List of top Mathematics Questions

If each observation of a Row data whose variance is σ² is multiplied by h, then the variance of the new set is

If a Chord which is normal to the parabola y² = 4ax at one end subtends a right angle at the vertex, then its slope is -

Match List-I and List-II

LIST I		LIST II
A.	The angle between the straight lines, 2x2+ 3y2-7xy=0 is	I.	\(\tan^{-1}\frac{3}{5}\)
B.	The circles x2+y2+x+y=0 and x2+y2 +x-y=0 intersect at angle	II.	25π
C.	The area of circle centered at (1,2) and passing through (4,6) is	III.	π/4
D.	The parabola y2=4x and x2 =32y intersect at point (16,8) at angle	IV.	π/2

Choose the correct answer from the options given below:

Given below are two statements :
Statement I: The number of different number each of 6 digits that can be formed by using all the digits 1, 2, 1, 0, 2, 2 is 50.
Statement II: These are 4536 possibilities of writing the four digit numbers which have all distinct digits.
In the light of the above statements, choose the correct answer from the options given below:

Which statistical method is best suitable for testing the goodness of fit between an observed and expected distribution?

If each of n numbers x_i = i is replaced by (i + 1)x_i, then the new mean is

Match List-I and List-II

LIST I		LIST II
A.	Addition Theorem on probability	I.	\(P(Ei/A)=\frac{p(Ei)P(A/Ei)}{\displaystyle\sum_{l=1}^nP(Ei)P(A/Ei)},i=1,2\)
B.	Binomial distribution	II.	\(P(A\cap B)=P(A)P(B/A),if P(A)\neq0\)
C.	Baye's rule	III.	\(P(A\cup B)=P(A)+P(A)+P(B)-P(A\cap B)\)
D.	Multiplication theorem on prob	IV.	\(P(x=r)=^nC_rp^rq^{n-r},r=0,1,.....,n\)

Choose the correct answer from the options given below:

If x,y,z are all distinct and \(\begin{vmatrix} x & x^2 & 1+x^3\\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3 \end{vmatrix}\)=0, then the value of xyz is

Given below are two statements:
If \(z_1\) and \(z_2\) are complex numbers
Statement-1 : \(arg(\frac{z_1} {z_2})=arg(z_1)-arg(z_2)\)
Statement-II : \(|z_1+z_2|^2=|z_1|^2+|z_2|^2-2Re(z_1\bar z_2)\)
In the light of the above statements, choose the correct answer from the options given below.

The number of vectors of unit length perpendicular to vectors \(\vec{a}\) = (1,1,0) and \(\vec{b}\) = (0,1,1) is

For x = 3, find the value of \(x^5+x^4-x^3-x^2+x-1.\)

The sum of two digits no. is 10, on reversing the digits of a number the number is decrease by 36. Find the number.

Given below are two statements: One is lebelled as Assertion A and the other is labelled as Reason R.
Assertion A: If two circles interesect at two points, then the line joining their centres is prependicular to the common chord.
Reason R: The perpendicular bisectors of two chords of a circle intersect at its centre.
In the light of the above statements, choose the correct answer from the options given below:

If A₁, A₂ be two AM's and G₁, G₂ be two GM's between a and b, then \(\frac{A1+A2}{G1G2}\) is equal to

Which of the following is true:
A. If a cos A = b cos B, then the triangle is isosceles or right angled.
B. If in a triangle ABC, cos A cos B + sin A sin B sin C =1 then the triangle is isosceles right angled.
C. If the ex-radii r1, r2, r3 of ΔABC are in the HP, then it's sides are not in AP
Choose the correct answer from the options given below :

Let A(3, 0, - 1) , B(2, 10, 6) and C(1, 2, 1) be the vertices of a triangle and M be the mid-point of AC. If G divides BM in the ratio 2:1, then cos( ∠GOA ) (O being the origin) is equal to______.

Mohan invest a certain sum at the rate of Simple Interest 5% per annum. Find the number of years for which Mohan has to invest the the sum to double his sum

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
3 Assertion A: \(\int\limits_{-x}^{3}(x^3+5)dx=30\)
Reason R: f(x) = x³ +5 is an odd function
In the light of the above statements, choose the correct answer from the options given below:

Given below are two statements :
Statement I: \(\int\limits_{-a}^af(x)dx=\int\limits_{0}^a[f(x)+f(-x)]dx\)
Statement II : \(\int\limits_{0}^1\sqrt{(1+x)(1+x^3)}dx\) is less than or equal to \(\frac{15}{8}\).
In the light of the above statements, choose the most appropriate answer from the options given below :

The line integral per unit area along the boundary of small area around a point in vector field \(\overrightarrow A\) is called

Let E be the ellipse\(\frac{x^2}{9}+\frac{y^2}{4}=1\) and C be the circle x² + y² = 9. Let P and Q be the points (1, 2) and (2, 1) respectively. Then

The tangent to the hyperbola x² - y² = 3 are parallel to the straight line 2x + y +8 = 0 at the following points:

Renu speaks truth in 70% of the cases and Bina in 75% of the cases. The percentage of ceses they are likely to contradict each other in stating the same fact is

If f and g are differentiable functions in (0, 1) satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6, then for some c ∈]0, 1[

Given below are two statements: One is lebelled as Assertion A and the other is labelled as Reason R.
Assertion A: The number of parallelograms in a chess board is 1296.
Reason R: The number of parallelograms when a set of m parallel lines is intersected by another set of n parallel lines is ^mC₂.ⁿC₂
In the light of the above statements, choose the correct answer from the options given below: