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In a right-angled triangle ABC, ∠B = 90°. If AB = 6 cm and BC = 8 cm, what is the distance between the centroid (G) and the orthocenter (H)?

Mensuration

Asked in: CGL MAINS 2026, SSC

Categories Mensuration, Maths, Triangles

A rectangle has area 48 cm² and perimeter 28 cm. If the midpoints of the sides are joined to form a rhombus, what is the area of the rhombus?

Surface Area and Volume

Asked in: CGL MAINS 2026, SSC

Categories Surface Area and Volume, Maths

A chord of a circle subtends an angle of 60° at the circumference of the circle. What is the ratio of the radius of the circle to the length of the chord respectively?

Circle

Asked in: SSC, CGL MAINS 2026

Categories Circle, Maths, Mensuration

Simplify the trigonometric expression (tan²θ − sin²θ) / (2 + tan²θ + cot²θ).

Trigonometry

Asked in: SSC, CGL MAINS 2026

Categories Trigonometry, Maths

What is the value of 3 − (sin 239° + sin 251°)?

Trigonometry

Asked in: SSC, CGL MAINS 2026

Categories Trigonometry, Maths

If (sinθ)/x = (cosθ)/y, prove that sinθ − cosθ = (x − y)/√(x² + y²).

Trigonometry

Asked in: SSC, CGL MAINS 2026

Categories Trigonometry, Maths

P and Q can do a work in 20 and 30 days respectively. They work together for 6 days, then Q is replaced by R. Remaining work is completed in 8 days. In how many days can R alone complete 60% of the work?

Time and Work

Asked in: SSC, CGL

Categories Time and Work, Maths

In a triangle △PQR, ∠R = 62°. The perpendicular bisector of PQ at S meets QR at T. If ∠TPR = 38°, what is the measure of ∠PQR?

Mensuration

Asked in: SSC, CGL MAINS 2026

Categories Mensuration, Maths, Triangles

In a right-angled triangle ABC, ∠B = 90°. If AB = 6 cm and BC = 8 cm, what is the distance between the centroid (G) and the orthocenter (H)?

Mensuration

Asked in: SSC, CGL MAINS 2026

Categories Mensuration, Maths, Triangles

The base of a right pyramid is an equilateral triangle with side 10 cm, and its vertical height is 24 cm. Find the volume (in cm³) of the pyramid.

Mensuration

Asked in: SSC, CGL MAINS 2026

Categories Mensuration, Maths, Triangles

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A rectangle has area 48 cm² and perimeter 28 cm. If the midpoints of the sides are joined to form a rhombus, what is the area of the rhombus?
In a right-angled triangle ABC, ∠B = 90°. If AB = 6 cm and BC = 8 cm, what is the distance between the centroid (G) and the orthocenter (H)?
In a right-angled triangle ABC, ∠B = 90°. If AB = 6 cm and BC = 8 cm, what is the distance between the centroid (G) and the orthocenter (H)?
In a triangle △PQR, ∠R = 62°. The perpendicular bisector of PQ at S meets QR at T. If ∠TPR = 38°, what is the measure of ∠PQR?
What is the value of 3 − (sin 239° + sin 251°)?
If (sinθ)/x = (cosθ)/y, prove that sinθ − cosθ = (x − y)/√(x² + y²).
Simplify the trigonometric expression (tan²θ − sin²θ) / (2 + tan²θ + cot²θ).
P and Q can do a work in 20 and 30 days respectively. They work together for 6 days, then Q is replaced by R. Remaining work is completed in 8 days. In how many days can R alone complete 60% of the work?
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