Mathematics Quiz Class 10

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Questions and Answers

Find the value of x if, log₅(x² – 5x + 11) = 1

6 or -1

Find the value of sin(15°) using compound angles.

1/√2 - 1/2√2

Find the intercepts of the line 2x + 3y = 6 on both the axes.

x-intercept: (3, 0) and y-intercept: (0, 2)

State whether the function is even or odd if, f(x) = x³ + 4x + sin x.

False Signup and view all the answers

At which point on the curve y = 3x – x², the slope of the tangent is –5?

(4, -4) Signup and view all the answers

Divide 100 into two parts such that their product is maximum.

50 and 50 Signup and view all the answers

If mean is 34.5 and standard deviation is 5, find the co-efficient of variance.

(5/34.5)*100% or approximately 14.49% Signup and view all the answers

Given the matrices A = [[-1, 7], [2, 4]] and B = [[-1, 2], [3, 0]], then find the matrix 'X' such that 2X + 3A - 4B = I, where I is the identity matrix of order 2.

[[2, 1/2], [-5/2, -3/2]] Signup and view all the answers

Given the matrices A = [[-2, 0, 2], [3, 4, 5]] and B = [[2, 1], [3, 5], [0, 2]], determine whether AB is singular or non-singular matrix.

True Signup and view all the answers

Resolve into partial fraction (3x - 2) / ((x + 2)(x)(x² + 4)).

1/2*(1/x) + 3/8*(1/(x + 2)) - 1/8*((3x + 2) / (x2 + 4)) Signup and view all the answers

If A and B are obtuse angles and sin A = 5/13 and cos B = 4/5, then find sin(A + B).

63/65 Signup and view all the answers

Prove that (sin 3A - sin A)/(cos 3A + cos A) = tan A

Apply the sum-to-product identities for sine and cosine to simplify each expression and then simplify algebraically. Signup and view all the answers

Prove that sin^-1(5/13) - sin^-1(17/85) = cos^-1(84/85)

Use the difference of arcsine formula (sin-1 x - sin-1 y = sin-1(x√(1-y2)- y√(1-x2)). Simplify by using the Pythagorean Identity and then use trigonometric identities to show the result. Signup and view all the answers

Find the equation of a straight line passing through the point of intersection of lines 4x + 3y = 8 and x + y = 1; and parallel to the line 5x - 7y = 3.

5x - 7y = -2 Signup and view all the answers

Find dy/ dx if x³ + x y² = y³ + y x².

(y3 + 2x y - 3x2) / (2x y - 3y2 - x3) Signup and view all the answers

If x = a(θ + sin θ) & y = a(1 - cos θ), find dy/ dx at θ = π/2.

-1 Signup and view all the answers

If y = (x)sinx + (tanx)^x, find dy/ dx.

sinx + xcosx + (tanx)x(sec2x ln(tanx*) + xsec2x/tanx) Signup and view all the answers

Find the range and co-efficient of range for the following data: Class Interval Frequency 10-19 15 20-29 25 30-39 13 40-49 17 50-59 10

Range: 40, Coefficient of Range: 0.4 Signup and view all the answers

Calculate the mean deviation about mean of the following data: 17, 15, 18, 23, 25, 22, 11, 5

4.14 Signup and view all the answers

The following data pertains to two workers doing the same job in a factory: Details Worker A Worker B Mean time of completing job 40 42 Standard deviation 8 6 Who is more consistent worker?

Worker B Signup and view all the answers

Solve the following system of equations by matrix inversion method: x + y + z = 3, 3x - 2y + 3z = 4, 5x + 5y + z = 11

x = 1, y = 1, z = 1 Signup and view all the answers

If tan A = (2/√3) and A is in the first quadrant, find the value of cos A.

1/√7 Signup and view all the answers

Evaluate tan 85° - tan 40° / 1 + tan 85° tan 40° without using a calculator.

tan 45° = 1 Signup and view all the answers

Find the distance between the parallel lines 3x + 2y = 5 and 3x + 2y = 6.

