Questions and Answers for SSC, Railway & Govt Exams 2026

A family consists of a grandfather, m sons and daughters and 2n grand children. They are to be seated in a row for dinner. The grand children wish to occupy the n seats at each end and the grandfather refuses to have a grand children on either side of him. In how many ways can the family be made to sit.

(2n)! m! (m - 1)

(2n)! m! m

(2n)! (m –1)! (m - 1)

(2n – 1)! m! (m-1)

View Answer & Solution

Correct Answer: A ((2n)! m! (m - 1))A

Question 2:

Mathematics (11)

A train is going from London to Cambridge stops at 12 intermediate stations. 75 persons enter the train after London with 75 different tickets of the same class. Number of different sets of tickets they may be holding is:

78C3

91C75

84C75

78C74

View Answer & Solution

Correct Answer: A (78C3)A

Question 3:

Mathematics (11)

The ends A , B of a fixed straight line of length ‘a’ and ends A¢ and B¢ of another fixed straight line of length ‘b’ slide upon the axis of X & the axis of Y (one end on axis of X & the other on axis of Y). Find the locus of the centre of the circle passing through A, B, A¢ and B¢.

(2ax +2by)² - (2bx - 2ay)² = (a² - b²)²

(2ax - 2by)² + (2bx - 2ay)² = (a² - b²)²

(2ax +2by)² + (2bx +2ay)² = (a² + b²)²

(D*) (2ax - 2by)² + (2bx - 2ay)² = (a² - b²)²

View Answer & Solution

Correct Answer: D ((D*) (2ax - 2by)² + (2bx - 2ay)² = (a² - b²)²)D

Question 4:

Mathematics (11)

A circle of constant radius ‘r’ passes through origin O and cuts the axes of coordinates in points P and Q, then find the equation of the locus of the foot of perpendicular from O to PQ.

(x² + y²)² (x^–2 - y^–2) = 4r²

(x² - y²)² (x^–2 - y^–2) = 4r²

(x² - y²)² (x^–2 + y^–2) = 4r²

x² + y²)² (x^–2 + y^–2) = 4r²

View Answer & Solution

Correct Answer: D (x2 + y2)2 (x–2 + y–2) = 4r2)D

Question 5:

Mathematics (11)

The curves whose equations are

S = ax2 + 2hxy + by2 + 2gx + 2fy + c = 0

S¢ = a¢x2 + 2h¢xy + b¢y2 + 2g¢x + 2f¢y + c¢ = 0

intersect in four concyclic points then find relation in a, b, h, a¢, b¢, h¢.

\(2 a+\frac{a-b}{h}=\frac{a^{\prime}-b^{\prime}}{h^{\prime}}\)

\(2 b+\frac{a-b}{h}=\frac{a^{\prime}-b^{\prime}}{h^{\prime}}\)

\(\frac{a-b}{h}=\frac{a^{\prime}-b^{\prime}}{h^{\prime}}\)

\(\text { 2b- } \frac{a-b}{h}=\frac{a^{\prime}-b^{\prime}}{h^{\prime}}\)

View Answer & Solution

Correct Answer: C (\(\frac{a-b}{h}=\frac{a^{\prime}-b^{\prime}}{h^{\prime}}\))C

Question 6:

Mathematics (11)

Let S1 be a circle passing through A(0, 1), B(–2, 2) and S2 is a circle of radius units such that AB is common chord of S1 and S2. Find the equation of S2.

x2 + y2 + 2x – 3y - 2 ±\(\sqrt{7}\) (x + 2y – 2) = 0

x2 + y2 + 2x – 3y + 2 ±\(\sqrt{7}\) (x + 2y + 2) = 0

x2 + y2 + 2x – 3y + 2 ±\(\sqrt{7}\) (x + 2y – 2) = 0

x2 + y2 + 3x – 3y + 2 ±\(\sqrt{7}\) (x - 2y – 2) = 0

View Answer & Solution

Correct Answer: C (x2 + y2 + 2x – 3y + 2 ±\(\sqrt{7}\) (x + 2y – 2) = 0)C

Question 7:

Mathematics (11)

A triangle has two of its sides along the axes, its third side touches the circle x² + y² - 2 ax - 2 ay + a² = 0. Find the equation of the locus of the circumcentre of the triangle.

\(3(x-y)-a=\frac{2 x y}{a}\)

\(3(x+y)-a=\frac{2 x y}{a}\)

\(2(x-y)-a=\frac{2 x y}{a}\)

\(2(x+y)-a=\frac{2 x y}{a}\)

View Answer & Solution

Correct Answer: D (\(2(x+y)-a=\frac{2 x y}{a}\))D

Question 8:

Mathematics (11)

Let circles S₁ and S₂ of radii r₁ and r₂ respectively (r₁ > r₂) touches each other externally. Circle S radii r touches S₁ and S₂ externally and also their direct common tangent. the triangle formed by joining centre of S₁, S₂and S is

right angled triangle.

acute angled triangle.

obtuse angled triangle.

equilateral triangle.

View Answer & Solution

Correct Answer: C (obtuse angled triangle.)C

Question 9:

Mathematics (11)

Let ABCD is a rectangle. Incircle of DABD touches BD at E. Incircle of DCBD toches BD at F. If AB = 8 units, and BC = 6 units, then find length of EF.

View Answer & Solution

Correct Answer: A (2)A

Question 10:

Mathematics (11)

Find the equation of the circle which cuts each of the circles, x² + y² = 4, x² + y² - 6x - 8y + 10 = 0 & x² + y² + 2x - 4y - 2 = 0 at the extremities of a diameter.

x² + y² - 4x - 6y + 4 = 0

x² + y² - 4x + 6y - 4 = 0

x² + y² + 4x - 6y - 4 = 0

x² + y² - 4x - 6y - 4 = 0

View Answer & Solution

Correct Answer: D (x² + y² - 4x - 6y - 4 = 0)D

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