iii) f(x) = 6 − 9x − x2(iv) f(x) = 2x3 − 12x2 + 18x + 15(v) f(x) = 5 + 36x + 3x2 − 2x3(vi) f(x) = 8 + 36x + 3x2 − 2x3(vii) f(x) = 5x3 − 15x2 − 120x + 3(viii) f(x) = x3 − 6x2 − 36x + 2(ix) f(x) = 2x3 − 15x2 + 36x + 1(x) f(x) = 2x3 + 9x2 + 12x + 20(xi) f(x) = 2x3 − 9x2 + 12x − 5(xii) f(x) = 6 + 12x + 3x2 − 2x3(xiii) f(x) = 2x3 − 24x + 107(xiv) f(x) = −2x3 − 9x2 − 12x + 1(xv) f(x) = (x − 1) (x − 2)2(xvi) f(x) = x3 − 12x2 + 36x + 17(xvii) f(x) = 2x3 − 24x + 7(xviii) fx=310x4-45x3-3x2+365x+11(xix) f(x) = x4 − 4x(xx) fx=x44+23x3-52x2-6x+7(xxi) f(x) = x4 − 4x3 + 4x2 + 15(xxii) f(x) = 5x32-3x52, x > 0(xxiii) f(x) = x8 + 6x2(xxiv) f(x) = x3 − 6x2 + 9x + 15(xxv) fx=x(x-2)2(xxvi) fx=3x4-4x3-12x2+5(xxvii) fx=32x4-4x3-45x2+51(xxviii) fx=log2+x-2x2+x, x∈R(xxix) fx=x44-x3-5x2+24x+12
Answer» Find the intervals in which the following functions are increasing or decreasing. (i) f(x) = 10 − 6x − 2x² (ii) f(x) = x² + 2x − 5 (iii) f(x) = 6 − 9x − x² (iv) f(x) = 2x³ − 12x² + 18x + 15 (v) f(x) = 5 + 36x + 3x² − 2x³ (vi) f(x) = 8 + 36x + 3x² − 2x³ (vii) f(x) = 5x³ − 15x² − 120x + 3 (viii) f(x) = x³ − 6x² − 36x + 2 (ix) f(x) = 2x³ − 15x² + 36x + 1 (x) f(x) = 2x³ + 9x² + 12x + 20 (xi) f(x) = 2x³ − 9x² + 12x − 5 (xii) f(x) = 6 + 12x + 3x² − 2x³ (xiii) f(x) = 2x³ − 24x + 107 (xiv) f(x) = −2x³ − 9x² − 12x + 1 (xv) f(x) = (x − 1) (x − 2)² (xvi) f(x) = x³ − 12x² + 36x + 17 (xvii) f(x) = 2x³ − 24x + 7 (xviii) $f (x) = \frac{3}{10} x^{4} - \frac{4}{5} x^{3} - 3 x^{2} + \frac{36}{5} x + 11$ (xix) f(x) = x⁴ − 4x (xx) $f (x) = \frac{x^{4}}{4} + \frac{2}{3} x^{3} - \frac{5}{2} x^{2} - 6 x + 7$ (xxi) f(x) = x⁴ − 4x³ + 4x² + 15 (xxii) f(x) = $5 x^{\frac{3}{2}} - 3 x^{\frac{5}{2}}$ , x > 0 (xxiii) f(x) = x⁸ + 6x² (xxiv) f(x) = x³ − 6x² + 9x + 15 (xxv) $f (x) = {\{x (x - 2)\}}^{2}$ (xxvi) $f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 5$ (xxvii) $f (x) = \frac{3}{2} x^{4} - 4 x^{3} - 45 x^{2} + 51$ (xxviii) $f (x) = \log (2 + x) - \frac{2 x}{2 + x}, x \in R$ (xxix) $f (x) = \frac{x^{4}}{4} - x^{3} - 5 x^{2} + 24 x + 12$

Discussion

34.	Find the area bounded by curves (x– 1)2 + y2 = 1 and x2+ y 2 = 1
Answer» Find the area bounded by curves (x – 1)² + y² = 1 and x² + y² = 1

Discussion

35.	Find the vector and the Cartesian equations of the line that passes through the points (3, −2, −5), (3, −2, 6).
Answer» Find the vector and the Cartesian equations of the line that passes through the points (3, −2, −5), (3, −2, 6).

