BITSAT PYQs for Various Forms of the Equation of a Line with Solutions: Practice BITSAT Previous Year Questions

Updated 3+ months ago

Various Forms of the Equation of a Line is an important topic in the Mathematics section in BITSAT exam. Practising this topic will increase your score overall and make your conceptual grip on BITSAT exam stronger.

This article gives you a full set of BITSAT PYQs for Various Forms of the Equation of a Line with explanations for effective preparation. Practice of BITSAT Mathematics PYQs including Various Forms of the Equation of a Line questions regularly will improve accuracy, speed, and confidence in the BITSAT 2026 exam.

BITSAT PYQs for Various Forms of the Equation of a Line with Solutions

1.
The sum of all the solutions of the equation $ \cos \theta \cos \left( \frac{\pi}{3} + \theta \right) \cos \left( \frac{\pi}{3} - \theta \right) = \frac{1}{4} $, for $ \theta \in [0, 6\pi] $ is:
- $ 15\pi $
- $ 30\pi $
- $ \frac{100\pi}{3} $
- None of these
View Solution
2.
The value of \[ \lim_{x \to 0} \frac{1 - \cos(1 - \cos x)}{x^4} \] is:
- $ \frac{1}{6} $
- $ \frac{1}{8} $
- $ \frac{1}{10} $
- $ \frac{1}{12} $
View Solution
3.
Let \[ A = \begin{pmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{pmatrix}, \quad 10B = \begin{pmatrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \end{pmatrix} \] If $ B $ is the inverse of $ A $, then the value of $ \alpha $ is:
- 4
- $ -4 $
- 3
- 5
View Solution
4.
Given \[ 2x - y + 2z = 2, \quad x - 2y + z = -4, \quad x + y + \lambda z = 4, \] then the value of $ \lambda $ such that the given system of equations has no solution is:
- -3
- 1
- 0
- 3
View Solution
5.
$(0, - 1)$ and $(0, 3)$ are two opposite vertices of a square. The other two vertices are :
- (0, 1), (0, - 3)
- (3, - 1), (0, 0)
- (2, 1), (- 2,1)
- (2, 2), (1, 1)
View Solution
6.
If $ x \in \left( 0, \frac{\pi}{2} \right) $, then the value of $ \cos^{-1} \left( \frac{7}{2} (1 + \cos 2x) + \sqrt{(\sin^2 x - 48\cos^2 x)\sin x} \right) $ is equal to:
- $ x - \cos^{-1}(7 \cos x) $
- $ x + \sin^{-1}(7 \cos x) $
- $ x + \cos^{-1}(6 \cos x) $
- $ x + \cos^{-1}(7 \cos x) $
View Solution
7.
If $ p \neq a $, $ q \neq b $, $ r \neq c $, and the system of equations \[ px + ay + az = 0 \] \[ bx + qy + bz = 0 \] \[ cx + cy + rz = 0 \] has a non-trivial solution, then the value of \[ \frac{p}{p - a} + \frac{q}{q - b} + \frac{r}{r - c} \] is:
- 1
- 2
- $ \frac{1}{2} $
- 0
View Solution
8.
The smallest positive integral value of $ n $ such that \[ \left( \frac{1 + \sin \frac{\pi}{8} + i \cos \frac{\pi}{8}}{1 + \sin \frac{\pi}{8} - i \cos \frac{\pi}{8}} \right)^n \] is purely imaginary, is equal to:
- 4
- 3
- 2
- 8
View Solution
9.
If $ \alpha $ be a root of the equation $ 4x^2 + 2x - 1 = 0 $, then the other root of the equation is
- $ 4\alpha^3 + 2\alpha $
- $ 4\alpha^2 - 2\alpha $
- $ 4\alpha^3 - 3\alpha $
- $ 4\alpha^3 + 3\alpha $
View Solution
10.
The value of \[ \int \frac{1}{x^1} \, dx, { is } \left[ \frac{(x - 1)^3}{(x + 2)^5} \right]_1^4 \]
- $ \frac{4}{3} \frac{x + 1}{x - 2} \left( \frac{1}{4} \right) + C $
- $ \frac{3}{4} \frac{x - 1}{x + 2} \left( \frac{1}{4} \right) + C $
- $ \frac{4}{3} \frac{x - 1}{x + 2} \left( \frac{1}{4} \right) + C $
- $ \frac{1}{3} \frac{2x - 1}{4x - 3} \left( \frac{1}{4} \right) + C $
View Solution
11.
The value of $ \lim_{x \to 0} \frac{(1 + x)^{\frac{1}{x}} - e + \frac{1}{2}e^x}{x^2} $ is:
- $\frac{11}{24e} $
- $-\frac{11}{24e} $
- $\frac{e}{24} $
- None of these
View Solution
12.
If the plane $ 3x + y + 2z + 6 = 0 $ { is parallel to the line} \[ \frac{3x - 1}{2b} = \frac{3 - y}{1} = \frac{z - 1}{a}, \] {then the value of $ 3a + 3b $ is:}
- $ \frac{1}{2} $
- $ \frac{3}{2} $
- 3
- 4
View Solution
13.
Let $ \alpha $ be the solution of the equation \[ 16 \sin^2 \theta + 16 \cos^2 \theta = 10, \quad \theta \in \left( 0, \frac{\pi}{4} \right) \] {If the shadow of a vertical pole is $ \frac{1}{\sqrt{3}} $ of its height, then the altitude of the sun is:}
- $ \alpha $
- $ \frac{\alpha}{2} $
- $ 2\alpha $
- $ \frac{\alpha}{3} $
View Solution