1/√13 Signup and view all the answers

Find the acute angle between the lines 3x = y - 4 and 2x + y + 3 = 0.

tan-1(11/5) or approximately 65.56° Signup and view all the answers

A manufacturer can sell 'x' items at a price of ₹ (330 - x) each. The cost of producing x items is ₹ (x² + 10x + 12). Determine the number of items to be sold so that the manufacturer can make the maximum profit.

150 items Signup and view all the answers

A beam is bent in the form of curve y = 2sin x - sin 2x. Find the radius of curvature of the beam at x = π/2.

1/2 Signup and view all the answers

Find the mean, standard deviation and co-efficient of variance of the following data: Class Interval Frequency 0-10 14 10-20 23 20-30 27 30-40 21 40-50 15

Mean: 25.2, Standard Deviation: 14.39, Co-efficient of Variance: 0.57 Signup and view all the answers

Study Notes

Instructions

All questions are compulsory
Answer each question on a new page
Use sketches where necessary
Figures indicate marks
Non-programmable calculators are permitted
Mobile phones, pagers and electronic communication devices are not allowed

Question 1

Attempt five of the following
- Find x if log₅(x² - 5x + 11) = 1
- Find sin(15°) using compound angles
- Find the intercepts of 2x + 3y = 6 on both axes
- Determine if f(x) = x³ + 4x + sin x is even or odd
- Find the point on y = 3x - x² where the tangent's slope is -5
- Divide 100 into two parts where their product is maximum
- If the mean is 34.5 and standard deviation is 5, find the coefficient of variance

Question 2

Attempt three of the following
- Given A = [3 -4], B = [1 -3]
  - Solve for matrix X if 2X + 3A - 4B = I, where I is a 2x2 identity matrix
- Given A = [2 -2 0], B = [3 5]
  - Determine if AB is singular or non-singular
- Resolve (3x – 2)/((x+2)(x)(x² +4)) into partial fractions
- If A and B are obtuse angles, sin A = 5/13 and cos B = 5/13, find sin(A+B)

Question 3

Attempt three of the following
- Prove (sin3A - sinA)/(cos3A + cosA) = tanA
- Prove sin⁻¹(3/5) - sin⁻¹(8/17) = cos⁻¹(84/85)
- Find the equation of a line passing through the intersection of 4x + 3y = 8 and x+y =1, parallel to 5x -7y = 3
- Find dy/dx if x³ + xy² = y³ + yx²

Question 4

Attempt three of the following
- If x = a(θ + sin θ) and y = a(1 - cos θ), find dx/dθ at θ = π/2
- If y = x sinx + (tan x)², find dy/dx

Question 5

Attempt two of the following
- Solve x + y + z = 3, 3x - 2y + 3z = 4, 5x + 5y + z = 11 using matrix inversion
- If tan A = 1/√3, find cos A
- Evaluate tan 85° - tan 40°/1 + tan 85° tan 40°
- Find the distance between the parallel lines 3x + 2y = 5 and 3x + 2y = 6
- Find the acute angle between 3x = y − 4 and 2x + y + 3 = 0

Question 6

Attempt two of the following
- A manufacturer sells x items at (330 - x) each. Cost of x items is x² + 10x +12. Find the number of items to maximize profit
- A beam is bent in the form of y = 2 sinx sin2x. Find the radius of curvature at x = π/2
- Find mean, standard deviation, and coefficient of variance of the following data:
  - Class interval | Frequency
    - 0-10 | 14
    - 10-20 | 23
    - 20-30 | 27
    - 30-40 | 21
    - 40-50 | 15

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Description

This quiz is designed for 10th-grade mathematics students, covering topics such as logarithms, trigonometry, algebra, and statistics. Students will need to solve a variety of mathematical problems, applying their knowledge of functions, matrices, and geometry. Be prepared to show your work and provide sketches where necessary.