Matrices & Determinants · NDA previous year questions

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2019 34 questions

Q352019 · 17 Nov 2019
If $A = [1 - 1 - 1 1]$ , then the expression $A^{3} - 2 A^{2}$ is
1. A.a null matrix
2. B.an identity matrix
3. C.equal to $A$
4. D.equal to $- A$
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Answer: A
Q362019 · 17 Nov 2019
If $A = (2334)$ and $B = (1221)$ , then which one of the following is correct?
1. A.Both $A B$ and $B A$ exist
2. B.Neither $A B$ nor $B A$ exists
3. C. $A B$ exists but $B A$ does not exist
4. D. $A B$ does not exist but $B A$ exists
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Answer: C
Q372019 · 17 Nov 2019
If $x + a + b + c = 0$ , then what is the value of $x + a a a b x + b b c c x + c$ ?
1. A.0
2. B. $(a + b + c)^{2}$
3. C. $a^{2} + b^{2} + c^{2}$
4. D. $a + b + c - 2$
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Answer: A
Q382019 · 17 Nov 2019
What are the values of $x$ that satisfy the equation $x 2 x 1 021211 + 3 x x^{2} 0 021211 = 0$ ?
1. A. $- 2 \pm 3$
2. B. $- 1 \pm 3$
3. C. $- 1 \pm 6$
4. D. $- 2 \pm 6$
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Answer: D
Q392019 · 17 Nov 2019
What is the value of the determinant $1! 2! 3! 2! 3! 4! 3! 4! 5!$ ?
1. A.0
2. B.12
3. C.24
4. D.36
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Answer: C
Q402019 · 17 Nov 2019
What is $tan 2 5^{\circ} tan 1 5^{\circ} + tan 1 5^{\circ} tan 5 0^{\circ} + tan 2 5^{\circ} tan 5 0^{\circ}$ equal to?
1. A.0
2. B.1
3. C.2
4. D.4
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Answer: B
Q412019 · 17 Nov 2019
What is $cot A + cosec A$ equal to?
1. A. $tan (\frac{A}{2})$
2. B. $cot (\frac{A}{2})$
3. C. $2 tan (\frac{A}{2})$
4. D. $2 cot (\frac{A}{2})$
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Answer: B
Q422019 · 17 Nov 2019
What is $cot (\frac{A}{2}) - tan (\frac{A}{2})$ equal to?
1. A. $tan A$
2. B. $cot A$
3. C. $2 tan A$
4. D. $2 cot A$
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Answer: D
Q432019 · 17 Nov 2019
If angle $C$ of a triangle $A B C$ is a right angle, then what is $tan A + tan B$ equal to?
1. A. $\frac{a ^{2} - b ^{2}}{ab}$
2. B. $\frac{a ^{2}}{b c}$
3. C. $\frac{b ^{2}}{c a}$
4. D. $\frac{c ^{2}}{ab}$
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Answer: D
Q442019 · 17 Nov 2019
What is $cos 8 0^{\circ} + cos 4 0^{\circ} - cos 2 0^{\circ}$ equal to?
1. A.2
2. B.1
3. C.0
4. D. $- 19$
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Answer: C
Q452019 · 17 Nov 2019
If $2 tan A = 3 tan B = 1$ , then what is $tan (A - B)$ equal to?
1. A. $\frac{1}{5}$
2. B. $\frac{1}{6}$
3. C. $\frac{1}{7}$
4. D. $\frac{1}{9}$
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Answer: C
Q462019 · 17 Nov 2019
If $tan A - tan B = x$ and $cot B - cot A = y$ , then what is the value of $cot (A - B)$ ?
1. A. $\frac{1}{x} + \frac{1}{y}$
2. B. $\frac{1}{y} - \frac{1}{x}$
3. C. $\frac{x y}{x + y}$
4. D. $1 + \frac{1}{x y}$
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Answer: A
Q252019 · 21 Apr 2019
1. A. $00 - 2 00 - 1 008$
2. B. $000000 - 2 - 1 8$
3. C. $[000021]$
4. D.It does not exist
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Answer: A
Q262019 · 21 Apr 2019
If $A = 0110$ , then the matrix A is a/an
1. A.Singular matrix
2. B.Involutory matrix
3. C.Nilpotent matrix
4. D.Idempotent matrix
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Answer: B
Q272019 · 21 Apr 2019
1. A. $- 3, 4$
2. B. $3, 4$
3. C. $3, - 4$
4. D. $- 3, - 4$
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Answer: A
Q282019 · 21 Apr 2019
If A is an identity matrix of order 3, then its inverse $(A^{- 1})$
1. A.is equal to null matrix
2. B.is equal to A
3. C.is equal to 3A
4. D.does not exist
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Answer: B
Q292019 · 21 Apr 2019
A is a square matrix of order 3 such that its determinant is 4. What is the determinant of its transpose?
