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: xÂ² – 5x + 6 = 0.

**Answer**

The roots are x = 2 and x = 3.

**Question**

If a + b = 12 and ab = 35, find the value of aÂ² + bÂ².

**Answer**

The value of aÂ² + bÂ² 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: 2xÂ² – 4x – 6 = 0.

**Answer**

The roots are x = 3 and x = -1.

**Question**

What is the sum of the roots of the quadratic equation 3xÂ² – 7x + 2 = 0?

**Answer**

The sum of the roots is 7/3.

**Question**

If x + 1/x = 5, find the value of xÂ² + 1/xÂ².

**Answer**

The value of xÂ² + 1/xÂ² is 23.

**Question**

Solve for x: 5x – 9 = 3x + 7.

**Answer**

The value of x is 8.

**Question**

If the roots of the equation xÂ² + px + q = 0 are equal, what is the relation between p and q?

**Answer**

The relation is pÂ² = 4q.

**Question**

Find the solution for x in the equation 2xÂ² – 3x + 1 = 0.

**Answer**

The solutions are x = 1 and x = 1/2.

**Question**

Find the value of x in the equation xÂ² + 2x – 15 = 0.

**Answer**

The value of x is -5 or 3.

**Question**

What is the product of the roots of the equation 3xÂ² – 5x + 1 = 0?

**Answer**

The product of the roots is 1/3.

**Question**

Solve the equation 4xÂ² – 12x + 9 = 0.

**Answer**

The roots are x = 3/2.

**Question**

Find the value of x if xÂ² + 2x – 8 = 0.

**Answer**

The value of x is -4 or 2.

**Question**

What is the discriminant of the quadratic equation xÂ² – 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: 2xÂ² + 3x – 5 = 0.

**Answer**

The values of x are 1 and -5/2.

**Question**

If the roots of the equation xÂ² – 6x + k = 0 are real and equal, find k.

**Answer**

The value of k is 9.

**Question**

Solve for x: 3xÂ² + 4x – 7 = 0.

**Answer**

The values of x are (-4 + âˆš76)/6 and (-4 – âˆš76)/6.

**Question**

Find the value of x in the equation 2xÂ² – 7x + 3 = 0.

**Answer**

The values of x are 3 and 1/2.

**Trigonometry**

**Question**

What is the value of sin 45Â°?

**Answer**

The value of sin 45Â° is 1/âˆš2.

**Question**

Find the value of tan 60Â°.

**Answer**

The value of tan 60Â° is âˆš3.

**Question**

What is the value of cos 30Â°?

**Answer**

The value of cos 30Â° is âˆš3/2.

**Question**

If sin Î¸ = 1/2, find the value of Î¸.

**Answer**

The value of Î¸ is 30Â°.

**Question**

Prove that sinÂ² Î¸ + cosÂ² Î¸ = 1.

**Answer**

The trigonometric identity sinÂ² Î¸ + cosÂ² Î¸ = 1 holds true for all angles Î¸.

**Question**

Find the value of sec 90Â°.

**Answer**

The value of sec 90Â° is undefined.

**Question**

If tan Î¸ = 3/4, find the value of sin Î¸.

**Answer**

The value of sin Î¸ is 3/5.

**Question**

Find the value of cot 45Â°.

**Answer**

The value of cot 45Â° is 1.

**Question**

What is the value of cos 90Â°?

**Answer**

The value of cos 90Â° is 0.

**Question**

Find the value of sin 60Â°.

**Answer**

The value of sin 60Â° is âˆš3/2.

**Question**

Find the value of cos 60Â°.

**Answer**

The value of cos 60Â° is 1/2.

**Question**

If tan Î¸ = 1, what is the value of Î¸?

**Answer**

The value of Î¸ is 45Â°.

**Question**

Find the value of sinÂ² 30Â°.

**Answer**

The value of sinÂ² 30Â° is 1/4.

**Question**

What is the value of sin 90Â°?

**Answer**

The value of sin 90Â° is 1.

**Question**

Find the value of cos 0Â°.

**Answer**

The value of cos 0Â° is 1.

**Question**

Prove that tan Î¸ = sin Î¸ / cos Î¸.

**Answer**

Using the definitions of sine and cosine, the identity tan Î¸ = sin Î¸ / cos Î¸ holds true.

**Question**

Find the value of cosec 30Â°.

**Answer**

The value of cosec 30Â° is 2.

**Question**

What is the value of cot 0Â°?

**Answer**

The value of cot 0Â° is undefined.

**Question**

If cos Î¸ = 0.5, find the value of Î¸.

**Answer**

The value of Î¸ is 60Â°.

**Question**

What is the value of sec 60Â°?

**Answer**

The value of sec 60Â° is 2/âˆš3.

**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 cmÂ².

**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 6âˆš2 cm.

**Question**

What is the area of a circle with a radius of 7 cm?

**Answer**

The area of the circle is 154 cmÂ².

**Question**

Find the volume of a cube with a side of 4 cm.

**Answer**

The volume of the cube is 64 cmÂ³.

**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 cmÂ².

**Question**

What is the surface area of a sphere with a radius of 3 cm?

**Answer**

The surface area is 113.04 cmÂ².

**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 cmÂ².

**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 cmÂ³.

**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 cmÂ².

**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 cmÂ².

**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 cmÂ³.

**Question**

What is the area of an equilateral triangle with side length 6 cm?

**Answer**

The area of the equilateral triangle is 15.59 cmÂ².

**Question**

Find the surface area of a cube with a side of 5 cm.

**Answer**

The surface area of the cube is 150 cmÂ².

**Question**

What is the area of a sector of a circle with a radius of 7 cm and an angle of 60Â°?

**Answer**

The area of the sector is 25.56 cmÂ².

**Question**

Find the area of a rhombus with diagonals of 8 cm and 6 cm.

**Answer**

The area of the rhombus is 24 cmÂ².

**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 cmÂ².

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