Discussion

36.	Give me value of R in all units
Answer» Give me value of R in all units

Discussion

37.	If circle x2+y2−6x−10y+c=0 does not touch (or) intersect the coordinates axes and the point (1,4) is inside the circle, then the range of c is
Answer» If circle $x^{2} + y^{2} - 6 x - 10 y + c = 0$ does not touch (or) intersect the coordinates axes and the point $(1, 4)$ is inside the circle, then the range of $c$ is

Discussion

38.	Question 1(vi)Check whether the following are quadratic equations:(vi) x2+3x+1=(x−2)2
Answer» Question 1(vi) Check whether the following are quadratic equations: (vi) $x^{2} + 3 x + 1 = (x - 2)^{2}$

Discussion

39.	The side of a triangle are in the ratio 1:√3:2, then the angles of the triangle are in the ratio
Answer» The side of a triangle are in the ratio $1 : \sqrt{3} : 2$ , then the angles of the triangle are in the ratio

Discussion

40.	The equation of the bisectors of the angle between lines represented by equation 4x2−16xy−7y2=0 is
Answer» The equation of the bisectors of the angle between lines represented by equation $4 x^{2} - 16 x y - 7 y^{2} = 0$ is

Discussion

41.	Inverse function is defined for which of the following type of function -
Answer» Inverse function is defined for which of the following type of function -

Discussion

42.	If the distance between the foci and the distance between two directrices of the hyperbola x2a2−y2b2=1 are in the ratio 3:2, then b:a is
Answer» If the distance between the foci and the distance between two directrices of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ are in the ratio $3 : 2$ , then $b : a$ is

Discussion

43.	If one of the diameters of the circle x2+y2−2x−6y+6=0 is a chord to the circle with centre (2,1), then the equation of the circle is
Answer» If one of the diameters of the circle $x^{2} + y^{2} - 2 x - 6 y + 6 = 0$ is a chord to the circle with centre $(2, 1)$ , then the equation of the circle is

Discussion

44.	If the roots of the equation px^2 + qx + r = 0, where 2p, q, 2r are in G.P, are of the form a^2 , 4a — 4. Then the value of 2p + 4q + 7r is :
Answer» If the roots of the equation px^2 + qx + r = 0, where 2p, q, 2r are in G.P, are of the form a^2 , 4a — 4. Then the value of 2p + 4q + 7r is :

Discussion

45.	What's the angle between a diagonal of a cube and the diagonal of face of the cube
Answer» What's the angle between a diagonal of a cube and the diagonal of face of the cube

Discussion

46.	If A and B are two independent events such that P(A)>0.5,P(B)>0.5, P(A∩¯¯¯¯B)=325, P(¯¯¯¯A∩B)=825, then P(A∩B)=k, then 25k2 is
Answer» If $A$ and $B$ are two independent events such that $P (A) > 0.5, P (B) > 0.5,$ $P (A \cap ¯ ¯¯ ¯ B) = \frac{3}{25}$ , $P (¯ ¯¯ ¯ A \cap B) = \frac{8}{25}$ , then $P (A \cap B) = k$ , then $\frac{25 k}{2}$ is

Discussion

47.	Integrate the following integrals:∫sinx cos2x sin3x dx
Answer» Integrate the following integrals: $\int \sin x \cos 2 x \sin 3 x d x$

Discussion

48.	The eccentricity of the conic 4x2+16y2−32x−32y=1 is
Answer» The eccentricity of the conic $4 x^{2} + 16 y^{2} - 32 x - 32 y = 1$ is

Discussion

49.	x2−y2+5x+8y−4=0 represents
Answer» $x^{2} - y^{2} + 5 x + 8 y - 4 = 0$ represents

Discussion

50.	The number of non-negtive integer(s) which lie in between the maximum and minimum value of x if −5≤2x−4≤−1 is
Answer» The number of non-negtive integer(s) which lie in between the maximum and minimum value of $x$ if $- 5 \leq 2 x - 4 \leq - 1$ is

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The value of x∈R for which vectors →a=(1,−2,1),→b=(−2,3,−4),→c=(1,−1,x) form a linearly dependent system, is equal to

Algebraic sum of the intercepts made by the plane x + 3y - 4z + 6 = 0 on the axes is

(3) Stee The length of an elastic string is X m when the tension is 8 N, and Y m when the tension is 10 N in metres when the tension is 18 N is (1) 4X- 5Y (3) 9x-4Y . The length (2) 5Y-4X 4) 4Y-9x

Match the following functions satisfying particular functional relationship Column-I (A) f(x+y)=f(x)+f(y) (B) f(xy)=f(x)+f(y) (C) f(x+y)=f(x)⋅f(y) (D) f(X)+f(y)=f(x+y1−xy) Column-II (p) log3x (q) tan−1x (r) 3x (s) 3x (t) A transcendental function

The acute angle of intersection of the curves y=[|sinx|+|cosx|] and x2+y2=5 (where [.] denotes the greatest integer function) is tan−1(k) then k is

11.4+14.7+17.10+...