1. A.64
2. B.36
3. C.32
4. D.4
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Answer: D
Q302019 · 21 Apr 2019
What is the least value of $25 cosec^{2} x + 36 sec^{2} x$ ?
1. A. $1$
2. B. $11$
3. C. $120$
4. D. $121$
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Answer: D
Q312019 · 21 Apr 2019
What is the value of $\frac{sin 3 4 ^{\circ} cos 23 6 ^{\circ} - sin 5 6 ^{\circ} sin 12 4 ^{\circ}}{cos 2 8 ^{\circ} cos 8 8 ^{\circ} + cos 17 8 ^{\circ} sin 20 8 ^{\circ}} ?$
1. A. $- 2$
2. B. $- 1$
3. C. $2$
4. D. $1$
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Answer: A
Q322019 · 21 Apr 2019
$tan 5 4^{\circ}$ can be expressed as
1. A. $\frac{s i n 9 ^{\circ} + c o s 9 ^{\circ}}{s i n 9 ^{\circ} - c o s 9 ^{\circ}}$
2. B. $\frac{s i n 9 ^{\circ} - c o s 9 ^{\circ}}{s i n 9 ^{\circ} + c o s 9 ^{\circ}}$
3. C. $\frac{c o s 9 ^{\circ} + s i n 9 ^{\circ}}{c o s 9 ^{\circ} - s i n 9 ^{\circ}}$
4. D. $\frac{s i n 3 6 ^{\circ}}{c o s 3 6 ^{\circ}}$
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Answer: C
Q332019 · 21 Apr 2019
Consider the following for the next 03 (three) items: If $p = X cos θ - Y sin θ$ , $q = X sin θ + Y cos θ$ and $p^{2} + 4 pq + q^{2} = A X^{2} + B Y^{2}$ , $0 \leq θ \leq \frac{π}{2}$ . What is the value of $θ$ ?
1. A. $\frac{π}{2}$
2. B. $\frac{π}{3}$
3. C. $\frac{π}{4}$
4. D. $\frac{π}{6}$
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Answer: C
Q342019 · 21 Apr 2019
Consider the following for the next 03 (three) items: If $p = X cos θ - Y sin θ$ , $q = X sin θ + Y cos θ$ and $p^{2} + 4 pq + q^{2} = A X^{2} + B Y^{2}$ , $0 \leq θ \leq \frac{π}{2}$ . What is the value of A?
1. A. $4$
2. B. $3$
3. C. $2$
4. D. $1$
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Answer: B
Q352019 · 21 Apr 2019
Consider the following for the next 03 (three) items: If $p = X cos θ - Y sin θ$ , $q = X sin θ + Y cos θ$ and $p^{2} + 4 pq + q^{2} = A X^{2} + B Y^{2}$ , $0 \leq θ \leq \frac{π}{2}$ . What is the value of B?
1. A. $- 1$
2. B. $0$
3. C. $1$
4. D. $2$
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Answer: A
Q362019 · 21 Apr 2019
Consider the following for the next 02 (two) items: It is given that $cos (θ - α) = a, cos (θ - β) = b$ . What is $cos (α - β)$ equal to?
1. A. $ab + 1 - a^{2} 1 - b^{2}$
2. B. $ab - 1 - a^{2} 1 - b^{2}$
3. C. $a 1 - b^{2} - b 1 - a^{2}$
4. D. $a 1 - b^{2} + b 1 - a^{2}$
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Answer: A
Q372019 · 21 Apr 2019
Consider the following for the next 02 (two) items: It is given that $cos (θ - α) = a, cos (θ - β) = b$ . What is $sin^{2} (α - β) + 2 ab cos (α - β)$ equal to?
1. A. $a^{2} + b^{2}$
2. B. $a^{2} - b^{2}$
3. C. $b^{2} - a^{2}$
4. D. $- (a^{2} + b^{2})$
Show answer
Answer: A