Available Questions 772 found Page 6 of 39
Standalone Questions
#1729
Mathematics
Three Dimensional Geometry
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If points $(2, 3)$, $(0, 4)$ and $(p, 2)$ are collinear, then the value of p is:
(A) $\frac{4}{7}$
(B) $-\frac{3}{7}$
(C) 4
(D) -4
Key:
Sol:
Sol:
#1728
Mathematics
Vector Algebra
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If $(3\hat{i}-2\hat{j}+5\hat{k})\times(4\hat{i}+p\hat{j}+q\hat{k})=\vec{0}$ then the values of p and q are :
(A) $p=-\frac{2}{3}, q=\frac{5}{3}$
(B) $p=-\frac{8}{3}, q=\frac{20}{3}$
(C) $p=\frac{20}{3}, q=-\frac{8}{3}$
(D) $p=0, q=0$
Key:
Sol:
Sol:
#1727
Mathematics
Vector Algebra
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If $(\vec{a}+\vec{b}).(\vec{a}-\vec{b})=198$ and $|\vec{a}|=10|\vec{b}|$, then :
(A) $|\vec{a}|=\sqrt{2}$
(B) $|\vec{b}|=\sqrt{2}$
(C) $|\vec{b}|=10\sqrt{2}$
(D) $|\vec{a}|=\frac{10}{\sqrt{2}}$
Key:
Sol:
Sol:
#1726
Mathematics
Vector Algebra
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
For any two vectors $\vec{a}$ and $\vec{b}$, which of the following statements is always true ?
(A) $\vec{a}.\vec{b}\le|\vec{a}||\vec{b}|$
(B) $|\vec{a}+\vec{b}|\ge|\vec{a}|+|\vec{b}|$
(C) $|\vec{a}-\vec{b}|=|\vec{a}|-|\vec{b}|$
(D) $|\vec{a}\times\vec{b}|\ge|\vec{a}||\vec{b}|$
Key:
Sol:
Sol:
#1725
Mathematics
Vector Algebra
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Vector of magnitude 3 making equal angles with x and y axes and perpendicular to z axis is
(A) $\hat{i}+2\sqrt{2}\hat{j}$
(B) $3\hat{k}$
(C) $\frac{3\sqrt{2}}{2}\hat{i}+\frac{3\sqrt{2}}{2}\hat{j}$
(D) $\sqrt{3}\hat{i}+\sqrt{3}\hat{j}+\sqrt{3}\hat{k}$
Key:
Sol:
Sol:
#1724
Mathematics
Vector Algebra
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Three points $A(0,1,1)$, $B(2,0,-1)$ and $C(1,0,3)$ form $\Delta ABC$. The ar ($\Delta ABC$) is:
(A) $\frac{\sqrt{53}}{2}$ sq. units
(B) $\sqrt{53}$ sq. units
(C) $\frac{\sqrt{11}}{2}$ sq. units
(D) $\sqrt{11}$ sq. units
Key:
Sol:
Sol:
#1723
Mathematics
Vector Algebra
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If position vector $\vec{p}$ of a point (24, n) is such that $|\vec{p}|=25$, then the value of n is:
(A) $\pm 49$
(B) $\pm 5$
(C) $\pm 1$
(D) $\pm 7$
Key:
Sol:
Sol:
#1722
Mathematics
Vector Algebra
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If $|\vec{a}|=5$ and $-2 \le \lambda \le 1$ then the sum of greatest and the smallest value of $|\lambda\vec{a}|$ is
(A) -5
(B) 5
(C) 10
(D) 15
Key:
Sol:
Sol:
#1721
Mathematics
Vector Algebra
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
If vectors $\vec{a}=3\hat{i}+2\hat{j}+\lambda\hat{k}$ and $\vec{b}=2\hat{i}-4\hat{j}+5\hat{k}$, represent the two strips of the Red Cross sign placed outside a doctor's clinic, then the value of $\lambda$ is :
(A) 1
(B) $\frac{5}{2}$
(C) $\frac{2}{5}$
Key:
Sol:
Sol:
#1720
Mathematics
Differential Equations
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The order and degree of the differential equation $1+(\frac{d^{3}y}{dx^{3}})^{3}=\lambda\frac{d^{2}y}{dx^{2}}$ is:
(A) Order = 3, Degree = 3
(B) Order = 2, Degree = 2
(C) Order = 3, Degree = 1
(D) Order = 2, Degree = 1
Key:
Sol:
Sol:
#1719
Mathematics
Differential Equations
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
$\frac{dy}{dx}=F(x,y)$ will be a homogeneous differential equation for which of the following functions? (i) $F(x,y)=3x+2y$ (ii) $F(x,y)=\sin\frac{y}{x}+\log y-\log x$ (iii) $F(x,y)=e^{y/x}+1$ (iv) $F(x,y)=\sqrt{x^{2}+y^{2}}-y$
(A) (i) and (ii)
(B) (i), (ii) and (iii)
(C) (ii), (iii) and (iv)
(D) (ii) and (iii)
Key:
Sol:
Sol:
#1718
Mathematics
Differential Equations
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Which of the following is not a Linear Differential Equation?