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BITSAT PYQs for Various Forms of the Equation of a Line with Solutions: Practice BITSAT Previous Year Questions

BITSAT PYQs for Various Forms of the Equation of a Line with Solutions

1.
The sum of all the solutions of the equation \( \cos \theta \cos \left( \frac{\pi}{3} + \theta \right) \cos \left( \frac{\pi}{3} - \theta \right) = \frac{1}{4} \), for \( \theta \in [0, 6\pi] \) is:

2.
The value of \[ \lim_{x \to 0} \frac{1 - \cos(1 - \cos x)}{x^4} \] is:

3.
Let \[ A = \begin{pmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{pmatrix}, \quad 10B = \begin{pmatrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \end{pmatrix} \] If \( B \) is the inverse of \( A \), then the value of \( \alpha \) is:

4.
Given \[ 2x - y + 2z = 2, \quad x - 2y + z = -4, \quad x + y + \lambda z = 4, \] then the value of \( \lambda \) such that the given system of equations has no solution is:

5.
$(0, - 1)$ and $(0, 3)$ are two opposite vertices of a square. The other two vertices are :

6.
If \( x \in \left( 0, \frac{\pi}{2} \right) \), then the value of \( \cos^{-1} \left( \frac{7}{2} (1 + \cos 2x) + \sqrt{(\sin^2 x - 48\cos^2 x)\sin x} \right) \) is equal to:

7.
If \( p \neq a \), \( q \neq b \), \( r \neq c \), and the system of equations \[ px + ay + az = 0 \] \[ bx + qy + bz = 0 \] \[ cx + cy + rz = 0 \] has a non-trivial solution, then the value of \[ \frac{p}{p - a} + \frac{q}{q - b} + \frac{r}{r - c} \] is:

8.
The smallest positive integral value of \( n \) such that \[ \left( \frac{1 + \sin \frac{\pi}{8} + i \cos \frac{\pi}{8}}{1 + \sin \frac{\pi}{8} - i \cos \frac{\pi}{8}} \right)^n \] is purely imaginary, is equal to:

9.
If \( \alpha \) be a root of the equation \( 4x^2 + 2x - 1 = 0 \), then the other root of the equation is

10.
The value of \[ \int \frac{1}{x^1} \, dx, { is } \left[ \frac{(x - 1)^3}{(x + 2)^5} \right]_1^4 \]

11.
The value of \( \lim_{x \to 0} \frac{(1 + x)^{\frac{1}{x}} - e + \frac{1}{2}e^x}{x^2} \) is:

12.
If the plane \( 3x + y + 2z + 6 = 0 \) { is parallel to the line} \[ \frac{3x - 1}{2b} = \frac{3 - y}{1} = \frac{z - 1}{a}, \] {then the value of \( 3a + 3b \) is:}

13.
Let \( \alpha \) be the solution of the equation \[ 16 \sin^2 \theta + 16 \cos^2 \theta = 10, \quad \theta \in \left( 0, \frac{\pi}{4} \right) \] {If the shadow of a vertical pole is \( \frac{1}{\sqrt{3}} \) of its height, then the altitude of the sun is:}

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BITSAT PYQs for Various Forms of the Equation of a Line with Solutions

1.The sum of all the solutions of the equation \( \cos \theta \cos \left( \frac{\pi}{3} + \theta \right) \cos \left( \frac{\pi}{3} - \theta \right) = \frac{1}{4} \), for \( \theta \in [0, 6\pi] \) is:

2.The value of \[ \lim_{x \to 0} \frac{1 - \cos(1 - \cos x)}{x^4} \] is:

3.Let \[ A = \begin{pmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{pmatrix}, \quad 10B = \begin{pmatrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \end{pmatrix} \] If \( B \) is the inverse of \( A \), then the value of \( \alpha \) is:

4.Given \[ 2x - y + 2z = 2, \quad x - 2y + z = -4, \quad x + y + \lambda z = 4, \] then the value of \( \lambda \) such that the given system of equations has no solution is:

5.$(0, - 1)$ and $(0, 3)$ are two opposite vertices of a square. The other two vertices are :

