PG TRB Maths exam preparation requires solving previous years’ question papers to understand the pattern and difficulty level. By going through these papers, you can strengthen your problem-solving skills and gain confidence in approaching the exam. The questions and answers provided here cover essential topics for your preparation.
Algebra
Question
Solve the quadratic equation: x² – 5x + 6 = 0.
Answer
The roots are x = 2 and x = 3.
Download PDFQuestion
If a + b = 12 and ab = 35, find the value of a² + b².
Answer
The value of a² + b² is 104.
Question
Solve for x: 2x + 3 = 11.
Answer
The value of x is 4.
Question
Solve for y: 3y – 7 = 2y + 5.
Answer
The value of y is 12.
Question
Find the roots of the equation: 2x² – 4x – 6 = 0.
Answer
The roots are x = 3 and x = -1.
Question
What is the sum of the roots of the quadratic equation 3x² – 7x + 2 = 0?
Answer
The sum of the roots is 7/3.
Question
If x + 1/x = 5, find the value of x² + 1/x².
Answer
The value of x² + 1/x² is 23.
Question
Solve for x: 5x – 9 = 3x + 7.
Answer
The value of x is 8.
Question
If the roots of the equation x² + px + q = 0 are equal, what is the relation between p and q?
Answer
The relation is p² = 4q.
Question
Find the solution for x in the equation 2x² – 3x + 1 = 0.
Answer
The solutions are x = 1 and x = 1/2.
Question
Find the value of x in the equation x² + 2x – 15 = 0.
Answer
The value of x is -5 or 3.
Question
What is the product of the roots of the equation 3x² – 5x + 1 = 0?
Answer
The product of the roots is 1/3.
Question
Solve the equation 4x² – 12x + 9 = 0.
Answer
The roots are x = 3/2.
Question
Find the value of x if x² + 2x – 8 = 0.
Answer
The value of x is -4 or 2.
Question
What is the discriminant of the quadratic equation x² – 4x + 4 = 0?
Answer
The discriminant is 0.
Question
If the sum of two numbers is 10 and their product is 21, find the numbers.
Answer
The numbers are 7 and 3.
Question
Solve for x: 2x² + 3x – 5 = 0.
Answer
The values of x are 1 and -5/2.
Question
If the roots of the equation x² – 6x + k = 0 are real and equal, find k.
Answer
The value of k is 9.
Question
Solve for x: 3x² + 4x – 7 = 0.
Answer
The values of x are (-4 + √76)/6 and (-4 – √76)/6.
Question
Find the value of x in the equation 2x² – 7x + 3 = 0.
Answer
The values of x are 3 and 1/2.
Trigonometry
Question
What is the value of sin 45°?
Answer
The value of sin 45° is 1/√2.
Question
Find the value of tan 60°.
Answer
The value of tan 60° is √3.
Question
What is the value of cos 30°?
Answer
The value of cos 30° is √3/2.
Question
If sin θ = 1/2, find the value of θ.
Answer
The value of θ is 30°.
Question
Prove that sin² θ + cos² θ = 1.
Answer
The trigonometric identity sin² θ + cos² θ = 1 holds true for all angles θ.
Question
Find the value of sec 90°.
Answer
The value of sec 90° is undefined.
Question
If tan θ = 3/4, find the value of sin θ.
Answer
The value of sin θ is 3/5.
Question
Find the value of cot 45°.
Answer
The value of cot 45° is 1.
Question
What is the value of cos 90°?
Answer
The value of cos 90° is 0.
Question
Find the value of sin 60°.
Answer
The value of sin 60° is √3/2.
Question
Find the value of cos 60°.
Answer
The value of cos 60° is 1/2.
Question
If tan θ = 1, what is the value of θ?
Answer
The value of θ is 45°.
Download PDFQuestion
Find the value of sin² 30°.
Answer
The value of sin² 30° is 1/4.
Question
What is the value of sin 90°?
Answer
The value of sin 90° is 1.
Question
Find the value of cos 0°.
Answer
The value of cos 0° is 1.
Question
Prove that tan θ = sin θ / cos θ.
Answer
Using the definitions of sine and cosine, the identity tan θ = sin θ / cos θ holds true.
Question
Find the value of cosec 30°.
Answer
The value of cosec 30° is 2.
Question
What is the value of cot 0°?
Answer
The value of cot 0° is undefined.
Question
If cos θ = 0.5, find the value of θ.
Answer
The value of θ is 60°.
Question
What is the value of sec 60°?
Answer
The value of sec 60° is 2/√3.
Geometry
Question
Find the area of a triangle with a base of 10 cm and a height of 8 cm.
Answer
The area of the triangle is 40 cm².
Question
What is the perimeter of a rectangle with a length of 5 cm and a width of 3 cm?
Answer
The perimeter of the rectangle is 16 cm.
Question
Find the length of the diagonal of a square with a side of 6 cm.
Answer
The length of the diagonal is 6√2 cm.
Question
What is the area of a circle with a radius of 7 cm?
Answer
The area of the circle is 154 cm².
Question
Find the volume of a cube with a side of 4 cm.
Answer
The volume of the cube is 64 cm³.
Question
What is the circumference of a circle with a diameter of 10 cm?
Answer
The circumference is 31.4 cm.
Question
Find the area of a parallelogram with a base of 12 cm and height of 5 cm.
Answer
The area of the parallelogram is 60 cm².
Question
What is the surface area of a sphere with a radius of 3 cm?
Answer
The surface area is 113.04 cm².
Question
Find the length of the hypotenuse in a right triangle with legs of 6 cm and 8 cm.
Answer
The length of the hypotenuse is 10 cm.
Question
What is the total surface area of a cylinder with a radius of 2 cm and a height of 5 cm?
Answer
The total surface area is 87.96 cm².
Question
What is the volume of a cone with a radius of 4 cm and a height of 9 cm?
Answer
The volume of the cone is 150.8 cm³.
Question
Find the area of a trapezium with parallel sides 6 cm and 8 cm, and a height of 5 cm.
Answer
The area of the trapezium is 35 cm².
Question
What is the lateral surface area of a cone with a radius of 3 cm and slant height of 5 cm?
Answer
The lateral surface area of the cone is 47.12 cm².
Question
Find the volume of a rectangular box with length 4 cm, width 3 cm, and height 2 cm.
Answer
The volume of the rectangular box is 24 cm³.
Question
What is the area of an equilateral triangle with side length 6 cm?
Answer
The area of the equilateral triangle is 15.59 cm².
Question
Find the surface area of a cube with a side of 5 cm.
Answer
The surface area of the cube is 150 cm².
Question
What is the area of a sector of a circle with a radius of 7 cm and an angle of 60°?
Answer
The area of the sector is 25.56 cm².
Question
Find the area of a rhombus with diagonals of 8 cm and 6 cm.
Answer
The area of the rhombus is 24 cm².
Question
What is the total surface area of a cylinder with a radius of 3 cm and a height of 7 cm?
Answer
The total surface area of the cylinder is 188.4 cm².
Download PDF
