Show that the relation R in the set R of real numbers, defined as R = {(a, b): a ≤ b^2} is neither

Let A, B and C be the sets such that A∪B = A∪C and A∩B = A∩C. Show that B = C.

Find the domain and Range of sqrt (9-x^2)

Find the domain of f(x) = sin inverse x square

In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many

Use the product of matrices solve the System of Linear Equations

Q6. Integration of limit 0 to pi of x upon a square cos square x plus b square sin square x into dx

Integral of x^2 +1 upon x^4 + 1

If e^x plus e^y equals e^x+y, then prove that the derivative of y with respect to x plus e^y-x = 0

Find the Domain of y = Sin x + Sin inverse x .

Differentiate Tan invers x upon sqrt(1-x^2) with respect to sin inverse 2x sqrt(1-x^2)

Continuity and Differentiability Class 12 || Important PYQ

If α = 3i + 4j + 5k and β = 2i + j - 4k then express in the form β= β1 + β2 where β1 is parallel to

Online Evaluation Class 12th || On Screen Copy checking

The sum of a two-digit number and the number obtained by reversing the digits is 88. If the digits

Let A = R-{3} and B = R-{2/3} . If f: A to B : f(x) = 2x-4 / 3x-9 then prove that f is a bijective

Case Study 38 Mathematics Set 3 Class 10

Class 12 Integration Miscellaneous Exercise PYQ

Integration of ( Sin x + Cos x )/ 9 + 16Sin 2x

Board Examination 2026 Mathematics || Class 10 Maths Questions Paper Solution

In Fig 6.13, OB is the perpendicular bisector of the line segment DE, FA⊥OB and FE intersects OB

Sides AB and AC and median AD of a ΔABC are respectively proportional to sides PQ and PR and median

In ∆ABC, D, E and F are midpoints of BC, CA and AB respectively. Prove that AFBD~ADEF and ADEF~ΔΑΒC.

In given figure AB parallel to PQ parallel to CD, AB=x units CD=y unit and PQ=z,prove that 1/x + 1/y

Integration of from 0 to pi/4 sin x cos x / (sin power 4 x + cos power 4)

Integrals Miscellaneous Exercise 7 || Integrals of 1 / sqrt (x + a) + sqrt (x + b)

Trigonometry Class 10 | Competitive based Trigonometry class 10

Prove that Sin A - Cos A + 1 upon Sin A + Cos A - 1 is equal to 1 upon Sec A - Tan A

If the Sum of First M Terms of an A.P. is the Same as the Sum of Its First N Terms, Show that the

If cosecθ - sinθ = l and secθ - cosθ = m , Show that l^2 m^2 (l^2 + m^2 + 3 ) = 1

Solve the differential equation (x - sin y) dy + (tan y) dx , given y(0) = 0

Trigonometry Class 10

If α and β are zeros of the polynomial x^2 - x + 2 then find the value of α/β + β/α .

Integration Miscellaneous Exercise || Most Repeatable PYQ Integration

A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present.

If α and β are zeros of polynomial ax^2 - x + c . Obtain a polynomial whose zeros are α-3 and β-3

Linear Equations in Two Variables Class 10

Three Girls Ishita, Isha and Nisha Are Playing a Game by Standing on a Circle of Radius 20 M Drawn

What is the probability that a leap year has 53 Sundays?

Find the point Q on the line (2x+4)/6 = (y+1)/2 = (-2z+6)/-4 at a distance of 3√2 from the point P

Integration of 1 upon 1 plus cot x

Find the shortest distance between the lines r = ( 2i - j + 3k )+λ( i - 2j + 3k ) and r = (i + 4k)+μ

PYQ of Trigonometry Class 10

If Cotθ + Cosθ = p and Cotθ - Cosθ = q then Prove that p square minus q square equal to 4 sq root pq

Find the derivative of Tan x by first principle .

If A is a non singular matrix then prove that inverse of Adjoint of A is equal to Adjoint of A^-1

If x power y equal to e power x-y then prove that dy/dx equal to log(x) upon log(ex) square

If a and b are two unit vector and angle between them is θ then prove that 1/2 | a-b| = sin θ/2

Vector Class 12

If vector a and vector b are two unit vector and angle between them is θ then prove that 1/2 modules

What is the probability that a leap year has 53 Sundays?

From a solid right circular cone, whose height is 6cm and radius of base is 12cm a right circular

A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5

In Figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB

In Figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB

In Figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB

Circle Class 10 || Class 10 Circle PYQ 2026

A survey regarding heights (in cm) of 51 girls of class X of a school Was | Sample Paper 2026

If Sinθ + Cosθ = √3 , then prove that Tanθ + Cotθ = 1.

3 January 2026