If x∈R, then the range of log5/4(5x2−8x+4) is

An urn contains 5 red and 2 black balls. Two balls are randomly drawn, without replacement. Let X represent the number of black balls. Drawn. What are the possible values of X? Is X a random variable ? If yes, find the mean and variance of X.

If A={x∶x is a multiple of 3} and B={x∶x is a multiple of 5}, then A−B=

The figure formed by the lines ax±by±c=0 is

Find the general solution of the equation sinx+sin3x+sin5x=0

In ΔABC, the median AD divides ∠BAC such that ∠BAD:∠CAD=2:1. Then cos(A3) is equal to

If sin x= cos x and x is acute, state the value of x

If tanα=2tt2−1, what is t?

Write the solution set of the inequation x+1x≥2

Find x if cos3x+sin(2x-7/6)=-2

Evaluate the following:a+xyzxa+yzxya+z

81.Three symmetrical dices are thrown .The probability that the same number will appear on each of them is? options: (a)1/216 (b)1/36 (c)35/36 (d)1/35

If parabola touches the x axis at one point then there will be one zero or two overlapping zeros?

What is the condition for a function y = f(x) to be a monotonically increasing function

Let (1−x+x4)10=a0+a1x+a2x2+⋯+a40x40. Then which of the following options is CORRECT?

If 2 sin θ + 3 cos θ = 2, then 3 sin θ – 2 cos θ = _________.

{ If }l_1=∫_0^{mπ}f(\vert\operatorname{cos}x\vert)dx and }l_2=∫_0^{5π}f(\vert\operatorname{cos}x\vert)dx} then

23.At far off distant places, electricity is supplied with high voltage and low current. Explain why

The value of 1∫−1x√1−x2⋅sin−1(2x√1−x2)dx is equal to

If f(x) = exg(x), g(0) = 2, g'(0) = 1, then f'(0) = __________________.

Hybridisation of Xe in XeF4 molecule isXeF4 अणु में Xe का संकरण क्या है?

The sum of all values of x for which the matrix [3x2xx+1x−1] is NOT invertible, is[2 marks]

The differential equation that represents the family of curves y=12x2−c, where c is an arbitrary constant is

Solve the given inequality for real x:

The value of the determinant ∆=sec2θtan2θ1tan2θsec2θ-122202 is _____________.

Find the area bounded by curves (x– 1)2 + y2 = 1 and x2+ y 2 = 1

Find the vector and the Cartesian equations of the line that passes through the points (3, −2, −5), (3, −2, 6).

Give me value of R in all units

If circle x2+y2−6x−10y+c=0 does not touch (or) intersect the coordinates axes and the point (1,4) is inside the circle, then the range of c is

Question 1(vi)Check whether the following are quadratic equations:(vi) x2+3x+1=(x−2)2

The side of a triangle are in the ratio 1:√3:2, then the angles of the triangle are in the ratio

The equation of the bisectors of the angle between lines represented by equation 4x2−16xy−7y2=0 is

Inverse function is defined for which of the following type of function -

If the distance between the foci and the distance between two directrices of the hyperbola x2a2−y2b2=1 are in the ratio 3:2, then b:a is

If one of the diameters of the circle x2+y2−2x−6y+6=0 is a chord to the circle with centre (2,1), then the equation of the circle is

If the roots of the equation px^2 + qx + r = 0, where 2p, q, 2r are in G.P, are of the form a^2 , 4a — 4. Then the value of 2p + 4q + 7r is :

What's the angle between a diagonal of a cube and the diagonal of face of the cube

If A and B are two independent events such that P(A)&gt;0.5,P(B)&gt;0.5, P(A∩¯¯¯¯B)=325, P(¯¯¯¯A∩B)=825, then P(A∩B)=k, then 25k2 is

Integrate the following integrals:∫sinx cos2x sin3x dx

The eccentricity of the conic 4x2+16y2−32x−32y=1 is

x2−y2+5x+8y−4=0 represents

The number of non-negtive integer(s) which lie in between the maximum and minimum value of x if −5≤2x−4≤−1 is

If A and B are two independent events such that P(A)>0.5,P(B)>0.5, P(A∩¯¯¯¯B)=325, P(¯¯¯¯A∩B)=825, then P(A∩B)=k, then 25k2 is