PG TRB Maths Previous Year Question Papers With Answers PDF

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.

Question
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°.

Question
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.