6.If \( x \in \left( 0, \frac{\pi}{2} \right) \), then the value of \( \cos^{-1} \left( \frac{7}{2} (1 + \cos 2x) + \sqrt{(\sin^2 x - 48\cos^2 x)\sin x} \right) \) is equal to:

7.If \( p \neq a \), \( q \neq b \), \( r \neq c \), and the system of equations \[ px + ay + az = 0 \] \[ bx + qy + bz = 0 \] \[ cx + cy + rz = 0 \] has a non-trivial solution, then the value of \[ \frac{p}{p - a} + \frac{q}{q - b} + \frac{r}{r - c} \] is:

8.The smallest positive integral value of \( n \) such that \[ \left( \frac{1 + \sin \frac{\pi}{8} + i \cos \frac{\pi}{8}}{1 + \sin \frac{\pi}{8} - i \cos \frac{\pi}{8}} \right)^n \] is purely imaginary, is equal to:

9.If \( \alpha \) be a root of the equation \( 4x^2 + 2x - 1 = 0 \), then the other root of the equation is

10.The value of \[ \int \frac{1}{x^1} \, dx, { is } \left[ \frac{(x - 1)^3}{(x + 2)^5} \right]_1^4 \]

11.The value of \( \lim_{x \to 0} \frac{(1 + x)^{\frac{1}{x}} - e + \frac{1}{2}e^x}{x^2} \) is:

12.If the plane \( 3x + y + 2z + 6 = 0 \) { is parallel to the line} \[ \frac{3x - 1}{2b} = \frac{3 - y}{1} = \frac{z - 1}{a}, \] {then the value of \( 3a + 3b \) is:}

13.Let \( \alpha \) be the solution of the equation \[ 16 \sin^2 \theta + 16 \cos^2 \theta = 10, \quad \theta \in \left( 0, \frac{\pi}{4} \right) \] {If the shadow of a vertical pole is \( \frac{1}{\sqrt{3}} \) of its height, then the altitude of the sun is:}

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1.
The sum of all the solutions of the equation \( \cos \theta \cos \left( \frac{\pi}{3} + \theta \right) \cos \left( \frac{\pi}{3} - \theta \right) = \frac{1}{4} \), for \( \theta \in [0, 6\pi] \) is:

2.
The value of \[ \lim_{x \to 0} \frac{1 - \cos(1 - \cos x)}{x^4} \] is:

3.
Let \[ A = \begin{pmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{pmatrix}, \quad 10B = \begin{pmatrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \end{pmatrix} \] If \( B \) is the inverse of \( A \), then the value of \( \alpha \) is:

4.
Given \[ 2x - y + 2z = 2, \quad x - 2y + z = -4, \quad x + y + \lambda z = 4, \] then the value of \( \lambda \) such that the given system of equations has no solution is:

5.
$(0, - 1)$ and $(0, 3)$ are two opposite vertices of a square. The other two vertices are :

6.
If \( x \in \left( 0, \frac{\pi}{2} \right) \), then the value of \( \cos^{-1} \left( \frac{7}{2} (1 + \cos 2x) + \sqrt{(\sin^2 x - 48\cos^2 x)\sin x} \right) \) is equal to:

7.
If \( p \neq a \), \( q \neq b \), \( r \neq c \), and the system of equations \[ px + ay + az = 0 \] \[ bx + qy + bz = 0 \] \[ cx + cy + rz = 0 \] has a non-trivial solution, then the value of \[ \frac{p}{p - a} + \frac{q}{q - b} + \frac{r}{r - c} \] is:

8.
The smallest positive integral value of \( n \) such that \[ \left( \frac{1 + \sin \frac{\pi}{8} + i \cos \frac{\pi}{8}}{1 + \sin \frac{\pi}{8} - i \cos \frac{\pi}{8}} \right)^n \] is purely imaginary, is equal to:

9.
If \( \alpha \) be a root of the equation \( 4x^2 + 2x - 1 = 0 \), then the other root of the equation is

10.
The value of \[ \int \frac{1}{x^1} \, dx, { is } \left[ \frac{(x - 1)^3}{(x + 2)^5} \right]_1^4 \]

11.
The value of \( \lim_{x \to 0} \frac{(1 + x)^{\frac{1}{x}} - e + \frac{1}{2}e^x}{x^2} \) is:

12.
If the plane \( 3x + y + 2z + 6 = 0 \) { is parallel to the line} \[ \frac{3x - 1}{2b} = \frac{3 - y}{1} = \frac{z - 1}{a}, \] {then the value of \( 3a + 3b \) is:}

13.
Let \( \alpha \) be the solution of the equation \[ 16 \sin^2 \theta + 16 \cos^2 \theta = 10, \quad \theta \in \left( 0, \frac{\pi}{4} \right) \] {If the shadow of a vertical pole is \( \frac{1}{\sqrt{3}} \) of its height, then the altitude of the sun is:}