(A) $(1+x^{2})dy+2xy~dx=\cot x~dx$
(B) $y+\frac{d}{dx}(xy)=x(\sin x+\log x)$
(C) $x(1+y^{2})dx-y(1+x^{2})dy=0$
(D) $y~dx-(x+3y^{2})dy=0$
Key:
Sol:
Sol:
#1717
Mathematics
Differential Equations
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The general solution for the differential equation $\frac{dy}{dx}=e^{3x-y}$ is:
(A) $3e^{y}=e^{3x}+C$
(B) $\log(3x-y)=C$
(C) $e^{3x-y}=C$
(D) $-e^{y}+3e^{3x}=C$
Key:
Sol:
Sol:
#1716
Mathematics
Differential Equations
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The integrating factor of the differential equation $2x\frac{dy}{dx}-y=3$ is
(A) $\sqrt{x}$
(B) $\frac{1}{\sqrt{x}}$
(C) $e^{x}$
(D) $e^{-x}$
Key:
Sol:
Sol:
#1715
Mathematics
Differential Equations
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The general solution of the differential equation $\frac{dy}{dx}=\frac{\sqrt{y}}{\sqrt{x}}$ is
(A) $\log\sqrt{y}=\log\sqrt{x}+C$
(B) $\sqrt{y}+\sqrt{x}=C$
(C) $\sqrt{y}-\sqrt{x}=C$
(D) $\log\sqrt{y}+\log\sqrt{x}=C$
Key:
Sol:
Sol:
#1714
Mathematics
Differential Equations
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Product of the order and degree of differential equation $1+(\frac{dy}{dx})^{3}=\lambda(\frac{d^{3}y}{dx^{3}})^{2}$ is:
(A) 5
(B) 6
(C) 2
(D) 3
Key:
Sol:
Sol:
#1713
Mathematics
Applications of Integrals
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
An ant is observed crawling on a sheet of paper along a straight line given by equation $y=2x-4$. Area of the surface covered by the ant bounded by y-axis, x-axis and $x=1$ is :
(A) 1 sq. unit
(B) 3 sq. units
(C) 2 sq. units
(D) 4 sq. units
Key:
Sol:
Sol:
#1712
Mathematics
Applications of Integrals
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The area of the region bounded by the curve $y=x$ and x-axis, between $x=0$ and $x=2$ is:
(A) 2 sq. units
(B) $\frac{1}{2}$ sq. unit
(C) 1 sq. unit
(D) 4 sq. units
Key:
Sol:
Sol:
#1711
Mathematics
Applications of Integrals
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The area of the shaded region of the circle given below is equal to :
(A) $\int_{1}^{3}\sqrt{9-y^{2}}dy$
(B) $2\int_{1}^{3}\sqrt{9-y^{2}}dy$
(C) $\int_{0}^{3}\sqrt{9-x^{2}}dx$
(D) $2\int_{0}^{3}\sqrt{9-x^{2}}dx$
Key:
Sol:
Sol:
#1710
Mathematics
Applications of Integrals
MCQ_SINGLE
2026
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Which of the following expressions will give the area of region bounded by the curve $y=x^{2}$ and line $y=16$?
(A) $\int_{0}^{4}x^{2}dx$
(B) $2\int_{0}^{4}x^{2}dx$
(C) $\int_{0}^{16}\sqrt{y}dy$
(D) $2\int_{0}^{16}\sqrt{y}dy$
Key:
Sol:
Sol: